setting up ipynb files
This commit is contained in:
mhjensen
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<title>Week 46: Support Vector Machines</title>
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{'highest level': 2,
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'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
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||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
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('A $p$-dimensional space of features', 2, None, '___sec3'),
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('The two-dimensional case', 2, None, '___sec4'),
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('Getting into the details', 2, None, '___sec5'),
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('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
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('Code Example', 2, None, '___sec8'),
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||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
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||||
('A better approach', 2, None, '___sec10'),
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||||
('A quick Reminder on Lagrangian Multipliers',
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2,
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None,
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'___sec11'),
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||||
('Adding the Multiplier', 2, None, '___sec12'),
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||||
('Setting up the Problem', 2, None, '___sec13'),
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||||
('The problem to solve', 2, None, '___sec14'),
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||||
('The last steps', 2, None, '___sec15'),
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||||
('A soft classifier', 2, None, '___sec16'),
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||||
('Soft optmization problem', 2, None, '___sec17'),
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||||
('Kernels and non-linearity', 2, None, '___sec18'),
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||||
('The equations', 2, None, '___sec19'),
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||||
('The problem to solve', 2, None, '___sec20'),
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||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
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||||
('The moons example', 2, None, '___sec22'),
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||||
('Mathematical optimization of convex functions',
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2,
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None,
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'___sec23'),
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||||
('How do we solve these problems?', 2, None, '___sec24'),
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('A simple example', 2, None, '___sec25'),
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('Back to the more realistic cases', 2, None, '___sec26')]}
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<span class="icon-bar"></span>
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<a class="navbar-brand" href="week46-bs.html">Week 46: Support Vector Machines</a>
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</div>
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<div class="navbar-collapse collapse navbar-responsive-collapse">
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<ul class="nav navbar-nav navbar-right">
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<li class="dropdown">
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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||||
<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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</ul>
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</li>
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</ul>
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</div>
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</div>
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</div> <!-- end of navigation bar -->
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0000"></a>
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<!-- ------------------- main content ---------------------- -->
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<div class="jumbotron">
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<center><h1>Week 46: Support Vector Machines</h1></center> <!-- document title -->
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<p>
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<!-- author(s): Morten Hjorth-Jensen -->
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<center>
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<b>Morten Hjorth-Jensen</b> [1, 2]
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</center>
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<p>
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<!-- institution(s) -->
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<center>[1] <b>Department of Physics, University of Oslo</b></center>
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<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
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<br>
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<p>
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<center><h4>Sep 16, 2020</h4></center> <!-- date -->
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<br>
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<p>
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<p><a href="._week46-bs001.html" class="btn btn-primary btn-lg">Read »</a></p>
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</div> <!-- end jumbotron -->
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<p>
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<!-- navigation buttons at the bottom of the page -->
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<ul class="pagination">
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<li class="active"><a href="._week46-bs000.html">1</a></li>
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<li><a href="._week46-bs001.html">2</a></li>
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<li><a href="._week46-bs002.html">3</a></li>
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<li><a href="._week46-bs003.html">4</a></li>
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<li><a href="._week46-bs004.html">5</a></li>
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<li><a href="._week46-bs005.html">6</a></li>
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<li><a href="._week46-bs006.html">7</a></li>
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<li><a href="._week46-bs007.html">8</a></li>
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<li><a href="._week46-bs008.html">9</a></li>
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<li><a href="._week46-bs009.html">10</a></li>
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<li><a href="">...</a></li>
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<li><a href="._week46-bs027.html">28</a></li>
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<li><a href="._week46-bs001.html">»</a></li>
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</ul>
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<!-- ------------------- end of main content --------------- -->
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</div> <!-- end container -->
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<!-- include javascript, jQuery *first* -->
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<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
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<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
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-->
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<center style="font-size:80%">
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<!-- copyright --> © 1999-2020, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
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</center>
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</body>
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</html>
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@@ -0,0 +1,228 @@
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<!--
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Automatically generated HTML file from DocOnce source
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(https://github.com/hplgit/doconce/)
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-->
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<html>
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<head>
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<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
||||
<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
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<meta name="viewport" content="width=device-width, initial-scale=1.0" />
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||||
<meta name="description" content="Week 46: Support Vector Machines">
|
||||
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<title>Week 46: Support Vector Machines</title>
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||||
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||||
<!-- Bootstrap style: bootstrap -->
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||||
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
|
||||
<!-- not necessary
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||||
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
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||||
-->
|
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<style type="text/css">
|
||||
|
||||
/* Add scrollbar to dropdown menus in bootstrap navigation bar */
|
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.dropdown-menu {
|
||||
height: auto;
|
||||
max-height: 400px;
|
||||
overflow-x: hidden;
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||||
}
|
||||
|
||||
/* Adds an invisible element before each target to offset for the navigation
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||||
bar */
|
||||
.anchor::before {
|
||||
content:"";
|
||||
display:block;
|
||||
height:50px; /* fixed header height for style bootstrap */
|
||||
margin:-50px 0 0; /* negative fixed header height */
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||||
}
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||||
</style>
|
||||
|
||||
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||||
</head>
|
||||
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||||
<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
|
||||
|
||||
|
||||
<script type="text/x-mathjax-config">
|
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MathJax.Hub.Config({
|
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TeX: {
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equationNumbers: { autoNumber: "none" },
|
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extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
|
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}
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});
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</script>
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<!-- Bootstrap navigation bar -->
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<div class="navbar navbar-default navbar-fixed-top">
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<div class="navbar-header">
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<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
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<span class="icon-bar"></span>
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<span class="icon-bar"></span>
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<span class="icon-bar"></span>
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</button>
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<a class="navbar-brand" href="week46-bs.html">Week 46: Support Vector Machines</a>
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<div class="navbar-collapse collapse navbar-responsive-collapse">
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<ul class="nav navbar-nav navbar-right">
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<li class="dropdown">
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||||
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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|
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<a name="part0001"></a>
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<!-- !split -->
|
||||
|
||||
<h2 id="___sec0" class="anchor">Support Vector Machines, overarching aims </h2>
|
||||
|
||||
<p>
|
||||
A Support Vector Machine (SVM) is a very powerful and versatile
|
||||
Machine Learning method, capable of performing linear or nonlinear
|
||||
classification, regression, and even outlier detection. It is one of
|
||||
the most popular models in Machine Learning, and anyone interested in
|
||||
Machine Learning should have it in their toolbox. SVMs are
|
||||
particularly well suited for classification of complex but small-sized or
|
||||
medium-sized datasets.
|
||||
|
||||
<p>
|
||||
The case with two well-separated classes only can be understood in an
|
||||
intuitive way in terms of lines in a two-dimensional space separating
|
||||
the two classes (see figure below).
|
||||
|
||||
<p>
|
||||
The basic mathematics behind the SVM is however less familiar to most of us.
|
||||
It relies on the definition of hyperplanes and the
|
||||
definition of a <b>margin</b> which separates classes (in case of
|
||||
classification problems) of variables. It is also used for regression
|
||||
problems.
|
||||
|
||||
<p>
|
||||
With SVMs we distinguish between hard margin and soft margins. The
|
||||
latter introduces a so-called softening parameter to be discussed
|
||||
below. We distinguish also between linear and non-linear
|
||||
approaches. The latter are the most frequent ones since it is rather
|
||||
unlikely that we can separate classes easily by say straight lines.
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'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
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|
||||
('Solving the equations', 2, None, '___sec7'),
|
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|
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|
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|
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|
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2,
|
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|
||||
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|
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('Adding the Multiplier', 2, None, '___sec12'),
|
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|
||||
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|
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('The last steps', 2, None, '___sec15'),
|
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('A soft classifier', 2, None, '___sec16'),
|
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('Soft optmization problem', 2, None, '___sec17'),
|
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('Kernels and non-linearity', 2, None, '___sec18'),
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('The equations', 2, None, '___sec19'),
|
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('The problem to solve', 2, None, '___sec20'),
|
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("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
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('The moons example', 2, None, '___sec22'),
|
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('Mathematical optimization of convex functions',
|
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2,
|
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None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
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('A simple example', 2, None, '___sec25'),
|
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('Back to the more realistic cases', 2, None, '___sec26')]}
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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<a name="part0002"></a>
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<!-- !split -->
|
||||
|
||||
<h2 id="___sec1" class="anchor">Hyperplanes and all that </h2>
|
||||
|
||||
<p>
|
||||
The theory behind support vector machines (SVM hereafter) is based on
|
||||
the mathematical description of so-called hyperplanes. Let us start
|
||||
with a two-dimensional case. This will also allow us to introduce our
|
||||
first SVM examples. These will be tailored to the case of two specific
|
||||
classes, as displayed in the figure here based on the usage of the petal data.
|
||||
|
||||
<p>
|
||||
We assume here that our data set can be well separated into two
|
||||
domains, where a straight line does the job in the separating the two
|
||||
classes. Here the two classes are represented by either squares or
|
||||
circles.
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVC, LinearSVC
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> SGDClassifier
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'axes.labelsize'</span>] <span style="color: #666666">=</span> <span style="color: #666666">14</span>
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'xtick.labelsize'</span>] <span style="color: #666666">=</span> <span style="color: #666666">12</span>
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'ytick.labelsize'</span>] <span style="color: #666666">=</span> <span style="color: #666666">12</span>
|
||||
|
||||
|
||||
iris <span style="color: #666666">=</span> datasets<span style="color: #666666">.</span>load_iris()
|
||||
X <span style="color: #666666">=</span> iris[<span style="color: #BA2121">"data"</span>][:, (<span style="color: #666666">2</span>, <span style="color: #666666">3</span>)] <span style="color: #408080; font-style: italic"># petal length, petal width</span>
|
||||
y <span style="color: #666666">=</span> iris[<span style="color: #BA2121">"target"</span>]
|
||||
|
||||
setosa_or_versicolor <span style="color: #666666">=</span> (y <span style="color: #666666">==</span> <span style="color: #666666">0</span>) <span style="color: #666666">|</span> (y <span style="color: #666666">==</span> <span style="color: #666666">1</span>)
|
||||
X <span style="color: #666666">=</span> X[setosa_or_versicolor]
|
||||
y <span style="color: #666666">=</span> y[setosa_or_versicolor]
|
||||
|
||||
|
||||
|
||||
C <span style="color: #666666">=</span> <span style="color: #666666">5</span>
|
||||
alpha <span style="color: #666666">=</span> <span style="color: #666666">1</span> <span style="color: #666666">/</span> (C <span style="color: #666666">*</span> <span style="color: #008000">len</span>(X))
|
||||
|
||||
lin_clf <span style="color: #666666">=</span> LinearSVC(loss<span style="color: #666666">=</span><span style="color: #BA2121">"hinge"</span>, C<span style="color: #666666">=</span>C, random_state<span style="color: #666666">=42</span>)
|
||||
svm_clf <span style="color: #666666">=</span> SVC(kernel<span style="color: #666666">=</span><span style="color: #BA2121">"linear"</span>, C<span style="color: #666666">=</span>C)
|
||||
sgd_clf <span style="color: #666666">=</span> SGDClassifier(loss<span style="color: #666666">=</span><span style="color: #BA2121">"hinge"</span>, learning_rate<span style="color: #666666">=</span><span style="color: #BA2121">"constant"</span>, eta0<span style="color: #666666">=0.001</span>, alpha<span style="color: #666666">=</span>alpha,
|
||||
max_iter<span style="color: #666666">=100000</span>, random_state<span style="color: #666666">=42</span>)
|
||||
|
||||
scaler <span style="color: #666666">=</span> StandardScaler()
|
||||
X_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>fit_transform(X)
|
||||
|
||||
lin_clf<span style="color: #666666">.</span>fit(X_scaled, y)
|
||||
svm_clf<span style="color: #666666">.</span>fit(X_scaled, y)
|
||||
sgd_clf<span style="color: #666666">.</span>fit(X_scaled, y)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"LinearSVC: "</span>, lin_clf<span style="color: #666666">.</span>intercept_, lin_clf<span style="color: #666666">.</span>coef_)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"SVC: "</span>, svm_clf<span style="color: #666666">.</span>intercept_, svm_clf<span style="color: #666666">.</span>coef_)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"SGDClassifier(alpha={:.5f}):"</span><span style="color: #666666">.</span>format(sgd_clf<span style="color: #666666">.</span>alpha), sgd_clf<span style="color: #666666">.</span>intercept_, sgd_clf<span style="color: #666666">.</span>coef_)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Compute the slope and bias of each decision boundary</span>
|
||||
w1 <span style="color: #666666">=</span> <span style="color: #666666">-</span>lin_clf<span style="color: #666666">.</span>coef_[<span style="color: #666666">0</span>, <span style="color: #666666">0</span>]<span style="color: #666666">/</span>lin_clf<span style="color: #666666">.</span>coef_[<span style="color: #666666">0</span>, <span style="color: #666666">1</span>]
|
||||
b1 <span style="color: #666666">=</span> <span style="color: #666666">-</span>lin_clf<span style="color: #666666">.</span>intercept_[<span style="color: #666666">0</span>]<span style="color: #666666">/</span>lin_clf<span style="color: #666666">.</span>coef_[<span style="color: #666666">0</span>, <span style="color: #666666">1</span>]
|
||||
w2 <span style="color: #666666">=</span> <span style="color: #666666">-</span>svm_clf<span style="color: #666666">.</span>coef_[<span style="color: #666666">0</span>, <span style="color: #666666">0</span>]<span style="color: #666666">/</span>svm_clf<span style="color: #666666">.</span>coef_[<span style="color: #666666">0</span>, <span style="color: #666666">1</span>]
|
||||
b2 <span style="color: #666666">=</span> <span style="color: #666666">-</span>svm_clf<span style="color: #666666">.</span>intercept_[<span style="color: #666666">0</span>]<span style="color: #666666">/</span>svm_clf<span style="color: #666666">.</span>coef_[<span style="color: #666666">0</span>, <span style="color: #666666">1</span>]
|
||||
w3 <span style="color: #666666">=</span> <span style="color: #666666">-</span>sgd_clf<span style="color: #666666">.</span>coef_[<span style="color: #666666">0</span>, <span style="color: #666666">0</span>]<span style="color: #666666">/</span>sgd_clf<span style="color: #666666">.</span>coef_[<span style="color: #666666">0</span>, <span style="color: #666666">1</span>]
|
||||
b3 <span style="color: #666666">=</span> <span style="color: #666666">-</span>sgd_clf<span style="color: #666666">.</span>intercept_[<span style="color: #666666">0</span>]<span style="color: #666666">/</span>sgd_clf<span style="color: #666666">.</span>coef_[<span style="color: #666666">0</span>, <span style="color: #666666">1</span>]
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Transform the decision boundary lines back to the original scale</span>
|
||||
line1 <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>inverse_transform([[<span style="color: #666666">-10</span>, <span style="color: #666666">-10</span> <span style="color: #666666">*</span> w1 <span style="color: #666666">+</span> b1], [<span style="color: #666666">10</span>, <span style="color: #666666">10</span> <span style="color: #666666">*</span> w1 <span style="color: #666666">+</span> b1]])
|
||||
line2 <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>inverse_transform([[<span style="color: #666666">-10</span>, <span style="color: #666666">-10</span> <span style="color: #666666">*</span> w2 <span style="color: #666666">+</span> b2], [<span style="color: #666666">10</span>, <span style="color: #666666">10</span> <span style="color: #666666">*</span> w2 <span style="color: #666666">+</span> b2]])
|
||||
line3 <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>inverse_transform([[<span style="color: #666666">-10</span>, <span style="color: #666666">-10</span> <span style="color: #666666">*</span> w3 <span style="color: #666666">+</span> b3], [<span style="color: #666666">10</span>, <span style="color: #666666">10</span> <span style="color: #666666">*</span> w3 <span style="color: #666666">+</span> b3]])
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Plot all three decision boundaries</span>
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>, <span style="color: #666666">4</span>))
|
||||
plt<span style="color: #666666">.</span>plot(line1[:, <span style="color: #666666">0</span>], line1[:, <span style="color: #666666">1</span>], <span style="color: #BA2121">"k:"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"LinearSVC"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(line2[:, <span style="color: #666666">0</span>], line2[:, <span style="color: #666666">1</span>], <span style="color: #BA2121">"b--"</span>, linewidth<span style="color: #666666">=2</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"SVC"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(line3[:, <span style="color: #666666">0</span>], line3[:, <span style="color: #666666">1</span>], <span style="color: #BA2121">"r-"</span>, label<span style="color: #666666">=</span><span style="color: #BA2121">"SGDClassifier"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==1</span>], X[:, <span style="color: #666666">1</span>][y<span style="color: #666666">==1</span>], <span style="color: #BA2121">"bs"</span>) <span style="color: #408080; font-style: italic"># label="Iris-Versicolor"</span>
|
||||
plt<span style="color: #666666">.</span>plot(X[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==0</span>], X[:, <span style="color: #666666">1</span>][y<span style="color: #666666">==0</span>], <span style="color: #BA2121">"yo"</span>) <span style="color: #408080; font-style: italic"># label="Iris-Setosa"</span>
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">"Petal length"</span>, fontsize<span style="color: #666666">=14</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">"Petal width"</span>, fontsize<span style="color: #666666">=14</span>)
|
||||
plt<span style="color: #666666">.</span>legend(loc<span style="color: #666666">=</span><span style="color: #BA2121">"upper center"</span>, fontsize<span style="color: #666666">=14</span>)
|
||||
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">0</span>, <span style="color: #666666">5.5</span>, <span style="color: #666666">0</span>, <span style="color: #666666">2</span>])
|
||||
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
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{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
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('Back to the more realistic cases', 2, None, '___sec26')]}
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
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<a name="part0003"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec2" class="anchor">What is a hyperplane? </h2>
|
||||
|
||||
<p>
|
||||
The aim of the SVM algorithm is to find a hyperplane in a
|
||||
\( p \)-dimensional space, where \( p \) is the number of features that
|
||||
distinctly classifies the data points.
|
||||
|
||||
<p>
|
||||
In a \( p \)-dimensional space, a hyperplane is what we call an affine subspace of dimension of \( p-1 \).
|
||||
As an example, in two dimension, a hyperplane is simply as straight line while in three dimensions it is
|
||||
a two-dimensional subspace, or stated simply, a plane.
|
||||
|
||||
<p>
|
||||
In two dimensions, with the variables \( x_1 \) and \( x_2 \), the hyperplane is defined as
|
||||
$$
|
||||
b+w_1x_1+w_2x_2=0,
|
||||
$$
|
||||
|
||||
<p>
|
||||
where \( b \) is the intercept and \( w_1 \) and \( w_2 \) define the elements of a vector orthogonal to the line
|
||||
\( b+w_1x_1+w_2x_2=0 \).
|
||||
In two dimensions we define the vectors \( \boldsymbol{x} =[x1,x2] \) and \( \boldsymbol{w}=[w1,w2] \).
|
||||
We can then rewrite the above equation as
|
||||
|
||||
$$
|
||||
\boldsymbol{x}^T\boldsymbol{w}+b=0.
|
||||
$$
|
||||
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{'highest level': 2,
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'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
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|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
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|
||||
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|
||||
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|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
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|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
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|
||||
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|
||||
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|
||||
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|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
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|
||||
('Mathematical optimization of convex functions',
|
||||
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|
||||
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|
||||
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|
||||
('How do we solve these problems?', 2, None, '___sec24'),
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||||
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|
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
|
||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
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<div class="container">
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|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
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||||
|
||||
<a name="part0004"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec3" class="anchor">A \( p \)-dimensional space of features </h2>
|
||||
|
||||
<p>
|
||||
We limit ourselves to two classes of outputs \( y_i \) and assign these classes the values \( y_i = \pm 1 \).
|
||||
In a \( p \)-dimensional space of say \( p \) features we have a hyperplane defines as
|
||||
$$
|
||||
b+wx_1+w_2x_2+\dots +w_px_p=0.
|
||||
$$
|
||||
|
||||
If we define a
|
||||
matrix \( \boldsymbol{X}=\left[\boldsymbol{x}_1,\boldsymbol{x}_2,\dots, \boldsymbol{x}_p\right] \)
|
||||
of dimension \( n\times p \), where \( n \) represents the observations for each feature and each vector \( x_i \) is a column vector of the matrix \( \boldsymbol{X} \),
|
||||
$$
|
||||
\boldsymbol{x}_i = \begin{bmatrix} x_{i1} \\ x_{i2} \\ \dots \\ \dots \\ x_{ip} \end{bmatrix}.
|
||||
$$
|
||||
|
||||
If the above condition is not met for a given vector \( \boldsymbol{x}_i \) we have
|
||||
$$
|
||||
b+w_1x_{i1}+w_2x_{i2}+\dots +w_px_{ip} >0,
|
||||
$$
|
||||
|
||||
if our output \( y_i=1 \).
|
||||
In this case we say that \( \boldsymbol{x}_i \) lies on one of the sides of the hyperplane and if
|
||||
$$
|
||||
b+w_1x_{i1}+w_2x_{i2}+\dots +w_px_{ip} < 0,
|
||||
$$
|
||||
|
||||
for the class of observations \( y_i=-1 \),
|
||||
then \( \boldsymbol{x}_i \) lies on the other side.
|
||||
|
||||
<p>
|
||||
Equivalently, for the two classes of observations we have
|
||||
$$
|
||||
y_i\left(b+w_1x_{i1}+w_2x_{i2}+\dots +w_px_{ip}\right) > 0.
|
||||
$$
|
||||
|
||||
<p>
|
||||
When we try to separate hyperplanes, if it exists, we can use it to construct a natural classifier: a test observation is assigned a given class depending on which side of the hyperplane it is located.
|
||||
|
||||
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|
||||
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max-height: 400px;
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|
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</head>
|
||||
|
||||
<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
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|
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|
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|
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<script type="text/x-mathjax-config">
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
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|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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<a name="part0005"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec4" class="anchor">The two-dimensional case </h2>
|
||||
|
||||
<p>
|
||||
Let us try to develop our intuition about SVMs by limiting ourselves to a two-dimensional
|
||||
plane. To separate the two classes of data points, there are many
|
||||
possible lines (hyperplanes if you prefer a more strict naming)
|
||||
that could be chosen. Our objective is to find a
|
||||
plane that has the maximum margin, i.e the maximum distance between
|
||||
data points of both classes. Maximizing the margin distance provides
|
||||
some reinforcement so that future data points can be classified with
|
||||
more confidence.
|
||||
|
||||
<p>
|
||||
What a linear classifier attempts to accomplish is to split the
|
||||
feature space into two half spaces by placing a hyperplane between the
|
||||
data points. This hyperplane will be our decision boundary. All
|
||||
points on one side of the plane will belong to class one and all points
|
||||
on the other side of the plane will belong to the second class two.
|
||||
|
||||
<p>
|
||||
Unfortunately there are many ways in which we can place a hyperplane
|
||||
to divide the data. Below is an example of two candidate hyperplanes
|
||||
for our data sample.
|
||||
|
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<p>
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</head>
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<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
||||
end of tocinfo -->
|
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|
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<body>
|
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<script type="text/x-mathjax-config">
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MathJax.Hub.Config({
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}
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});
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</script>
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<script type="text/javascript" async
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src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
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</li>
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<a name="part0006"></a>
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||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec5" class="anchor">Getting into the details </h2>
|
||||
|
||||
<p>
|
||||
Let us define the function
|
||||
$$
|
||||
f(x) = \boldsymbol{w}^T\boldsymbol{x}+b = 0,
|
||||
$$
|
||||
|
||||
as the function that determines the line \( L \) that separates two classes (our two features), see the figure here.
|
||||
|
||||
<p>
|
||||
Any point defined by \( \boldsymbol{x}_i \) and \( \boldsymbol{x}_2 \) on the line \( L \) will satisfy \( \boldsymbol{w}^T(\boldsymbol{x}_1-\boldsymbol{x}_2)=0 \).
|
||||
|
||||
<p>
|
||||
The signed distance \( \delta \) from any point defined by a vector \( \boldsymbol{x} \) and a point \( \boldsymbol{x}_0 \) on the line \( L \) is then
|
||||
$$
|
||||
\delta = \frac{1}{\vert\vert \boldsymbol{w}\vert\vert}(\boldsymbol{w}^T\boldsymbol{x}+b).
|
||||
$$
|
||||
|
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|
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|
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|
||||
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|
||||
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|
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|
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|
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|
||||
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|
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|
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<a class="navbar-brand" href="week46-bs.html">Week 46: Support Vector Machines</a>
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<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
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<!-- !split -->
|
||||
|
||||
<h2 id="___sec6" class="anchor">First attempt at a minimization approach </h2>
|
||||
|
||||
<p>
|
||||
How do we find the parameter \( b \) and the vector \( \boldsymbol{w} \)? What we could
|
||||
do is to define a cost function which now contains the set of all
|
||||
misclassified points \( M \) and attempt to minimize this function
|
||||
|
||||
$$
|
||||
C(\boldsymbol{w},b) = -\sum_{i\in M} y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b).
|
||||
$$
|
||||
|
||||
<p>
|
||||
We could now for example define all values \( y_i =1 \) as misclassified in case we have \( \boldsymbol{w}^T\boldsymbol{x}_i+b < 0 \) and the opposite if we have \( y_i=-1 \). Taking the derivatives gives us
|
||||
$$
|
||||
\frac{\partial C}{\partial b} = -\sum_{i\in M} y_i,
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
\frac{\partial C}{\partial \boldsymbol{w}} = -\sum_{i\in M} y_ix_i.
|
||||
$$
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</head>
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|
||||
<!-- tocinfo
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{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
||||
end of tocinfo -->
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
|
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
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|
||||
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<!-- !split -->
|
||||
|
||||
<h2 id="___sec7" class="anchor">Solving the equations </h2>
|
||||
|
||||
<p>
|
||||
We can now use the Newton-Raphson method or different variants of the gradient descent family (from plain gradient descent to various stochastic gradient descent approaches) to solve the equations
|
||||
$$
|
||||
b \leftarrow b +\eta \frac{\partial C}{\partial b},
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
\boldsymbol{w} \leftarrow \boldsymbol{w} +\eta \frac{\partial C}{\partial \boldsymbol{w}},
|
||||
$$
|
||||
|
||||
where \( \eta \) is our by now well-known learning rate.
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|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
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||||
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|
||||
('Solving the equations', 2, None, '___sec7'),
|
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|
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|
||||
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|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
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('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
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end of tocinfo -->
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
|
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</li>
|
||||
</ul>
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<a name="part0009"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec8" class="anchor">Code Example </h2>
|
||||
|
||||
<p>
|
||||
The equations we discussed above can be coded rather easily (the
|
||||
framework is similar to what we developed for logistic
|
||||
regression). We are going to set up a simple case with two classes only and we want to find a line which separates them the best possible way.
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>
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<p>
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<!-- tocinfo
|
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{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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<!-- !split -->
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<h2 id="___sec9" class="anchor">Problems with the Simpler Approach </h2>
|
||||
|
||||
<p>
|
||||
There are however problems with this approach, although it looks
|
||||
pretty straightforward to implement. When running the above code, we see that we can easily end up with many diffeent lines which separate the two classes.
|
||||
|
||||
<p>
|
||||
For small
|
||||
gaps between the entries, we may also end up needing many iterations
|
||||
before the solutions converge and if the data cannot be separated
|
||||
properly into two distinct classes, we may not experience a converge
|
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at all.
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'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
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||||
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|
||||
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|
||||
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|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
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|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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<a name="part0011"></a>
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<!-- !split -->
|
||||
|
||||
<h2 id="___sec10" class="anchor">A better approach </h2>
|
||||
|
||||
<p>
|
||||
A better approach is rather to try to define a large margin between
|
||||
the two classes (if they are well separated from the beginning).
|
||||
|
||||
<p>
|
||||
Thus, we wish to find a margin \( M \) with \( \boldsymbol{w} \) normalized to
|
||||
\( \vert\vert \boldsymbol{w}\vert\vert =1 \) subject to the condition
|
||||
|
||||
$$
|
||||
y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, p.
|
||||
$$
|
||||
|
||||
All points are thus at a signed distance from the decision boundary defined by the line \( L \). The parameters \( b \) and \( w_1 \) and \( w_2 \) define this line.
|
||||
|
||||
<p>
|
||||
We seek thus the largest value \( M \) defined by
|
||||
$$
|
||||
\frac{1}{\vert \vert \boldsymbol{w}\vert\vert}y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) \geq M \hspace{0.1cm}\forall i=1,2,\dots, n,
|
||||
$$
|
||||
|
||||
or just
|
||||
$$
|
||||
y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) \geq M\vert \vert \boldsymbol{w}\vert\vert \hspace{0.1cm}\forall i.
|
||||
$$
|
||||
|
||||
If we scale the equation so that \( \vert \vert \boldsymbol{w}\vert\vert = 1/M \), we have to find the minimum of
|
||||
\( \boldsymbol{w}^T\boldsymbol{w}=\vert \vert \boldsymbol{w}\vert\vert \) (the norm) subject to the condition
|
||||
$$
|
||||
y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) \geq 1 \hspace{0.1cm}\forall i.
|
||||
$$
|
||||
|
||||
<p>
|
||||
We have thus defined our margin as the invers of the norm of
|
||||
\( \boldsymbol{w} \). We want to minimize the norm in order to have a as large as
|
||||
possible margin \( M \). Before we proceed, we need to remind ourselves
|
||||
about Lagrangian multipliers.
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|
||||
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|
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|
||||
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|
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||||
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|
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
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||||
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||||
<a name="part0012"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec11" class="anchor">A quick Reminder on Lagrangian Multipliers </h2>
|
||||
|
||||
<p>
|
||||
Consider a function of three independent variables \( f(x,y,z) \) . For the function \( f \) to be an
|
||||
extreme we have
|
||||
$$
|
||||
df=0.
|
||||
$$
|
||||
|
||||
A necessary and sufficient condition is
|
||||
$$
|
||||
\frac{\partial f}{\partial x} =\frac{\partial f}{\partial y}=\frac{\partial f}{\partial z}=0,
|
||||
$$
|
||||
|
||||
due to
|
||||
$$
|
||||
df = \frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy+\frac{\partial f}{\partial z}dz.
|
||||
$$
|
||||
|
||||
In many problems the variables \( x,y,z \) are often subject to constraints (such as those above for the margin)
|
||||
so that they are no longer all independent. It is possible at least in principle to use each
|
||||
constraint to eliminate one variable
|
||||
and to proceed with a new and smaller set of independent varables.
|
||||
|
||||
<p>
|
||||
The use of so-called Lagrangian multipliers is an alternative technique when the elimination
|
||||
of variables is incovenient or undesirable. Assume that we have an equation of constraint on
|
||||
the variables \( x,y,z \)
|
||||
$$
|
||||
\phi(x,y,z) = 0,
|
||||
$$
|
||||
|
||||
resulting in
|
||||
$$
|
||||
d\phi = \frac{\partial \phi}{\partial x}dx+\frac{\partial \phi}{\partial y}dy+\frac{\partial \phi}{\partial z}dz =0.
|
||||
$$
|
||||
|
||||
Now we cannot set anymore
|
||||
$$
|
||||
\frac{\partial f}{\partial x} =\frac{\partial f}{\partial y}=\frac{\partial f}{\partial z}=0,
|
||||
$$
|
||||
|
||||
if \( df=0 \) is wanted
|
||||
because there are now only two independent variables! Assume \( x \) and \( y \) are the independent
|
||||
variables.
|
||||
Then \( dz \) is no longer arbitrary.
|
||||
|
||||
<p>
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||||
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<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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<!-- !split -->
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||||
<h2 id="___sec12" class="anchor">Adding the Multiplier </h2>
|
||||
|
||||
<p>
|
||||
However, we can add to
|
||||
$$
|
||||
df = \frac{\partial f}{\partial x}dx+\frac{\partial f}{\partial y}dy+\frac{\partial f}{\partial z}dz,
|
||||
$$
|
||||
|
||||
a multiplum of \( d\phi \), viz. \( \lambda d\phi \), resulting in
|
||||
$$
|
||||
df+\lambda d\phi = (\frac{\partial f}{\partial z}+\lambda
|
||||
\frac{\partial \phi}{\partial x})dx+(\frac{\partial f}{\partial y}+\lambda\frac{\partial \phi}{\partial y})dy+
|
||||
(\frac{\partial f}{\partial z}+\lambda\frac{\partial \phi}{\partial z})dz =0.
|
||||
$$
|
||||
|
||||
Our multiplier is chosen so that
|
||||
$$
|
||||
\frac{\partial f}{\partial z}+\lambda\frac{\partial \phi}{\partial z} =0.
|
||||
$$
|
||||
|
||||
<p>
|
||||
We need to remember that we took \( dx \) and \( dy \) to be arbitrary and thus we must have
|
||||
$$
|
||||
\frac{\partial f}{\partial x}+\lambda\frac{\partial \phi}{\partial x} =0,
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
\frac{\partial f}{\partial y}+\lambda\frac{\partial \phi}{\partial y} =0.
|
||||
$$
|
||||
|
||||
When all these equations are satisfied, \( df=0 \). We have four unknowns, \( x,y,z \) and
|
||||
\( \lambda \). Actually we want only \( x,y,z \), \( \lambda \) needs not to be determined,
|
||||
it is therefore often called
|
||||
Lagrange's undetermined multiplier.
|
||||
If we have a set of constraints \( \phi_k \) we have the equations
|
||||
$$
|
||||
\frac{\partial f}{\partial x_i}+\sum_k\lambda_k\frac{\partial \phi_k}{\partial x_i} =0.
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$$
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<!-- tocinfo
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{'highest level': 2,
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||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
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('First attempt at a minimization approach', 2, None, '___sec6'),
|
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('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
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end of tocinfo -->
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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<a name="part0014"></a>
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<!-- !split -->
|
||||
|
||||
<h2 id="___sec13" class="anchor">Setting up the Problem </h2>
|
||||
In order to solve the above problem, we define the following Lagrangian function to be minimized
|
||||
$$
|
||||
{\cal L}(\lambda,b,\boldsymbol{w})=\frac{1}{2}\boldsymbol{w}^T\boldsymbol{w}-\sum_{i=1}^n\lambda_i\left[y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)-1\right],
|
||||
$$
|
||||
|
||||
where \( \lambda_i \) is a so-called Lagrange multiplier subject to the condition \( \lambda_i \geq 0 \).
|
||||
|
||||
<p>
|
||||
Taking the derivatives with respect to \( b \) and \( \boldsymbol{w} \) we obtain
|
||||
$$
|
||||
\frac{\partial {\cal L}}{\partial b} = -\sum_{i} \lambda_iy_i=0,
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
\frac{\partial {\cal L}}{\partial \boldsymbol{w}} = 0 = \boldsymbol{w}-\sum_{i} \lambda_iy_i\boldsymbol{x}_i.
|
||||
$$
|
||||
|
||||
Inserting these constraints into the equation for \( {\cal L} \) we obtain
|
||||
$$
|
||||
{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\boldsymbol{x}_i^T\boldsymbol{x}_j,
|
||||
$$
|
||||
|
||||
subject to the constraints \( \lambda_i\geq 0 \) and \( \sum_i\lambda_iy_i=0 \).
|
||||
We must in addition satisfy the <a href="https://en.wikipedia.org/wiki/Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions" target="_self">Karush-Kuhn-Tucker</a> (KKT) condition
|
||||
$$
|
||||
\lambda_i\left[y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) -1\right] \hspace{0.1cm}\forall i.
|
||||
$$
|
||||
|
||||
|
||||
<ol>
|
||||
<li> If \( \lambda_i > 0 \), then \( y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)=1 \) and we say that \( x_i \) is on the boundary.</li>
|
||||
<li> If \( y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)> 1 \), we say \( x_i \) is not on the boundary and we set \( \lambda_i=0 \).</li>
|
||||
</ol>
|
||||
|
||||
When \( \lambda_i > 0 \), the vectors \( \boldsymbol{x}_i \) are called support vectors. They are the vectors closest to the line (or hyperplane) and define the margin \( M \).
|
||||
|
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<p>
|
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{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
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end of tocinfo -->
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
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||||
<a name="part0015"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec14" class="anchor">The problem to solve </h2>
|
||||
|
||||
<p>
|
||||
We can rewrite
|
||||
$$
|
||||
{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\boldsymbol{x}_i^T\boldsymbol{x}_j,
|
||||
$$
|
||||
|
||||
and its constraints in terms of a matrix-vector problem where we minimize w.r.t. \( \lambda \) the following problem
|
||||
$$
|
||||
\frac{1}{2} \boldsymbol{\lambda}^T\begin{bmatrix} y_1y_1\boldsymbol{x}_1^T\boldsymbol{x}_1 & y_1y_2\boldsymbol{x}_1^T\boldsymbol{x}_2 & \dots & \dots & y_1y_n\boldsymbol{x}_1^T\boldsymbol{x}_n \\
|
||||
y_2y_1\boldsymbol{x}_2^T\boldsymbol{x}_1 & y_2y_2\boldsymbol{x}_2^T\boldsymbol{x}_2 & \dots & \dots & y_1y_n\boldsymbol{x}_2^T\boldsymbol{x}_n \\
|
||||
\dots & \dots & \dots & \dots & \dots \\
|
||||
\dots & \dots & \dots & \dots & \dots \\
|
||||
y_ny_1\boldsymbol{x}_n^T\boldsymbol{x}_1 & y_ny_2\boldsymbol{x}_n^T\boldsymbol{x}_2 & \dots & \dots & y_ny_n\boldsymbol{x}_n^T\boldsymbol{x}_n \\
|
||||
\end{bmatrix}\boldsymbol{\lambda}-\mathbb{1}\boldsymbol{\lambda},
|
||||
$$
|
||||
|
||||
subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vectors \( \boldsymbol{\lambda} =[\lambda_1,\lambda_2,\dots,\lambda_n] \) and
|
||||
\( \boldsymbol{y}=[y_1,y_2,\dots,y_n] \).
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<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
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||||
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|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
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|
||||
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|
||||
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|
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|
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|
||||
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|
||||
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="#___sec15" style="font-size: 80%;">The last steps</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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|
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<!-- !split -->
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<h2 id="___sec15" class="anchor">The last steps </h2>
|
||||
|
||||
<p>
|
||||
Solving the above problem, yields the values of \( \lambda_i \).
|
||||
To find the coefficients of your hyperplane we need simply to compute
|
||||
$$
|
||||
\boldsymbol{w}=\sum_{i} \lambda_iy_i\boldsymbol{x}_i.
|
||||
$$
|
||||
|
||||
With our vector \( \boldsymbol{w} \) we can in turn find the value of the intercept \( b \) (here in two dimensions) via
|
||||
$$
|
||||
y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)=1,
|
||||
$$
|
||||
|
||||
resulting in
|
||||
$$
|
||||
b = \frac{1}{y_i}-\boldsymbol{w}^T\boldsymbol{x}_i,
|
||||
$$
|
||||
|
||||
or if we write it out in terms of the support vectors only, with \( N_s \) being their number, we have
|
||||
$$
|
||||
b = \frac{1}{N_s}\sum_{j\in N_s}\left(y_j-\sum_{i=1}^n\lambda_iy_i\boldsymbol{x}_i^T\boldsymbol{x}_j\right).
|
||||
$$
|
||||
|
||||
With our hyperplane coefficients we can use our classifier to assign any observation by simply using
|
||||
$$
|
||||
y_i = \mathrm{sign}(\boldsymbol{w}^T\boldsymbol{x}_i+b).
|
||||
$$
|
||||
|
||||
Below we discuss how to find the optimal values of \( \lambda_i \). Before we proceed however, we discuss now the so-called soft classifier.
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|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
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|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
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|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
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('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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<!-- !split -->
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<h2 id="___sec16" class="anchor">A soft classifier </h2>
|
||||
|
||||
<p>
|
||||
Till now, the margin is strictly defined by the support vectors. This defines what is called a hard classifier, that is the margins are well defined.
|
||||
|
||||
<p>
|
||||
Suppose now that classes overlap in feature space, as shown in the
|
||||
figure here. One way to deal with this problem before we define the
|
||||
so-called <b>kernel approach</b>, is to allow a kind of slack in the sense
|
||||
that we allow some points to be on the wrong side of the margin.
|
||||
|
||||
<p>
|
||||
We introduce thus the so-called <b>slack</b> variables \( \boldsymbol{\xi} =[\xi_1,x_2,\dots,x_n] \) and
|
||||
modify our previous equation
|
||||
$$
|
||||
y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)=1,
|
||||
$$
|
||||
|
||||
to
|
||||
$$
|
||||
y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)=1-\xi_i,
|
||||
$$
|
||||
|
||||
with the requirement \( \xi_i\geq 0 \). The total violation is now \( \sum_i\xi \).
|
||||
The value \( \xi_i \) in the constraint the last constraint corresponds to the amount by which the prediction
|
||||
\( y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)=1 \) is on the wrong side of its margin. Hence by bounding the sum \( \sum_i \xi_i \),
|
||||
we bound the total amount by which predictions fall on the wrong side of their margins.
|
||||
|
||||
<p>
|
||||
Misclassifications occur when \( \xi_i > 1 \). Thus bounding the total sum by some value \( C \) bounds in turn the total number of
|
||||
misclassifications.
|
||||
|
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|
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||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
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|
||||
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|
||||
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|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
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|
||||
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|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
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end of tocinfo -->
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<body>
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<script type="text/x-mathjax-config">
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
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||||
<a name="part0018"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec17" class="anchor">Soft optmization problem </h2>
|
||||
|
||||
<p>
|
||||
This has in turn the consequences that we change our optmization problem to finding the minimum of
|
||||
$$
|
||||
{\cal L}=\frac{1}{2}\boldsymbol{w}^T\boldsymbol{w}-\sum_{i=1}^n\lambda_i\left[y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)-(1-\xi_)\right]+C\sum_{i=1}^n\xi_i-\sum_{i=1}^n\gamma_i\xi_i,
|
||||
$$
|
||||
|
||||
subject to
|
||||
$$
|
||||
y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b)=1-\xi_i \hspace{0.1cm}\forall i,
|
||||
$$
|
||||
|
||||
with the requirement \( \xi_i\geq 0 \).
|
||||
|
||||
<p>
|
||||
Taking the derivatives with respect to \( b \) and \( \boldsymbol{w} \) we obtain
|
||||
$$
|
||||
\frac{\partial {\cal L}}{\partial b} = -\sum_{i} \lambda_iy_i=0,
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
\frac{\partial {\cal L}}{\partial \boldsymbol{w}} = 0 = \boldsymbol{w}-\sum_{i} \lambda_iy_i\boldsymbol{x}_i,
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
\lambda_i = C-\gamma_i \hspace{0.1cm}\forall i.
|
||||
$$
|
||||
|
||||
Inserting these constraints into the equation for \( {\cal L} \) we obtain the same equation as before
|
||||
$$
|
||||
{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\boldsymbol{x}_i^T\boldsymbol{x}_j,
|
||||
$$
|
||||
|
||||
but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and \( 0\leq\lambda_i \leq C \).
|
||||
We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
|
||||
$$
|
||||
\lambda_i\left[y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
|
||||
$$
|
||||
|
||||
$$
|
||||
\gamma_i\xi_i = 0,
|
||||
$$
|
||||
|
||||
and
|
||||
$$
|
||||
y_i(\boldsymbol{w}^T\boldsymbol{x}_i+b) -(1-\xi_) \geq 0 \hspace{0.1cm}\forall i.
|
||||
$$
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|
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||||
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||||
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||||
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
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|
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||||
<a name="part0019"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec18" class="anchor">Kernels and non-linearity </h2>
|
||||
|
||||
<p>
|
||||
The cases we have studied till now, were all characterized by two classes
|
||||
with a close to linear separability. The classifiers we have described
|
||||
so far find linear boundaries in our input feature space. It is
|
||||
possible to make our procedure more flexible by exploring the feature
|
||||
space using other basis expansions such as higher-order polynomials,
|
||||
wavelets, splines etc.
|
||||
|
||||
<p>
|
||||
If our feature space is not easy to separate, as shown in the figure
|
||||
here, we can achieve a better separation by introducing more complex
|
||||
basis functions. The ideal would be, as shown in the next figure, to, via a specific transformation to
|
||||
obtain a separation between the classes which is almost linear.
|
||||
|
||||
<p>
|
||||
The change of basis, from \( x\rightarrow z=\phi(x) \) leads to the same type of equations to be solved, except that
|
||||
we need to introduce for example a polynomial transformation to a two-dimensional training set.
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">os</span>
|
||||
|
||||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">42</span>)
|
||||
|
||||
<span style="color: #408080; font-style: italic"># To plot pretty figures</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'axes.labelsize'</span>] <span style="color: #666666">=</span> <span style="color: #666666">14</span>
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'xtick.labelsize'</span>] <span style="color: #666666">=</span> <span style="color: #666666">12</span>
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'ytick.labelsize'</span>] <span style="color: #666666">=</span> <span style="color: #666666">12</span>
|
||||
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVC
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
|
||||
|
||||
|
||||
|
||||
X1D <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">-4</span>, <span style="color: #666666">4</span>, <span style="color: #666666">9</span>)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
|
||||
X2D <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[X1D, X1D<span style="color: #666666">**2</span>]
|
||||
y <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">0</span>, <span style="color: #666666">0</span>, <span style="color: #666666">1</span>, <span style="color: #666666">1</span>, <span style="color: #666666">1</span>, <span style="color: #666666">1</span>, <span style="color: #666666">1</span>, <span style="color: #666666">0</span>, <span style="color: #666666">0</span>])
|
||||
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>, <span style="color: #666666">4</span>))
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">121</span>)
|
||||
plt<span style="color: #666666">.</span>grid(<span style="color: #008000">True</span>, which<span style="color: #666666">=</span><span style="color: #BA2121">'both'</span>)
|
||||
plt<span style="color: #666666">.</span>axhline(y<span style="color: #666666">=0</span>, color<span style="color: #666666">=</span><span style="color: #BA2121">'k'</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X1D[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==0</span>], np<span style="color: #666666">.</span>zeros(<span style="color: #666666">4</span>), <span style="color: #BA2121">"bs"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X1D[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==1</span>], np<span style="color: #666666">.</span>zeros(<span style="color: #666666">5</span>), <span style="color: #BA2121">"g^"</span>)
|
||||
plt<span style="color: #666666">.</span>gca()<span style="color: #666666">.</span>get_yaxis()<span style="color: #666666">.</span>set_ticks([])
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r"$x_1$"</span>, fontsize<span style="color: #666666">=20</span>)
|
||||
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">-4.5</span>, <span style="color: #666666">4.5</span>, <span style="color: #666666">-0.2</span>, <span style="color: #666666">0.2</span>])
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">122</span>)
|
||||
plt<span style="color: #666666">.</span>grid(<span style="color: #008000">True</span>, which<span style="color: #666666">=</span><span style="color: #BA2121">'both'</span>)
|
||||
plt<span style="color: #666666">.</span>axhline(y<span style="color: #666666">=0</span>, color<span style="color: #666666">=</span><span style="color: #BA2121">'k'</span>)
|
||||
plt<span style="color: #666666">.</span>axvline(x<span style="color: #666666">=0</span>, color<span style="color: #666666">=</span><span style="color: #BA2121">'k'</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X2D[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==0</span>], X2D[:, <span style="color: #666666">1</span>][y<span style="color: #666666">==0</span>], <span style="color: #BA2121">"bs"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X2D[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==1</span>], X2D[:, <span style="color: #666666">1</span>][y<span style="color: #666666">==1</span>], <span style="color: #BA2121">"g^"</span>)
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r"$x_1$"</span>, fontsize<span style="color: #666666">=20</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r"$x_2$"</span>, fontsize<span style="color: #666666">=20</span>, rotation<span style="color: #666666">=0</span>)
|
||||
plt<span style="color: #666666">.</span>gca()<span style="color: #666666">.</span>get_yaxis()<span style="color: #666666">.</span>set_ticks([<span style="color: #666666">0</span>, <span style="color: #666666">4</span>, <span style="color: #666666">8</span>, <span style="color: #666666">12</span>, <span style="color: #666666">16</span>])
|
||||
plt<span style="color: #666666">.</span>plot([<span style="color: #666666">-4.5</span>, <span style="color: #666666">4.5</span>], [<span style="color: #666666">6.5</span>, <span style="color: #666666">6.5</span>], <span style="color: #BA2121">"r--"</span>, linewidth<span style="color: #666666">=3</span>)
|
||||
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">-4.5</span>, <span style="color: #666666">4.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">17</span>])
|
||||
plt<span style="color: #666666">.</span>subplots_adjust(right<span style="color: #666666">=1</span>)
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
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|
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|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
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<!-- !split -->
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||||
|
||||
<h2 id="___sec19" class="anchor">The equations </h2>
|
||||
|
||||
<p>
|
||||
Suppose we define a polynomial transformation of degree two only (we continue to live in a plane with \( x_i \) and \( y_i \) as variables)
|
||||
$$
|
||||
z = \phi(x_i) =\left(x_i^2, y_i^2, \sqrt{2}x_iy_i\right).
|
||||
$$
|
||||
|
||||
<p>
|
||||
With our new basis, the equations we solved earlier are basically the same, that is we have now (without the slack option for simplicity)
|
||||
$$
|
||||
{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\boldsymbol{z}_i^T\boldsymbol{z}_j,
|
||||
$$
|
||||
|
||||
subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \), and for the support vectors
|
||||
$$
|
||||
y_i(\boldsymbol{w}^T\boldsymbol{z}_i+b)= 1 \hspace{0.1cm}\forall i,
|
||||
$$
|
||||
|
||||
from which we also find \( b \).
|
||||
To compute \( \boldsymbol{z}_i^T\boldsymbol{z}_j \) we define the kernel \( K(\boldsymbol{x}_i,\boldsymbol{x}_j) \) as
|
||||
$$
|
||||
K(\boldsymbol{x}_i,\boldsymbol{x}_j)=\boldsymbol{z}_i^T\boldsymbol{z}_j= \phi(\boldsymbol{x}_i)^T\phi(\boldsymbol{x}_j).
|
||||
$$
|
||||
|
||||
For the above example, the kernel reads
|
||||
$$
|
||||
K(\boldsymbol{x}_i,\boldsymbol{x}_j)=[x_i^2, y_i^2, \sqrt{2}x_iy_i]^T\begin{bmatrix} x_j^2 \\ y_j^2 \\ \sqrt{2}x_jy_j \end{bmatrix}=x_i^2x_j^2+2x_ix_jy_iy_j+y_i^2y_j^2.
|
||||
$$
|
||||
|
||||
<p>
|
||||
We note that this is nothing but the dot product of the two original
|
||||
vectors \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \). Instead of thus computing the
|
||||
product in the Lagrangian of \( \boldsymbol{z}_i^T\boldsymbol{z}_j \) we simply compute
|
||||
the dot product \( (\boldsymbol{x}_i^T\boldsymbol{x}_j)^2 \).
|
||||
|
||||
<p>
|
||||
This leads to the so-called
|
||||
kernel trick and the result leads to the same as if we went through
|
||||
the trouble of performing the transformation
|
||||
\( \phi(\boldsymbol{x}_i)^T\phi(\boldsymbol{x}_j) \) during the SVM calculations.
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{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
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end of tocinfo -->
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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|
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|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec20" class="anchor">The problem to solve </h2>
|
||||
Using our definition of the kernel We can rewrite again the Lagrangian
|
||||
$$
|
||||
{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\boldsymbol{x}_i^T\boldsymbol{z}_j,
|
||||
$$
|
||||
|
||||
subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) in terms of a convex optimization problem
|
||||
$$
|
||||
\frac{1}{2} \boldsymbol{\lambda}^T\begin{bmatrix} y_1y_1K(\boldsymbol{x}_1,\boldsymbol{x}_1) & y_1y_2K(\boldsymbol{x}_1,\boldsymbol{x}_2) & \dots & \dots & y_1y_nK(\boldsymbol{x}_1,\boldsymbol{x}_n) \\
|
||||
y_2y_1K(\boldsymbol{x}_2,\boldsymbol{x}_1) & y_2y_2(\boldsymbol{x}_2,\boldsymbol{x}_2) & \dots & \dots & y_1y_nK(\boldsymbol{x}_2,\boldsymbol{x}_n) \\
|
||||
\dots & \dots & \dots & \dots & \dots \\
|
||||
\dots & \dots & \dots & \dots & \dots \\
|
||||
y_ny_1K(\boldsymbol{x}_n,\boldsymbol{x}_1) & y_ny_2K(\boldsymbol{x}_n\boldsymbol{x}_2) & \dots & \dots & y_ny_nK(\boldsymbol{x}_n,\boldsymbol{x}_n) \\
|
||||
\end{bmatrix}\boldsymbol{\lambda}-\mathbb{1}\boldsymbol{\lambda},
|
||||
$$
|
||||
|
||||
subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vectors \( \boldsymbol{\lambda} =[\lambda_1,\lambda_2,\dots,\lambda_n] \) and
|
||||
\( \boldsymbol{y}=[y_1,y_2,\dots,y_n] \).
|
||||
If we add the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \).
|
||||
|
||||
<p>
|
||||
We can rewrite this (see the solutions below) in terms of a convex optimization problem of the type
|
||||
$$
|
||||
\begin{align*}
|
||||
&\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber
|
||||
&\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \hspace{0.2cm} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
Below we discuss how to solve these equations. Here we note that the matrix \( \boldsymbol{P} \) has matrix elements \( p_{ij}=y_iy_jK(\boldsymbol{x}_i,\boldsymbol{x}_j) \).
|
||||
Given a kernel \( K \) and the targets \( y_i \) this matrix is easy to set up. The constraint \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \) leads to \( f=0 \) and \( \boldsymbol{A}=\boldsymbol{y} \). How to set up the matrix \( \boldsymbol{G} \) is discussed later. Here note that the inequalities \( 0\leq \lambda_i \leq C \) can be split up into
|
||||
\( 0\leq \lambda_i \) and \( \lambda_i \leq C \). These two inequalities define then the matrix \( \boldsymbol{G} \) and the vector \( \boldsymbol{h} \).
|
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<!-- tocinfo
|
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{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
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('A $p$-dimensional space of features', 2, None, '___sec3'),
|
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('The two-dimensional case', 2, None, '___sec4'),
|
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('Getting into the details', 2, None, '___sec5'),
|
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('First attempt at a minimization approach', 2, None, '___sec6'),
|
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('Solving the equations', 2, None, '___sec7'),
|
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('Code Example', 2, None, '___sec8'),
|
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('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
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('A quick Reminder on Lagrangian Multipliers',
|
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2,
|
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None,
|
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'___sec11'),
|
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('Adding the Multiplier', 2, None, '___sec12'),
|
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('Setting up the Problem', 2, None, '___sec13'),
|
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('The problem to solve', 2, None, '___sec14'),
|
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('The last steps', 2, None, '___sec15'),
|
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('A soft classifier', 2, None, '___sec16'),
|
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('Soft optmization problem', 2, None, '___sec17'),
|
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('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
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('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
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None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
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('A simple example', 2, None, '___sec25'),
|
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('Back to the more realistic cases', 2, None, '___sec26')]}
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end of tocinfo -->
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
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||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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<a name="part0022"></a>
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<!-- !split -->
|
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|
||||
<h2 id="___sec21" class="anchor">Different kernels and Mercer's theorem </h2>
|
||||
|
||||
<p>
|
||||
There are several popular kernels being used. These are
|
||||
|
||||
<ol>
|
||||
<li> Linear: \( K(\boldsymbol{x},\boldsymbol{y})=\boldsymbol{x}^T\boldsymbol{y} \),</li>
|
||||
<li> Polynomial: \( K(\boldsymbol{x},\boldsymbol{y})=(\boldsymbol{x}^T\boldsymbol{y}+\gamma)^d \),</li>
|
||||
<li> Gaussian Radial Basis Function: \( K(\boldsymbol{x},\boldsymbol{y})=\exp{\left(-\gamma\vert\vert\boldsymbol{x}-\boldsymbol{y}\vert\vert^2\right)} \),</li>
|
||||
<li> Tanh: \( K(\boldsymbol{x},\boldsymbol{y})=\tanh{(\boldsymbol{x}^T\boldsymbol{y}+\gamma)} \),</li>
|
||||
</ol>
|
||||
|
||||
and many other ones.
|
||||
|
||||
<p>
|
||||
An important theorem for us is <a href="https://en.wikipedia.org/wiki/Mercer%27s_theorem" target="_self">Mercer's
|
||||
theorem</a>. The
|
||||
theorem states that if a kernel function \( K \) is symmetric, continuous
|
||||
and leads to a positive semi-definite matrix \( \boldsymbol{P} \) then there
|
||||
exists a function \( \phi \) that maps \( \boldsymbol{x}_i \) and \( \boldsymbol{x}_j \) into
|
||||
another space (possibly with much higher dimensions) such that
|
||||
|
||||
$$
|
||||
K(\boldsymbol{x}_i,\boldsymbol{x}_j)=\phi(\boldsymbol{x}_i)^T\phi(\boldsymbol{x}_j).
|
||||
$$
|
||||
|
||||
<p>
|
||||
So you can use \( K \) as a kernel since you know \( \phi \) exists, even if
|
||||
you don’t know what \( \phi \) is.
|
||||
|
||||
<p>
|
||||
Note that some frequently used kernels (such as the Sigmoid kernel)
|
||||
don’t respect all of Mercer’s conditions, yet they generally work well
|
||||
in practice.
|
||||
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||||
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</head>
|
||||
|
||||
<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
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end of tocinfo -->
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<a class="navbar-brand" href="week46-bs.html">Week 46: Support Vector Machines</a>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
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||||
</li>
|
||||
</ul>
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</div>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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||||
<a name="part0023"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec22" class="anchor">The moons example </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">__future__</span> <span style="color: #008000; font-weight: bold">import</span> division, print_function, unicode_literals
|
||||
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
|
||||
np<span style="color: #666666">.</span>random<span style="color: #666666">.</span>seed(<span style="color: #666666">42</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'axes.labelsize'</span>] <span style="color: #666666">=</span> <span style="color: #666666">14</span>
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'xtick.labelsize'</span>] <span style="color: #666666">=</span> <span style="color: #666666">12</span>
|
||||
plt<span style="color: #666666">.</span>rcParams[<span style="color: #BA2121">'ytick.labelsize'</span>] <span style="color: #666666">=</span> <span style="color: #666666">12</span>
|
||||
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVC
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> datasets
|
||||
|
||||
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.pipeline</span> <span style="color: #008000; font-weight: bold">import</span> Pipeline
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> StandardScaler
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> LinearSVC
|
||||
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> make_moons
|
||||
X, y <span style="color: #666666">=</span> make_moons(n_samples<span style="color: #666666">=100</span>, noise<span style="color: #666666">=0.15</span>, random_state<span style="color: #666666">=42</span>)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">plot_dataset</span>(X, y, axes):
|
||||
plt<span style="color: #666666">.</span>plot(X[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==0</span>], X[:, <span style="color: #666666">1</span>][y<span style="color: #666666">==0</span>], <span style="color: #BA2121">"bs"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X[:, <span style="color: #666666">0</span>][y<span style="color: #666666">==1</span>], X[:, <span style="color: #666666">1</span>][y<span style="color: #666666">==1</span>], <span style="color: #BA2121">"g^"</span>)
|
||||
plt<span style="color: #666666">.</span>axis(axes)
|
||||
plt<span style="color: #666666">.</span>grid(<span style="color: #008000">True</span>, which<span style="color: #666666">=</span><span style="color: #BA2121">'both'</span>)
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r"$x_1$"</span>, fontsize<span style="color: #666666">=20</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r"$x_2$"</span>, fontsize<span style="color: #666666">=20</span>, rotation<span style="color: #666666">=0</span>)
|
||||
|
||||
plot_dataset(X, y, [<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>])
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> make_moons
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.pipeline</span> <span style="color: #008000; font-weight: bold">import</span> Pipeline
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> PolynomialFeatures
|
||||
|
||||
polynomial_svm_clf <span style="color: #666666">=</span> Pipeline([
|
||||
(<span style="color: #BA2121">"poly_features"</span>, PolynomialFeatures(degree<span style="color: #666666">=3</span>)),
|
||||
(<span style="color: #BA2121">"scaler"</span>, StandardScaler()),
|
||||
(<span style="color: #BA2121">"svm_clf"</span>, LinearSVC(C<span style="color: #666666">=10</span>, loss<span style="color: #666666">=</span><span style="color: #BA2121">"hinge"</span>, random_state<span style="color: #666666">=42</span>))
|
||||
])
|
||||
|
||||
polynomial_svm_clf<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">plot_predictions</span>(clf, axes):
|
||||
x0s <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(axes[<span style="color: #666666">0</span>], axes[<span style="color: #666666">1</span>], <span style="color: #666666">100</span>)
|
||||
x1s <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(axes[<span style="color: #666666">2</span>], axes[<span style="color: #666666">3</span>], <span style="color: #666666">100</span>)
|
||||
x0, x1 <span style="color: #666666">=</span> np<span style="color: #666666">.</span>meshgrid(x0s, x1s)
|
||||
X <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[x0<span style="color: #666666">.</span>ravel(), x1<span style="color: #666666">.</span>ravel()]
|
||||
y_pred <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(X)<span style="color: #666666">.</span>reshape(x0<span style="color: #666666">.</span>shape)
|
||||
y_decision <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>decision_function(X)<span style="color: #666666">.</span>reshape(x0<span style="color: #666666">.</span>shape)
|
||||
plt<span style="color: #666666">.</span>contourf(x0, x1, y_pred, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>brg, alpha<span style="color: #666666">=0.2</span>)
|
||||
plt<span style="color: #666666">.</span>contourf(x0, x1, y_decision, cmap<span style="color: #666666">=</span>plt<span style="color: #666666">.</span>cm<span style="color: #666666">.</span>brg, alpha<span style="color: #666666">=0.1</span>)
|
||||
|
||||
plot_predictions(polynomial_svm_clf, [<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>])
|
||||
plot_dataset(X, y, [<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>])
|
||||
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVC
|
||||
|
||||
poly_kernel_svm_clf <span style="color: #666666">=</span> Pipeline([
|
||||
(<span style="color: #BA2121">"scaler"</span>, StandardScaler()),
|
||||
(<span style="color: #BA2121">"svm_clf"</span>, SVC(kernel<span style="color: #666666">=</span><span style="color: #BA2121">"poly"</span>, degree<span style="color: #666666">=3</span>, coef0<span style="color: #666666">=1</span>, C<span style="color: #666666">=5</span>))
|
||||
])
|
||||
poly_kernel_svm_clf<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
poly100_kernel_svm_clf <span style="color: #666666">=</span> Pipeline([
|
||||
(<span style="color: #BA2121">"scaler"</span>, StandardScaler()),
|
||||
(<span style="color: #BA2121">"svm_clf"</span>, SVC(kernel<span style="color: #666666">=</span><span style="color: #BA2121">"poly"</span>, degree<span style="color: #666666">=10</span>, coef0<span style="color: #666666">=100</span>, C<span style="color: #666666">=5</span>))
|
||||
])
|
||||
poly100_kernel_svm_clf<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>, <span style="color: #666666">4</span>))
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">121</span>)
|
||||
plot_predictions(poly_kernel_svm_clf, [<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>])
|
||||
plot_dataset(X, y, [<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>])
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r"$d=3, r=1, C=5$"</span>, fontsize<span style="color: #666666">=18</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">122</span>)
|
||||
plot_predictions(poly100_kernel_svm_clf, [<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>])
|
||||
plot_dataset(X, y, [<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>])
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r"$d=10, r=100, C=5$"</span>, fontsize<span style="color: #666666">=18</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">gaussian_rbf</span>(x, landmark, gamma):
|
||||
<span style="color: #008000; font-weight: bold">return</span> np<span style="color: #666666">.</span>exp(<span style="color: #666666">-</span>gamma <span style="color: #666666">*</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>norm(x <span style="color: #666666">-</span> landmark, axis<span style="color: #666666">=1</span>)<span style="color: #666666">**2</span>)
|
||||
|
||||
gamma <span style="color: #666666">=</span> <span style="color: #666666">0.3</span>
|
||||
|
||||
x1s <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linspace(<span style="color: #666666">-4.5</span>, <span style="color: #666666">4.5</span>, <span style="color: #666666">200</span>)<span style="color: #666666">.</span>reshape(<span style="color: #666666">-1</span>, <span style="color: #666666">1</span>)
|
||||
x2s <span style="color: #666666">=</span> gaussian_rbf(x1s, <span style="color: #666666">-2</span>, gamma)
|
||||
x3s <span style="color: #666666">=</span> gaussian_rbf(x1s, <span style="color: #666666">1</span>, gamma)
|
||||
|
||||
XK <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c_[gaussian_rbf(X1D, <span style="color: #666666">-2</span>, gamma), gaussian_rbf(X1D, <span style="color: #666666">1</span>, gamma)]
|
||||
yk <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">0</span>, <span style="color: #666666">0</span>, <span style="color: #666666">1</span>, <span style="color: #666666">1</span>, <span style="color: #666666">1</span>, <span style="color: #666666">1</span>, <span style="color: #666666">1</span>, <span style="color: #666666">0</span>, <span style="color: #666666">0</span>])
|
||||
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>, <span style="color: #666666">4</span>))
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">121</span>)
|
||||
plt<span style="color: #666666">.</span>grid(<span style="color: #008000">True</span>, which<span style="color: #666666">=</span><span style="color: #BA2121">'both'</span>)
|
||||
plt<span style="color: #666666">.</span>axhline(y<span style="color: #666666">=0</span>, color<span style="color: #666666">=</span><span style="color: #BA2121">'k'</span>)
|
||||
plt<span style="color: #666666">.</span>scatter(x<span style="color: #666666">=</span>[<span style="color: #666666">-2</span>, <span style="color: #666666">1</span>], y<span style="color: #666666">=</span>[<span style="color: #666666">0</span>, <span style="color: #666666">0</span>], s<span style="color: #666666">=150</span>, alpha<span style="color: #666666">=0.5</span>, c<span style="color: #666666">=</span><span style="color: #BA2121">"red"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X1D[:, <span style="color: #666666">0</span>][yk<span style="color: #666666">==0</span>], np<span style="color: #666666">.</span>zeros(<span style="color: #666666">4</span>), <span style="color: #BA2121">"bs"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(X1D[:, <span style="color: #666666">0</span>][yk<span style="color: #666666">==1</span>], np<span style="color: #666666">.</span>zeros(<span style="color: #666666">5</span>), <span style="color: #BA2121">"g^"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(x1s, x2s, <span style="color: #BA2121">"g--"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(x1s, x3s, <span style="color: #BA2121">"b:"</span>)
|
||||
plt<span style="color: #666666">.</span>gca()<span style="color: #666666">.</span>get_yaxis()<span style="color: #666666">.</span>set_ticks([<span style="color: #666666">0</span>, <span style="color: #666666">0.25</span>, <span style="color: #666666">0.5</span>, <span style="color: #666666">0.75</span>, <span style="color: #666666">1</span>])
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r"$x_1$"</span>, fontsize<span style="color: #666666">=20</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r"Similarity"</span>, fontsize<span style="color: #666666">=14</span>)
|
||||
plt<span style="color: #666666">.</span>annotate(<span style="color: #BA2121">r'$\mathbf{x}$'</span>,
|
||||
xy<span style="color: #666666">=</span>(X1D[<span style="color: #666666">3</span>, <span style="color: #666666">0</span>], <span style="color: #666666">0</span>),
|
||||
xytext<span style="color: #666666">=</span>(<span style="color: #666666">-0.5</span>, <span style="color: #666666">0.20</span>),
|
||||
ha<span style="color: #666666">=</span><span style="color: #BA2121">"center"</span>,
|
||||
arrowprops<span style="color: #666666">=</span><span style="color: #008000">dict</span>(facecolor<span style="color: #666666">=</span><span style="color: #BA2121">'black'</span>, shrink<span style="color: #666666">=0.1</span>),
|
||||
fontsize<span style="color: #666666">=18</span>,
|
||||
)
|
||||
plt<span style="color: #666666">.</span>text(<span style="color: #666666">-2</span>, <span style="color: #666666">0.9</span>, <span style="color: #BA2121">"$x_2$"</span>, ha<span style="color: #666666">=</span><span style="color: #BA2121">"center"</span>, fontsize<span style="color: #666666">=20</span>)
|
||||
plt<span style="color: #666666">.</span>text(<span style="color: #666666">1</span>, <span style="color: #666666">0.9</span>, <span style="color: #BA2121">"$x_3$"</span>, ha<span style="color: #666666">=</span><span style="color: #BA2121">"center"</span>, fontsize<span style="color: #666666">=20</span>)
|
||||
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">-4.5</span>, <span style="color: #666666">4.5</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">1.1</span>])
|
||||
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">122</span>)
|
||||
plt<span style="color: #666666">.</span>grid(<span style="color: #008000">True</span>, which<span style="color: #666666">=</span><span style="color: #BA2121">'both'</span>)
|
||||
plt<span style="color: #666666">.</span>axhline(y<span style="color: #666666">=0</span>, color<span style="color: #666666">=</span><span style="color: #BA2121">'k'</span>)
|
||||
plt<span style="color: #666666">.</span>axvline(x<span style="color: #666666">=0</span>, color<span style="color: #666666">=</span><span style="color: #BA2121">'k'</span>)
|
||||
plt<span style="color: #666666">.</span>plot(XK[:, <span style="color: #666666">0</span>][yk<span style="color: #666666">==0</span>], XK[:, <span style="color: #666666">1</span>][yk<span style="color: #666666">==0</span>], <span style="color: #BA2121">"bs"</span>)
|
||||
plt<span style="color: #666666">.</span>plot(XK[:, <span style="color: #666666">0</span>][yk<span style="color: #666666">==1</span>], XK[:, <span style="color: #666666">1</span>][yk<span style="color: #666666">==1</span>], <span style="color: #BA2121">"g^"</span>)
|
||||
plt<span style="color: #666666">.</span>xlabel(<span style="color: #BA2121">r"$x_2$"</span>, fontsize<span style="color: #666666">=20</span>)
|
||||
plt<span style="color: #666666">.</span>ylabel(<span style="color: #BA2121">r"$x_3$ "</span>, fontsize<span style="color: #666666">=20</span>, rotation<span style="color: #666666">=0</span>)
|
||||
plt<span style="color: #666666">.</span>annotate(<span style="color: #BA2121">r'$\phi\left(\mathbf{x}\right)$'</span>,
|
||||
xy<span style="color: #666666">=</span>(XK[<span style="color: #666666">3</span>, <span style="color: #666666">0</span>], XK[<span style="color: #666666">3</span>, <span style="color: #666666">1</span>]),
|
||||
xytext<span style="color: #666666">=</span>(<span style="color: #666666">0.65</span>, <span style="color: #666666">0.50</span>),
|
||||
ha<span style="color: #666666">=</span><span style="color: #BA2121">"center"</span>,
|
||||
arrowprops<span style="color: #666666">=</span><span style="color: #008000">dict</span>(facecolor<span style="color: #666666">=</span><span style="color: #BA2121">'black'</span>, shrink<span style="color: #666666">=0.1</span>),
|
||||
fontsize<span style="color: #666666">=18</span>,
|
||||
)
|
||||
plt<span style="color: #666666">.</span>plot([<span style="color: #666666">-0.1</span>, <span style="color: #666666">1.1</span>], [<span style="color: #666666">0.57</span>, <span style="color: #666666">-0.1</span>], <span style="color: #BA2121">"r--"</span>, linewidth<span style="color: #666666">=3</span>)
|
||||
plt<span style="color: #666666">.</span>axis([<span style="color: #666666">-0.1</span>, <span style="color: #666666">1.1</span>, <span style="color: #666666">-0.1</span>, <span style="color: #666666">1.1</span>])
|
||||
|
||||
plt<span style="color: #666666">.</span>subplots_adjust(right<span style="color: #666666">=1</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
|
||||
x1_example <span style="color: #666666">=</span> X1D[<span style="color: #666666">3</span>, <span style="color: #666666">0</span>]
|
||||
<span style="color: #008000; font-weight: bold">for</span> landmark <span style="color: #AA22FF; font-weight: bold">in</span> (<span style="color: #666666">-2</span>, <span style="color: #666666">1</span>):
|
||||
k <span style="color: #666666">=</span> gaussian_rbf(np<span style="color: #666666">.</span>array([[x1_example]]), np<span style="color: #666666">.</span>array([[landmark]]), gamma)
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Phi({}, {}) = {}"</span><span style="color: #666666">.</span>format(x1_example, landmark, k))
|
||||
|
||||
rbf_kernel_svm_clf <span style="color: #666666">=</span> Pipeline([
|
||||
(<span style="color: #BA2121">"scaler"</span>, StandardScaler()),
|
||||
(<span style="color: #BA2121">"svm_clf"</span>, SVC(kernel<span style="color: #666666">=</span><span style="color: #BA2121">"rbf"</span>, gamma<span style="color: #666666">=5</span>, C<span style="color: #666666">=0.001</span>))
|
||||
])
|
||||
rbf_kernel_svm_clf<span style="color: #666666">.</span>fit(X, y)
|
||||
|
||||
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVC
|
||||
|
||||
gamma1, gamma2 <span style="color: #666666">=</span> <span style="color: #666666">0.1</span>, <span style="color: #666666">5</span>
|
||||
C1, C2 <span style="color: #666666">=</span> <span style="color: #666666">0.001</span>, <span style="color: #666666">1000</span>
|
||||
hyperparams <span style="color: #666666">=</span> (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)
|
||||
|
||||
svm_clfs <span style="color: #666666">=</span> []
|
||||
<span style="color: #008000; font-weight: bold">for</span> gamma, C <span style="color: #AA22FF; font-weight: bold">in</span> hyperparams:
|
||||
rbf_kernel_svm_clf <span style="color: #666666">=</span> Pipeline([
|
||||
(<span style="color: #BA2121">"scaler"</span>, StandardScaler()),
|
||||
(<span style="color: #BA2121">"svm_clf"</span>, SVC(kernel<span style="color: #666666">=</span><span style="color: #BA2121">"rbf"</span>, gamma<span style="color: #666666">=</span>gamma, C<span style="color: #666666">=</span>C))
|
||||
])
|
||||
rbf_kernel_svm_clf<span style="color: #666666">.</span>fit(X, y)
|
||||
svm_clfs<span style="color: #666666">.</span>append(rbf_kernel_svm_clf)
|
||||
|
||||
plt<span style="color: #666666">.</span>figure(figsize<span style="color: #666666">=</span>(<span style="color: #666666">11</span>, <span style="color: #666666">7</span>))
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i, svm_clf <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">enumerate</span>(svm_clfs):
|
||||
plt<span style="color: #666666">.</span>subplot(<span style="color: #666666">221</span> <span style="color: #666666">+</span> i)
|
||||
plot_predictions(svm_clf, [<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>])
|
||||
plot_dataset(X, y, [<span style="color: #666666">-1.5</span>, <span style="color: #666666">2.5</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">1.5</span>])
|
||||
gamma, C <span style="color: #666666">=</span> hyperparams[i]
|
||||
plt<span style="color: #666666">.</span>title(<span style="color: #BA2121">r"$\gamma = {}, C = {}$"</span><span style="color: #666666">.</span>format(gamma, C), fontsize<span style="color: #666666">=16</span>)
|
||||
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
</pre></div>
|
||||
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|
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</head>
|
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|
||||
<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
||||
end of tocinfo -->
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
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<!-- navigation toc: --> <li><a href="#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
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<h2 id="___sec23" class="anchor">Mathematical optimization of convex functions </h2>
|
||||
|
||||
<p>
|
||||
A mathematical (quadratic) optimization problem, or just optimization problem, has the form
|
||||
$$
|
||||
\begin{align*}
|
||||
&\mathrm{min}_{\lambda}\hspace{0.2cm} \frac{1}{2}\boldsymbol{\lambda}^T\boldsymbol{P}\boldsymbol{\lambda}+\boldsymbol{q}^T\boldsymbol{\lambda},\\ \nonumber
|
||||
&\mathrm{subject\hspace{0.1cm}to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{\lambda} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{\lambda}=f.
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
subject to some constraints for say a selected set \( i=1,2,\dots, n \).
|
||||
In our case we are optimizing with respect to the Lagrangian multipliers \( \lambda_i \), and the
|
||||
vector \( \boldsymbol{\lambda}=[\lambda_1, \lambda_2,\dots, \lambda_n] \) is the optimization variable we are dealing with.
|
||||
|
||||
<p>
|
||||
In our case we are particularly interested in a class of optimization problems called convex optmization problems.
|
||||
In our discussion on gradient descent methods we discussed at length the definition of a convex function.
|
||||
|
||||
<p>
|
||||
Convex optimization problems play a central role in applied mathematics and we recommend strongly <a href="http://web.stanford.edu/~boyd/cvxbook/" target="_self">Boyd and Vandenberghe's text on the topics</a>.
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|
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|
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|
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|
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('The problem to solve', 2, None, '___sec20'),
|
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("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
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('The moons example', 2, None, '___sec22'),
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('Mathematical optimization of convex functions',
|
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2,
|
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None,
|
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'___sec23'),
|
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('How do we solve these problems?', 2, None, '___sec24'),
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('A simple example', 2, None, '___sec25'),
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('Back to the more realistic cases', 2, None, '___sec26')]}
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
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<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
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<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
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<!-- navigation toc: --> <li><a href="#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
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<!-- !split -->
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<h2 id="___sec24" class="anchor">How do we solve these problems? </h2>
|
||||
|
||||
<p>
|
||||
If we use Python as programming language and wish to venture beyond
|
||||
<b>scikit-learn</b>, <b>tensorflow</b> and similar software which makes our
|
||||
lives so much easier, we need to dive into the wonderful world of
|
||||
quadratic programming. We can, if we wish, solve the minimization
|
||||
problem using say standard gradient methods or conjugate gradient
|
||||
methods. However, these methods tend to exhibit a rather slow
|
||||
converge. So, welcome to the promised land of quadratic programming.
|
||||
|
||||
<p>
|
||||
The functions we need are contained in the quadratic programming package <b>CVXOPT</b> and we need to import it together with <b>numpy</b> as
|
||||
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">cvxopt</span>
|
||||
</pre></div>
|
||||
<p>
|
||||
This will make our life much easier. You don't need t write your own optimizer.
|
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{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
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('Back to the more realistic cases', 2, None, '___sec26')]}
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end of tocinfo -->
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs027.html#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
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</div>
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<p> </p><p> </p><p> </p> <!-- add vertical space -->
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<a name="part0026"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec25" class="anchor">A simple example </h2>
|
||||
|
||||
<p>
|
||||
We remind ourselves about the general problem we want to solve
|
||||
$$
|
||||
\begin{align*}
|
||||
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}\boldsymbol{x}^T\boldsymbol{P}\boldsymbol{x}+\boldsymbol{q}^T\boldsymbol{x},\\ \nonumber
|
||||
&\mathrm{subject\hspace{0.1cm} to} \hspace{0.2cm} \boldsymbol{G}\boldsymbol{x} \preceq \boldsymbol{h} \wedge \boldsymbol{A}\boldsymbol{x}=f.
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
<p>
|
||||
Let us show how to perform the optmization using a simple case. Assume we want to optimize the following problem
|
||||
$$
|
||||
\begin{align*}
|
||||
&\mathrm{min}_{x}\hspace{0.2cm} \frac{1}{2}x^2+5x+3y \\ \nonumber
|
||||
&\mathrm{subject to} \\ \nonumber
|
||||
&x, y \geq 0 \\ \nonumber
|
||||
&x+3y \geq 15 \\ \nonumber
|
||||
&2x+5y \leq 100 \\ \nonumber
|
||||
&3x+4y \leq 80. \\ \nonumber
|
||||
\end{align*}
|
||||
$$
|
||||
|
||||
The minimization problem can be rewritten in terms of vectors and matrices as (with \( x \) and \( y \) being the unknowns)
|
||||
$$
|
||||
\frac{1}{2}\begin{bmatrix} x\\ y \end{bmatrix}^T \begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} + \begin{bmatrix}3\\ 4 \end{bmatrix}^T \begin{bmatrix}x \\ y \end{bmatrix}.
|
||||
$$
|
||||
|
||||
Similarly, we can now set up the inequalities (we need to change \( \geq \) to \( \leq \) by multiplying with \( -1 \) on bot sides) as the following matrix-vector equation
|
||||
$$
|
||||
\begin{bmatrix} -1 & 0 \\ 0 & -1 \\ -1 & -3 \\ 2 & 5 \\ 3 & 4\end{bmatrix}\begin{bmatrix} x \\ y\end{bmatrix} \preceq \begin{bmatrix}0 \\ 0\\ -15 \\ 100 \\ 80\end{bmatrix}.
|
||||
$$
|
||||
|
||||
We have collapsed all the inequalities into a single matrix \( \boldsymbol{G} \). We see also that our matrix
|
||||
$$
|
||||
\boldsymbol{P} =\begin{bmatrix} 1 & 0\\ 0 & 0 \end{bmatrix}
|
||||
$$
|
||||
|
||||
is clearly positive semi-definite (all eigenvalues larger or equal zero).
|
||||
Finally, the vector \( \boldsymbol{h} \) is defined as
|
||||
$$
|
||||
\boldsymbol{h} = \begin{bmatrix}0 \\ 0\\ -15 \\ 100 \\ 80\end{bmatrix}.
|
||||
$$
|
||||
|
||||
<p>
|
||||
Since we don't have any equalities the matrix \( \boldsymbol{A} \) is set to zero
|
||||
The following code solves the equations for us
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #408080; font-style: italic"># Import the necessary packages</span>
|
||||
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span>
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">cvxopt</span> <span style="color: #008000; font-weight: bold">import</span> matrix
|
||||
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">cvxopt</span> <span style="color: #008000; font-weight: bold">import</span> solvers
|
||||
P <span style="color: #666666">=</span> matrix(numpy<span style="color: #666666">.</span>diag([<span style="color: #666666">1</span>,<span style="color: #666666">0</span>]), tc<span style="color: #666666">=</span>’d’)
|
||||
q <span style="color: #666666">=</span> matrix(numpy<span style="color: #666666">.</span>array([<span style="color: #666666">3</span>,<span style="color: #666666">4</span>]), tc<span style="color: #666666">=</span>’d’)
|
||||
G <span style="color: #666666">=</span> matrix(numpy<span style="color: #666666">.</span>array([[<span style="color: #666666">-1</span>,<span style="color: #666666">0</span>],[<span style="color: #666666">0</span>,<span style="color: #666666">-1</span>],[<span style="color: #666666">-1</span>,<span style="color: #666666">-3</span>],[<span style="color: #666666">2</span>,<span style="color: #666666">5</span>],[<span style="color: #666666">3</span>,<span style="color: #666666">4</span>]]), tc<span style="color: #666666">=</span>’d’)
|
||||
h <span style="color: #666666">=</span> matrix(numpy<span style="color: #666666">.</span>array([<span style="color: #666666">0</span>,<span style="color: #666666">0</span>,<span style="color: #666666">-15</span>,<span style="color: #666666">100</span>,<span style="color: #666666">80</span>]), tc<span style="color: #666666">=</span>’d’)
|
||||
<span style="color: #408080; font-style: italic"># Construct the QP, invoke solver</span>
|
||||
sol <span style="color: #666666">=</span> solvers<span style="color: #666666">.</span>qp(P,q,G,h)
|
||||
<span style="color: #408080; font-style: italic"># Extract optimal value and solution</span>
|
||||
sol[’x’]
|
||||
sol[’primal objective’]
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
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margin:-50px 0 0; /* negative fixed header height */
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}
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</head>
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|
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<!-- tocinfo
|
||||
{'highest level': 2,
|
||||
'sections': [('Support Vector Machines, overarching aims', 2, None, '___sec0'),
|
||||
('Hyperplanes and all that', 2, None, '___sec1'),
|
||||
('What is a hyperplane?', 2, None, '___sec2'),
|
||||
('A $p$-dimensional space of features', 2, None, '___sec3'),
|
||||
('The two-dimensional case', 2, None, '___sec4'),
|
||||
('Getting into the details', 2, None, '___sec5'),
|
||||
('First attempt at a minimization approach', 2, None, '___sec6'),
|
||||
('Solving the equations', 2, None, '___sec7'),
|
||||
('Code Example', 2, None, '___sec8'),
|
||||
('Problems with the Simpler Approach', 2, None, '___sec9'),
|
||||
('A better approach', 2, None, '___sec10'),
|
||||
('A quick Reminder on Lagrangian Multipliers',
|
||||
2,
|
||||
None,
|
||||
'___sec11'),
|
||||
('Adding the Multiplier', 2, None, '___sec12'),
|
||||
('Setting up the Problem', 2, None, '___sec13'),
|
||||
('The problem to solve', 2, None, '___sec14'),
|
||||
('The last steps', 2, None, '___sec15'),
|
||||
('A soft classifier', 2, None, '___sec16'),
|
||||
('Soft optmization problem', 2, None, '___sec17'),
|
||||
('Kernels and non-linearity', 2, None, '___sec18'),
|
||||
('The equations', 2, None, '___sec19'),
|
||||
('The problem to solve', 2, None, '___sec20'),
|
||||
("Different kernels and Mercer's theorem", 2, None, '___sec21'),
|
||||
('The moons example', 2, None, '___sec22'),
|
||||
('Mathematical optimization of convex functions',
|
||||
2,
|
||||
None,
|
||||
'___sec23'),
|
||||
('How do we solve these problems?', 2, None, '___sec24'),
|
||||
('A simple example', 2, None, '___sec25'),
|
||||
('Back to the more realistic cases', 2, None, '___sec26')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
|
||||
|
||||
|
||||
<script type="text/x-mathjax-config">
|
||||
MathJax.Hub.Config({
|
||||
TeX: {
|
||||
equationNumbers: { autoNumber: "none" },
|
||||
extensions: ["AMSmath.js", "AMSsymbols.js", "autobold.js", "color.js"]
|
||||
}
|
||||
});
|
||||
</script>
|
||||
<script type="text/javascript" async
|
||||
src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML">
|
||||
</script>
|
||||
|
||||
|
||||
|
||||
|
||||
<!-- Bootstrap navigation bar -->
|
||||
<div class="navbar navbar-default navbar-fixed-top">
|
||||
<div class="navbar-header">
|
||||
<button type="button" class="navbar-toggle" data-toggle="collapse" data-target=".navbar-responsive-collapse">
|
||||
<span class="icon-bar"></span>
|
||||
<span class="icon-bar"></span>
|
||||
<span class="icon-bar"></span>
|
||||
</button>
|
||||
<a class="navbar-brand" href="week46-bs.html">Week 46: Support Vector Machines</a>
|
||||
</div>
|
||||
|
||||
<div class="navbar-collapse collapse navbar-responsive-collapse">
|
||||
<ul class="nav navbar-nav navbar-right">
|
||||
<li class="dropdown">
|
||||
<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
|
||||
<ul class="dropdown-menu">
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs001.html#___sec0" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs002.html#___sec1" style="font-size: 80%;">Hyperplanes and all that</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs003.html#___sec2" style="font-size: 80%;">What is a hyperplane?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs004.html#___sec3" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs005.html#___sec4" style="font-size: 80%;">The two-dimensional case</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs006.html#___sec5" style="font-size: 80%;">Getting into the details</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs007.html#___sec6" style="font-size: 80%;">First attempt at a minimization approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs008.html#___sec7" style="font-size: 80%;">Solving the equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs009.html#___sec8" style="font-size: 80%;">Code Example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs010.html#___sec9" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs011.html#___sec10" style="font-size: 80%;">A better approach</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs012.html#___sec11" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs013.html#___sec12" style="font-size: 80%;">Adding the Multiplier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs014.html#___sec13" style="font-size: 80%;">Setting up the Problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs015.html#___sec14" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs016.html#___sec15" style="font-size: 80%;">The last steps</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs017.html#___sec16" style="font-size: 80%;">A soft classifier</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs018.html#___sec17" style="font-size: 80%;">Soft optmization problem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs019.html#___sec18" style="font-size: 80%;">Kernels and non-linearity</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs020.html#___sec19" style="font-size: 80%;">The equations</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs021.html#___sec20" style="font-size: 80%;">The problem to solve</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs022.html#___sec21" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs023.html#___sec22" style="font-size: 80%;">The moons example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs024.html#___sec23" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs025.html#___sec24" style="font-size: 80%;">How do we solve these problems?</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._week46-bs026.html#___sec25" style="font-size: 80%;">A simple example</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec26" style="font-size: 80%;">Back to the more realistic cases</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
</ul>
|
||||
</div>
|
||||
</div>
|
||||
</div> <!-- end of navigation bar -->
|
||||
|
||||
<div class="container">
|
||||
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
|
||||
<a name="part0027"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec26" class="anchor">Back to the more realistic cases </h2>
|
||||
|
||||
<p>
|
||||
We are now ready to return to our setup of the optmization problem for a more realistic case. Introducing the <b>slack</b> parameter \( C \) we have
|
||||
$$
|
||||
\frac{1}{2} \boldsymbol{\lambda}^T\begin{bmatrix} y_1y_1K(\boldsymbol{x}_1,\boldsymbol{x}_1) & y_1y_2K(\boldsymbol{x}_1,\boldsymbol{x}_2) & \dots & \dots & y_1y_nK(\boldsymbol{x}_1,\boldsymbol{x}_n) \\
|
||||
y_2y_1K(\boldsymbol{x}_2,\boldsymbol{x}_1) & y_2y_2K(\boldsymbol{x}_2,\boldsymbol{x}_2) & \dots & \dots & y_1y_nK(\boldsymbol{x}_2,\boldsymbol{x}_n) \\
|
||||
\dots & \dots & \dots & \dots & \dots \\
|
||||
\dots & \dots & \dots & \dots & \dots \\
|
||||
y_ny_1K(\boldsymbol{x}_n,\boldsymbol{x}_1) & y_ny_2K(\boldsymbol{x}_n\boldsymbol{x}_2) & \dots & \dots & y_ny_nK(\boldsymbol{x}_n,\boldsymbol{x}_n) \\
|
||||
\end{bmatrix}\boldsymbol{\lambda}-\mathbb{I}\boldsymbol{\lambda},
|
||||
$$
|
||||
|
||||
subject to \( \boldsymbol{y}^T\boldsymbol{\lambda}=0 \). Here we defined the vectors \( \boldsymbol{\lambda} =[\lambda_1,\lambda_2,\dots,\lambda_n] \) and
|
||||
\( \boldsymbol{y}=[y_1,y_2,\dots,y_n] \).
|
||||
With the slack constants this leads to the additional constraint \( 0\leq \lambda_i \leq C \).
|
||||
|
||||
<p>
|
||||
<b>code will be added</b>
|
||||
|
||||
<p>
|
||||
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
<ul class="pagination">
|
||||
<li><a href="._week46-bs026.html">«</a></li>
|
||||
<li><a href="._week46-bs000.html">1</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._week46-bs019.html">20</a></li>
|
||||
<li><a href="._week46-bs020.html">21</a></li>
|
||||
<li><a href="._week46-bs021.html">22</a></li>
|
||||
<li><a href="._week46-bs022.html">23</a></li>
|
||||
<li><a href="._week46-bs023.html">24</a></li>
|
||||
<li><a href="._week46-bs024.html">25</a></li>
|
||||
<li><a href="._week46-bs025.html">26</a></li>
|
||||
<li><a href="._week46-bs026.html">27</a></li>
|
||||
<li class="active"><a href="._week46-bs027.html">28</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
</div> <!-- end container -->
|
||||
<!-- include javascript, jQuery *first* -->
|
||||
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.10.2/jquery.min.js"></script>
|
||||
<script src="https://netdna.bootstrapcdn.com/bootstrap/3.0.0/js/bootstrap.min.js"></script>
|
||||
|
||||
<!-- Bootstrap footer
|
||||
<footer>
|
||||
<a href="http://..."><img width="250" align=right src="http://..."></a>
|
||||
</footer>
|
||||
-->
|
||||
|
||||
|
||||
<center style="font-size:80%">
|
||||
<!-- copyright only on the titlepage -->
|
||||
</center>
|
||||
|
||||
|
||||
</body>
|
||||
</html>
|
||||
|
||||
|
||||
@@ -0,0 +1,8 @@
|
||||
.DS_Store
|
||||
.svn
|
||||
log/*.log
|
||||
tmp/**
|
||||
node_modules/
|
||||
.sass-cache
|
||||
css/reveal.min.css
|
||||
js/reveal.min.js
|
||||
@@ -0,0 +1,5 @@
|
||||
language: node_js
|
||||
node_js:
|
||||
- 0.10
|
||||
before_script:
|
||||
- npm install -g grunt-cli
|
||||
@@ -0,0 +1,23 @@
|
||||
## Contributing
|
||||
|
||||
Please keep the [issue tracker](http://github.com/hakimel/reveal.js/issues) limited to **bug reports**, **feature requests** and **pull requests**.
|
||||
|
||||
|
||||
### Personal Support
|
||||
If you have personal support or setup questions the best place to ask those are [StackOverflow](http://stackoverflow.com/questions/tagged/reveal.js).
|
||||
|
||||
|
||||
### Bug Reports
|
||||
When reporting a bug make sure to include information about which browser and operating system you are on as well as the necessary steps to reproduce the issue. If possible please include a link to a sample presentation where the bug can be tested.
|
||||
|
||||
|
||||
### Pull Requests
|
||||
- Should follow the coding style of the file you work in, most importantly:
|
||||
- Tabs to indent
|
||||
- Single-quoted strings
|
||||
- Should be made towards the **dev branch**
|
||||
- Should be submitted from a feature/topic branch (not your master)
|
||||
|
||||
|
||||
### Plugins
|
||||
Please do not submit plugins as pull requests. They should be maintained in their own separate repository. More information here: https://github.com/hakimel/reveal.js/wiki/Plugin-Guidelines
|
||||
@@ -0,0 +1,140 @@
|
||||
/* global module:false */
|
||||
module.exports = function(grunt) {
|
||||
var port = grunt.option('port') || 8000;
|
||||
// Project configuration
|
||||
grunt.initConfig({
|
||||
pkg: grunt.file.readJSON('package.json'),
|
||||
meta: {
|
||||
banner:
|
||||
'/*!\n' +
|
||||
' * reveal.js <%= pkg.version %> (<%= grunt.template.today("yyyy-mm-dd, HH:MM") %>)\n' +
|
||||
' * http://lab.hakim.se/reveal-js\n' +
|
||||
' * MIT licensed\n' +
|
||||
' *\n' +
|
||||
' * Copyright (C) 2014 Hakim El Hattab, http://hakim.se\n' +
|
||||
' */'
|
||||
},
|
||||
|
||||
qunit: {
|
||||
files: [ 'test/*.html' ]
|
||||
},
|
||||
|
||||
uglify: {
|
||||
options: {
|
||||
banner: '<%= meta.banner %>\n'
|
||||
},
|
||||
build: {
|
||||
src: 'js/reveal.js',
|
||||
dest: 'js/reveal.min.js'
|
||||
}
|
||||
},
|
||||
|
||||
cssmin: {
|
||||
compress: {
|
||||
files: {
|
||||
'css/reveal.min.css': [ 'css/reveal.css' ]
|
||||
}
|
||||
}
|
||||
},
|
||||
|
||||
sass: {
|
||||
main: {
|
||||
files: {
|
||||
'css/theme/darkgray.css': 'css/theme/source/darkgray.scss',
|
||||
'css/theme/beigesmall.css': 'css/theme/source/beigesmall.scss',
|
||||
'css/theme/cbc.css': 'css/theme/source/cbc.scss',
|
||||
'css/theme/default.css': 'css/theme/source/default.scss',
|
||||
'css/theme/beige.css': 'css/theme/source/beige.scss',
|
||||
'css/theme/night.css': 'css/theme/source/night.scss',
|
||||
'css/theme/serif.css': 'css/theme/source/serif.scss',
|
||||
'css/theme/simple.css': 'css/theme/source/simple.scss',
|
||||
'css/theme/sky.css': 'css/theme/source/sky.scss',
|
||||
'css/theme/moon.css': 'css/theme/source/moon.scss',
|
||||
'css/theme/solarized.css': 'css/theme/source/solarized.scss',
|
||||
'css/theme/blood.css': 'css/theme/source/blood.scss'
|
||||
}
|
||||
}
|
||||
},
|
||||
|
||||
jshint: {
|
||||
options: {
|
||||
curly: false,
|
||||
eqeqeq: true,
|
||||
immed: true,
|
||||
latedef: true,
|
||||
newcap: true,
|
||||
noarg: true,
|
||||
sub: true,
|
||||
undef: true,
|
||||
eqnull: true,
|
||||
browser: true,
|
||||
expr: true,
|
||||
globals: {
|
||||
head: false,
|
||||
module: false,
|
||||
console: false,
|
||||
unescape: false
|
||||
}
|
||||
},
|
||||
files: [ 'Gruntfile.js', 'js/reveal.js' ]
|
||||
},
|
||||
|
||||
connect: {
|
||||
server: {
|
||||
options: {
|
||||
port: port,
|
||||
base: '.'
|
||||
}
|
||||
}
|
||||
},
|
||||
|
||||
zip: {
|
||||
'reveal-js-presentation.zip': [
|
||||
'index.html',
|
||||
'css/**',
|
||||
'js/**',
|
||||
'lib/**',
|
||||
'images/**',
|
||||
'plugin/**'
|
||||
]
|
||||
},
|
||||
|
||||
watch: {
|
||||
main: {
|
||||
files: [ 'Gruntfile.js', 'js/reveal.js', 'css/reveal.css' ],
|
||||
tasks: 'default'
|
||||
},
|
||||
theme: {
|
||||
files: [ 'css/theme/source/*.scss', 'css/theme/template/*.scss' ],
|
||||
tasks: 'themes'
|
||||
}
|
||||
}
|
||||
|
||||
});
|
||||
|
||||
// Dependencies
|
||||
grunt.loadNpmTasks( 'grunt-contrib-qunit' );
|
||||
grunt.loadNpmTasks( 'grunt-contrib-jshint' );
|
||||
grunt.loadNpmTasks( 'grunt-contrib-cssmin' );
|
||||
grunt.loadNpmTasks( 'grunt-contrib-uglify' );
|
||||
grunt.loadNpmTasks( 'grunt-contrib-watch' );
|
||||
grunt.loadNpmTasks( 'grunt-contrib-sass' );
|
||||
grunt.loadNpmTasks( 'grunt-contrib-connect' );
|
||||
grunt.loadNpmTasks( 'grunt-zip' );
|
||||
|
||||
// Default task
|
||||
grunt.registerTask( 'default', [ 'jshint', 'cssmin', 'uglify', 'qunit' ] );
|
||||
|
||||
// Theme task
|
||||
grunt.registerTask( 'themes', [ 'sass' ] );
|
||||
|
||||
// Package presentation to archive
|
||||
grunt.registerTask( 'package', [ 'default', 'zip' ] );
|
||||
|
||||
// Serve presentation locally
|
||||
grunt.registerTask( 'serve', [ 'connect', 'watch' ] );
|
||||
|
||||
// Run tests
|
||||
grunt.registerTask( 'test', [ 'jshint', 'qunit' ] );
|
||||
|
||||
};
|
||||
@@ -0,0 +1,19 @@
|
||||
Copyright (C) 2015 Hakim El Hattab, http://hakim.se
|
||||
|
||||
Permission is hereby granted, free of charge, to any person obtaining a copy
|
||||
of this software and associated documentation files (the "Software"), to deal
|
||||
in the Software without restriction, including without limitation the rights
|
||||
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
|
||||
copies of the Software, and to permit persons to whom the Software is
|
||||
furnished to do so, subject to the following conditions:
|
||||
|
||||
The above copyright notice and this permission notice shall be included in
|
||||
all copies or substantial portions of the Software.
|
||||
|
||||
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
|
||||
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
|
||||
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
|
||||
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
|
||||
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
|
||||
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
|
||||
THE SOFTWARE.
|
||||
File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,27 @@
|
||||
{
|
||||
"name": "reveal.js",
|
||||
"version": "3.1.0",
|
||||
"main": [
|
||||
"js/reveal.js",
|
||||
"css/reveal.css"
|
||||
],
|
||||
"homepage": "http://lab.hakim.se/reveal-js/",
|
||||
"license": "MIT",
|
||||
"description": "The HTML Presentation Framework",
|
||||
"authors": [
|
||||
"Hakim El Hattab <hakim.elhattab@gmail.com>"
|
||||
],
|
||||
"dependencies": {
|
||||
"headjs": "~0.9.6"
|
||||
},
|
||||
"repository": {
|
||||
"type": "git",
|
||||
"url": "git://github.com/hakimel/reveal.js.git"
|
||||
},
|
||||
"ignore": [
|
||||
"**/.*",
|
||||
"node_modules",
|
||||
"bower_components",
|
||||
"test"
|
||||
]
|
||||
}
|
||||
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|
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|
After Width: | Height: | Size: 2.9 KiB |
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|
After Width: | Height: | Size: 2.5 KiB |
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|
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|
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|
After Width: | Height: | Size: 18 KiB |
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|
After Width: | Height: | Size: 11 KiB |
@@ -0,0 +1,202 @@
|
||||
/* Default Print Stylesheet Template
|
||||
by Rob Glazebrook of CSSnewbie.com
|
||||
Last Updated: June 4, 2008
|
||||
|
||||
Feel free (nay, compelled) to edit, append, and
|
||||
manipulate this file as you see fit. */
|
||||
|
||||
|
||||
@media print {
|
||||
|
||||
/* SECTION 1: Set default width, margin, float, and
|
||||
background. This prevents elements from extending
|
||||
beyond the edge of the printed page, and prevents
|
||||
unnecessary background images from printing */
|
||||
html {
|
||||
background: #fff;
|
||||
width: auto;
|
||||
height: auto;
|
||||
overflow: visible;
|
||||
}
|
||||
body {
|
||||
background: #fff;
|
||||
font-size: 20pt;
|
||||
width: auto;
|
||||
height: auto;
|
||||
border: 0;
|
||||
margin: 0 5%;
|
||||
padding: 0;
|
||||
overflow: visible;
|
||||
float: none !important;
|
||||
}
|
||||
|
||||
/* SECTION 2: Remove any elements not needed in print.
|
||||
This would include navigation, ads, sidebars, etc. */
|
||||
.nestedarrow,
|
||||
.controls,
|
||||
.fork-reveal,
|
||||
.share-reveal,
|
||||
.state-background,
|
||||
.reveal .progress,
|
||||
.reveal .backgrounds {
|
||||
display: none !important;
|
||||
}
|
||||
|
||||
/* SECTION 3: Set body font face, size, and color.
|
||||
Consider using a serif font for readability. */
|
||||
body, p, td, li, div {
|
||||
font-size: 20pt!important;
|
||||
font-family: Georgia, "Times New Roman", Times, serif !important;
|
||||
color: #000;
|
||||
}
|
||||
|
||||
/* SECTION 4: Set heading font face, sizes, and color.
|
||||
Differentiate your headings from your body text.
|
||||
Perhaps use a large sans-serif for distinction. */
|
||||
h1,h2,h3,h4,h5,h6 {
|
||||
color: #000!important;
|
||||
height: auto;
|
||||
line-height: normal;
|
||||
font-family: Georgia, "Times New Roman", Times, serif !important;
|
||||
text-shadow: 0 0 0 #000 !important;
|
||||
text-align: left;
|
||||
letter-spacing: normal;
|
||||
}
|
||||
/* Need to reduce the size of the fonts for printing */
|
||||
h1 { font-size: 28pt !important; }
|
||||
h2 { font-size: 24pt !important; }
|
||||
h3 { font-size: 22pt !important; }
|
||||
h4 { font-size: 22pt !important; font-variant: small-caps; }
|
||||
h5 { font-size: 21pt !important; }
|
||||
h6 { font-size: 20pt !important; font-style: italic; }
|
||||
|
||||
/* SECTION 5: Make hyperlinks more usable.
|
||||
Ensure links are underlined, and consider appending
|
||||
the URL to the end of the link for usability. */
|
||||
a:link,
|
||||
a:visited {
|
||||
color: #000 !important;
|
||||
font-weight: bold;
|
||||
text-decoration: underline;
|
||||
}
|
||||
/*
|
||||
.reveal a:link:after,
|
||||
.reveal a:visited:after {
|
||||
content: " (" attr(href) ") ";
|
||||
color: #222 !important;
|
||||
font-size: 90%;
|
||||
}
|
||||
*/
|
||||
|
||||
|
||||
/* SECTION 6: more reveal.js specific additions by @skypanther */
|
||||
ul, ol, div, p {
|
||||
visibility: visible;
|
||||
position: static;
|
||||
width: auto;
|
||||
height: auto;
|
||||
display: block;
|
||||
overflow: visible;
|
||||
margin: 0;
|
||||
text-align: left !important;
|
||||
}
|
||||
.reveal pre,
|
||||
.reveal table {
|
||||
margin-left: 0;
|
||||
margin-right: 0;
|
||||
}
|
||||
.reveal pre code {
|
||||
padding: 20px;
|
||||
border: 1px solid #ddd;
|
||||
}
|
||||
.reveal blockquote {
|
||||
margin: 20px 0;
|
||||
}
|
||||
.reveal .slides {
|
||||
position: static !important;
|
||||
width: auto !important;
|
||||
height: auto !important;
|
||||
|
||||
left: 0 !important;
|
||||
top: 0 !important;
|
||||
margin-left: 0 !important;
|
||||
margin-top: 0 !important;
|
||||
padding: 0 !important;
|
||||
zoom: 1 !important;
|
||||
|
||||
overflow: visible !important;
|
||||
display: block !important;
|
||||
|
||||
text-align: left !important;
|
||||
-webkit-perspective: none;
|
||||
-moz-perspective: none;
|
||||
-ms-perspective: none;
|
||||
perspective: none;
|
||||
|
||||
-webkit-perspective-origin: 50% 50%;
|
||||
-moz-perspective-origin: 50% 50%;
|
||||
-ms-perspective-origin: 50% 50%;
|
||||
perspective-origin: 50% 50%;
|
||||
}
|
||||
.reveal .slides section {
|
||||
visibility: visible !important;
|
||||
position: static !important;
|
||||
width: 100% !important;
|
||||
height: auto !important;
|
||||
display: block !important;
|
||||
overflow: visible !important;
|
||||
|
||||
left: 0 !important;
|
||||
top: 0 !important;
|
||||
margin-left: 0 !important;
|
||||
margin-top: 0 !important;
|
||||
padding: 60px 20px !important;
|
||||
z-index: auto !important;
|
||||
|
||||
opacity: 1 !important;
|
||||
|
||||
page-break-after: always !important;
|
||||
|
||||
-webkit-transform-style: flat !important;
|
||||
-moz-transform-style: flat !important;
|
||||
-ms-transform-style: flat !important;
|
||||
transform-style: flat !important;
|
||||
|
||||
-webkit-transform: none !important;
|
||||
-moz-transform: none !important;
|
||||
-ms-transform: none !important;
|
||||
transform: none !important;
|
||||
|
||||
-webkit-transition: none !important;
|
||||
-moz-transition: none !important;
|
||||
-ms-transition: none !important;
|
||||
transition: none !important;
|
||||
}
|
||||
.reveal .slides section.stack {
|
||||
padding: 0 !important;
|
||||
}
|
||||
.reveal section:last-of-type {
|
||||
page-break-after: avoid !important;
|
||||
}
|
||||
.reveal section .fragment {
|
||||
opacity: 1 !important;
|
||||
visibility: visible !important;
|
||||
|
||||
-webkit-transform: none !important;
|
||||
-moz-transform: none !important;
|
||||
-ms-transform: none !important;
|
||||
transform: none !important;
|
||||
}
|
||||
.reveal section img {
|
||||
display: block;
|
||||
margin: 15px 0px;
|
||||
background: rgba(255,255,255,1);
|
||||
border: 1px solid #666;
|
||||
box-shadow: none;
|
||||
}
|
||||
|
||||
.reveal section small {
|
||||
font-size: 0.8em;
|
||||
}
|
||||
|
||||
}
|
||||
@@ -0,0 +1,157 @@
|
||||
/* Default Print Stylesheet Template
|
||||
by Rob Glazebrook of CSSnewbie.com
|
||||
Last Updated: June 4, 2008
|
||||
|
||||
Feel free (nay, compelled) to edit, append, and
|
||||
manipulate this file as you see fit. */
|
||||
|
||||
|
||||
/* SECTION 1: Set default width, margin, float, and
|
||||
background. This prevents elements from extending
|
||||
beyond the edge of the printed page, and prevents
|
||||
unnecessary background images from printing */
|
||||
|
||||
* {
|
||||
-webkit-print-color-adjust: exact;
|
||||
}
|
||||
|
||||
body {
|
||||
margin: 0 auto !important;
|
||||
border: 0;
|
||||
padding: 0;
|
||||
float: none !important;
|
||||
overflow: visible;
|
||||
}
|
||||
|
||||
html {
|
||||
width: 100%;
|
||||
height: 100%;
|
||||
overflow: visible;
|
||||
}
|
||||
|
||||
/* SECTION 2: Remove any elements not needed in print.
|
||||
This would include navigation, ads, sidebars, etc. */
|
||||
.nestedarrow,
|
||||
.reveal .controls,
|
||||
.reveal .progress,
|
||||
.reveal .slide-number,
|
||||
.reveal .playback,
|
||||
.reveal.overview,
|
||||
.fork-reveal,
|
||||
.share-reveal,
|
||||
.state-background {
|
||||
display: none !important;
|
||||
}
|
||||
|
||||
/* SECTION 3: Set body font face, size, and color.
|
||||
Consider using a serif font for readability. */
|
||||
body, p, td, li, div {
|
||||
|
||||
}
|
||||
|
||||
/* SECTION 4: Set heading font face, sizes, and color.
|
||||
Differentiate your headings from your body text.
|
||||
Perhaps use a large sans-serif for distinction. */
|
||||
h1,h2,h3,h4,h5,h6 {
|
||||
text-shadow: 0 0 0 #000 !important;
|
||||
}
|
||||
|
||||
.reveal pre code {
|
||||
overflow: hidden !important;
|
||||
font-family: Courier, 'Courier New', monospace !important;
|
||||
}
|
||||
|
||||
|
||||
/* SECTION 5: more reveal.js specific additions by @skypanther */
|
||||
ul, ol, div, p {
|
||||
visibility: visible;
|
||||
position: static;
|
||||
width: auto;
|
||||
height: auto;
|
||||
display: block;
|
||||
overflow: visible;
|
||||
margin: auto;
|
||||
}
|
||||
.reveal {
|
||||
width: auto !important;
|
||||
height: auto !important;
|
||||
overflow: hidden !important;
|
||||
}
|
||||
.reveal .slides {
|
||||
position: static;
|
||||
width: 100%;
|
||||
height: auto;
|
||||
|
||||
left: auto;
|
||||
top: auto;
|
||||
margin: 0 !important;
|
||||
padding: 0 !important;
|
||||
|
||||
overflow: visible;
|
||||
display: block;
|
||||
|
||||
-webkit-perspective: none;
|
||||
-moz-perspective: none;
|
||||
-ms-perspective: none;
|
||||
perspective: none;
|
||||
|
||||
-webkit-perspective-origin: 50% 50%; /* there isn't a none/auto value but 50-50 is the default */
|
||||
-moz-perspective-origin: 50% 50%;
|
||||
-ms-perspective-origin: 50% 50%;
|
||||
perspective-origin: 50% 50%;
|
||||
}
|
||||
.reveal .slides section {
|
||||
page-break-after: always !important;
|
||||
|
||||
visibility: visible !important;
|
||||
position: relative !important;
|
||||
display: block !important;
|
||||
position: relative !important;
|
||||
|
||||
margin: 0 !important;
|
||||
padding: 0 !important;
|
||||
box-sizing: border-box !important;
|
||||
min-height: 1px;
|
||||
|
||||
opacity: 1 !important;
|
||||
|
||||
-webkit-transform-style: flat !important;
|
||||
-moz-transform-style: flat !important;
|
||||
-ms-transform-style: flat !important;
|
||||
transform-style: flat !important;
|
||||
|
||||
-webkit-transform: none !important;
|
||||
-moz-transform: none !important;
|
||||
-ms-transform: none !important;
|
||||
transform: none !important;
|
||||
}
|
||||
.reveal section.stack {
|
||||
margin: 0 !important;
|
||||
padding: 0 !important;
|
||||
page-break-after: avoid !important;
|
||||
height: auto !important;
|
||||
min-height: auto !important;
|
||||
}
|
||||
.reveal img {
|
||||
box-shadow: none;
|
||||
}
|
||||
.reveal .roll {
|
||||
overflow: visible;
|
||||
line-height: 1em;
|
||||
}
|
||||
|
||||
/* Slide backgrounds are placed inside of their slide when exporting to PDF */
|
||||
.reveal section .slide-background {
|
||||
display: block !important;
|
||||
position: absolute;
|
||||
top: 0;
|
||||
left: 0;
|
||||
width: 100%;
|
||||
z-index: -1;
|
||||
}
|
||||
/* All elements should be above the slide-background */
|
||||
.reveal section>* {
|
||||
position: relative;
|
||||
z-index: 1;
|
||||
}
|
||||
|
||||
File diff suppressed because it is too large
Load Diff
File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,23 @@
|
||||
## Dependencies
|
||||
|
||||
Themes are written using Sass to keep things modular and reduce the need for repeated selectors across files. Make sure that you have the reveal.js development environment including the Grunt dependencies installed before proceding: https://github.com/hakimel/reveal.js#full-setup
|
||||
|
||||
## Creating a Theme
|
||||
|
||||
To create your own theme, start by duplicating any ```.scss``` file in [/css/theme/source](https://github.com/hakimel/reveal.js/blob/master/css/theme/source) and adding it to the compilation list in the [Gruntfile](https://github.com/hakimel/reveal.js/blob/master/Gruntfile.js).
|
||||
|
||||
Each theme file does four things in the following order:
|
||||
|
||||
1. **Include [/css/theme/template/mixins.scss](https://github.com/hakimel/reveal.js/blob/master/css/theme/template/mixins.scss)**
|
||||
Shared utility functions.
|
||||
|
||||
2. **Include [/css/theme/template/settings.scss](https://github.com/hakimel/reveal.js/blob/master/css/theme/template/settings.scss)**
|
||||
Declares a set of custom variables that the template file (step 4) expects. Can be overridden in step 3.
|
||||
|
||||
3. **Override**
|
||||
This is where you override the default theme. Either by specifying variables (see [settings.scss](https://github.com/hakimel/reveal.js/blob/master/css/theme/template/settings.scss) for reference) or by adding any selectors and styles you please.
|
||||
|
||||
4. **Include [/css/theme/template/theme.scss](https://github.com/hakimel/reveal.js/blob/master/css/theme/template/theme.scss)**
|
||||
The template theme file which will generate final CSS output based on the currently defined variables.
|
||||
|
||||
When you are done, run `grunt css-themes` to compile the Sass file to CSS and you are ready to use your new theme.
|
||||
@@ -0,0 +1,154 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* Beige theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url("../../lib/font/league_gothic-webfont.eot");
|
||||
src: url("../../lib/font/league_gothic-webfont.eot?#iefix") format("embedded-opentype"), url("../../lib/font/league_gothic-webfont.woff") format("woff"), url("../../lib/font/league_gothic-webfont.ttf") format("truetype"), url("../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular") format("svg");
|
||||
font-weight: normal;
|
||||
font-style: normal; }
|
||||
|
||||
/* changed (by hpl) from #333; */
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #f7f2d3;
|
||||
background: -moz-radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background: -webkit-gradient(radial, center center, 0px, center center, 100%, color-stop(0%, white), color-stop(100%, #f7f2d3));
|
||||
background: -webkit-radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background: -o-radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background: -ms-radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background: radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background-color: #f7f3de; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Lato", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #333333; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: rgba(79, 64, 28, 0.99);
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #222222;
|
||||
font-family: "Helvetica", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0 1px 0 #cccccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbbbbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaaaaa, 0 6px 1px rgba(0, 0, 0, 0.1), 0 0 5px rgba(0, 0, 0, 0.1), 0 1px 3px rgba(0, 0, 0, 0.3), 0 3px 5px rgba(0, 0, 0, 0.2), 0 5px 10px rgba(0, 0, 0, 0.25), 0 20px 20px rgba(0, 0, 0, 0.15); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #8b743d;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #c0a86e;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #564826; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #333333;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #8b743d;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #8b743d; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #8b743d; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #8b743d; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #8b743d; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #c0a86e; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #c0a86e; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #c0a86e; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #c0a86e; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #8b743d;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #8b743d; }
|
||||
@@ -0,0 +1,155 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* Beige theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url("../../lib/font/league_gothic-webfont.eot");
|
||||
src: url("../../lib/font/league_gothic-webfont.eot?#iefix") format("embedded-opentype"), url("../../lib/font/league_gothic-webfont.woff") format("woff"), url("../../lib/font/league_gothic-webfont.ttf") format("truetype"), url("../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular") format("svg");
|
||||
font-weight: normal;
|
||||
font-style: normal; }
|
||||
|
||||
/* added/changed by hpl */
|
||||
/* changed (by hpl) from #333; */
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #f7f2d3;
|
||||
background: -moz-radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background: -webkit-gradient(radial, center center, 0px, center center, 100%, color-stop(0%, white), color-stop(100%, #f7f2d3));
|
||||
background: -webkit-radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background: -o-radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background: -ms-radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background: radial-gradient(center, circle cover, white 0%, #f7f2d3 100%);
|
||||
background-color: #f7f3de; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Lato", sans-serif;
|
||||
font-size: 25px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #333333; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: rgba(79, 64, 28, 0.99);
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #222222;
|
||||
font-family: "Helvetica", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0 1px 0 #cccccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbbbbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaaaaa, 0 6px 1px rgba(0, 0, 0, 0.1), 0 0 5px rgba(0, 0, 0, 0.1), 0 1px 3px rgba(0, 0, 0, 0.3), 0 3px 5px rgba(0, 0, 0, 0.2), 0 5px 10px rgba(0, 0, 0, 0.25), 0 20px 20px rgba(0, 0, 0, 0.15); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #8b743d;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #c0a86e;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #564826; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #333333;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #8b743d;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #8b743d; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #8b743d; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #8b743d; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #8b743d; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #c0a86e; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #c0a86e; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #c0a86e; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #c0a86e; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #8b743d;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #8b743d; }
|
||||
@@ -0,0 +1,273 @@
|
||||
@import url(../../lib/font/source-sans-pro/source-sans-pro.css);
|
||||
/**
|
||||
* Black theme for reveal.js. This is the opposite of the 'white' theme.
|
||||
*
|
||||
* Copyright (C) 2015 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
section.has-light-background, section.has-light-background h1, section.has-light-background h2, section.has-light-background h3, section.has-light-background h4, section.has-light-background h5, section.has-light-background h6 {
|
||||
color: #222; }
|
||||
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #222;
|
||||
background-color: #222; }
|
||||
|
||||
.reveal {
|
||||
font-family: 'Source Sans Pro', Helvetica, sans-serif;
|
||||
font-size: 30px; /* changed by hpl from 38px */
|
||||
font-weight: normal;
|
||||
color: #fff; }
|
||||
|
||||
::selection {
|
||||
color: #fff;
|
||||
background: #bee4fd;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal .slides > section, .reveal .slides > section > section {
|
||||
/* removed by hpl: line-height: 1.3; */
|
||||
font-weight: inherit; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1, .reveal h2, .reveal h3, .reveal h4, .reveal h5, .reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #fff;
|
||||
font-family: 'Source Sans Pro', Helvetica, sans-serif;
|
||||
font-weight: 600;
|
||||
line-height: 1.1em; /* changed by hpl from 1.2; */
|
||||
letter-spacing: normal;
|
||||
/* text-transform: uppercase; removed by hpl */
|
||||
text-shadow: none;
|
||||
word-wrap: break-word; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
}
|
||||
|
||||
/* Removed by hpl
|
||||
.reveal h1 {
|
||||
font-size: 2.5em; }
|
||||
|
||||
.reveal h2 {
|
||||
font-size: 1.6em; }
|
||||
|
||||
.reveal h3 {
|
||||
font-size: 1.3em; }
|
||||
|
||||
.reveal h4 {
|
||||
font-size: 1em; }
|
||||
*/
|
||||
|
||||
.reveal h1 {
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* OTHER
|
||||
*********************************************/
|
||||
.reveal p {
|
||||
margin: 20px 0;
|
||||
line-height: 1.3; }
|
||||
|
||||
/* Ensure certain elements are never larger than the slide itself */
|
||||
.reveal img, .reveal video, .reveal iframe {
|
||||
max-width: 95%;
|
||||
max-height: 95%; }
|
||||
|
||||
.reveal strong, .reveal b {
|
||||
font-weight: bold; }
|
||||
|
||||
.reveal em {
|
||||
font-style: italic; }
|
||||
|
||||
.reveal ol, .reveal dl, .reveal ul {
|
||||
display: inline-block;
|
||||
text-align: left;
|
||||
margin: 0 0 0 1em; }
|
||||
|
||||
.reveal ol {
|
||||
list-style-type: decimal; }
|
||||
|
||||
.reveal ul {
|
||||
list-style-type: disc; }
|
||||
|
||||
.reveal ul ul {
|
||||
list-style-type: square; }
|
||||
|
||||
.reveal ul ul ul {
|
||||
list-style-type: circle; }
|
||||
|
||||
.reveal ul ul, .reveal ul ol, .reveal ol ol, .reveal ol ul {
|
||||
display: block;
|
||||
margin-left: 40px; }
|
||||
|
||||
.reveal dt {
|
||||
font-weight: bold; }
|
||||
|
||||
.reveal dd {
|
||||
margin-left: 40px; }
|
||||
|
||||
.reveal q, .reveal blockquote {
|
||||
quotes: none; }
|
||||
|
||||
.reveal blockquote {
|
||||
display: block;
|
||||
position: relative;
|
||||
width: 70%;
|
||||
margin: 20px auto;
|
||||
padding: 5px;
|
||||
font-style: italic;
|
||||
background: rgba(255, 255, 255, 0.05);
|
||||
box-shadow: 0px 0px 2px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal blockquote p:first-child, .reveal blockquote p:last-child {
|
||||
display: inline-block; }
|
||||
|
||||
.reveal q {
|
||||
font-style: italic; }
|
||||
|
||||
.reveal pre {
|
||||
display: block;
|
||||
position: relative;
|
||||
width: 90%;
|
||||
margin: 20px auto;
|
||||
text-align: left;
|
||||
font-size: 0.55em;
|
||||
font-family: monospace;
|
||||
line-height: 1.2em;
|
||||
word-wrap: break-word;
|
||||
box-shadow: 0px 0px 6px rgba(0, 0, 0, 0.3); }
|
||||
|
||||
.reveal code {
|
||||
font-family: monospace; }
|
||||
|
||||
.reveal pre code {
|
||||
display: block;
|
||||
padding: 5px;
|
||||
overflow: auto;
|
||||
max-height: 400px;
|
||||
word-wrap: normal;
|
||||
background: #3F3F3F;
|
||||
color: #DCDCDC; }
|
||||
|
||||
.reveal table {
|
||||
margin: auto;
|
||||
border-collapse: collapse;
|
||||
border-spacing: 0; }
|
||||
|
||||
.reveal table th {
|
||||
font-weight: bold; }
|
||||
|
||||
.reveal table th, .reveal table td {
|
||||
/*text-align: left; */ /* hpl modification */
|
||||
padding: 0.2em 0.5em 0.2em 0.5em;
|
||||
border-bottom: 1px solid; }
|
||||
|
||||
.reveal table th[align="center"], .reveal table td[align="center"] {
|
||||
text-align: center; }
|
||||
|
||||
.reveal table th[align="right"], .reveal table td[align="right"] {
|
||||
text-align: right; }
|
||||
|
||||
.reveal table tr:last-child td {
|
||||
border-bottom: none; }
|
||||
|
||||
.reveal sup {
|
||||
vertical-align: super; }
|
||||
|
||||
.reveal sub {
|
||||
vertical-align: sub; }
|
||||
|
||||
.reveal small {
|
||||
display: inline-block;
|
||||
font-size: 0.6em;
|
||||
line-height: 1.2em;
|
||||
vertical-align: top; }
|
||||
|
||||
.reveal small * {
|
||||
vertical-align: top; }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a {
|
||||
color: #42affa;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color 0.15s ease;
|
||||
-moz-transition: color 0.15s ease;
|
||||
transition: color 0.15s ease; }
|
||||
|
||||
.reveal a:hover {
|
||||
color: #8dcffc;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #068ee9; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #fff;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15); }
|
||||
|
||||
.reveal a img {
|
||||
-webkit-transition: all 0.15s linear;
|
||||
-moz-transition: all 0.15s linear;
|
||||
transition: all 0.15s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #42affa;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left, .reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #42affa; }
|
||||
|
||||
.reveal .controls div.navigate-right, .reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #42affa; }
|
||||
|
||||
.reveal .controls div.navigate-up, .reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #42affa; }
|
||||
|
||||
.reveal .controls div.navigate-down, .reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #42affa; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #8dcffc; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #8dcffc; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #8dcffc; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #8dcffc; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #42affa;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #42affa; }
|
||||
@@ -0,0 +1,180 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Ubuntu:300,700,300italic,700italic);
|
||||
/**
|
||||
* Blood theme for reveal.js
|
||||
* Author: Walther http://github.com/Walther
|
||||
*
|
||||
* Designed to be used with highlight.js theme
|
||||
* "monokai_sublime.css" available from
|
||||
* https://github.com/isagalaev/highlight.js/
|
||||
*
|
||||
* For other themes, change $codeBackground accordingly.
|
||||
*
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #222222;
|
||||
background: -moz-radial-gradient(center, circle cover, #626262 0%, #222222 100%);
|
||||
background: -webkit-gradient(radial, center center, 0px, center center, 100%, color-stop(0%, #626262), color-stop(100%, #222222));
|
||||
background: -webkit-radial-gradient(center, circle cover, #626262 0%, #222222 100%);
|
||||
background: -o-radial-gradient(center, circle cover, #626262 0%, #222222 100%);
|
||||
background: -ms-radial-gradient(center, circle cover, #626262 0%, #222222 100%);
|
||||
background: radial-gradient(center, circle cover, #626262 0%, #222222 100%);
|
||||
background-color: #2b2b2b; }
|
||||
|
||||
.reveal {
|
||||
font-family: Ubuntu, "sans-serif";
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #eeeeee; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: #aa2233;
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #eeeeee;
|
||||
font-family: Ubuntu, "sans-serif";
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: 2px 2px 2px #222222; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0 1px 0 #cccccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbbbbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaaaaa, 0 6px 1px rgba(0, 0, 0, 0.1), 0 0 5px rgba(0, 0, 0, 0.1), 0 1px 3px rgba(0, 0, 0, 0.3), 0 3px 5px rgba(0, 0, 0, 0.2), 0 5px 10px rgba(0, 0, 0, 0.25), 0 20px 20px rgba(0, 0, 0, 0.15); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #aa2233;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #dd5566;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #6a1520; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #eeeeee;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #aa2233;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #aa2233; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #aa2233; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #aa2233; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #aa2233; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #dd5566; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #dd5566; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #dd5566; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #dd5566; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #aa2233;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #aa2233; }
|
||||
|
||||
.reveal p {
|
||||
font-weight: 300;
|
||||
text-shadow: 1px 1px #222222; }
|
||||
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
font-weight: 700; }
|
||||
|
||||
.reveal a:not(.image),
|
||||
.reveal a:not(.image):hover {
|
||||
text-shadow: 2px 2px 2px #000; }
|
||||
|
||||
.reveal small a:not(.image),
|
||||
.reveal small a:not(.image):hover {
|
||||
text-shadow: 1px 1px 1px #000; }
|
||||
|
||||
.reveal p code {
|
||||
background-color: #23241f;
|
||||
display: inline-block;
|
||||
border-radius: 7px; }
|
||||
|
||||
.reveal small code {
|
||||
vertical-align: baseline; }
|
||||
@@ -0,0 +1,144 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* A simple theme for reveal.js presentations, similar
|
||||
* to the default theme. The accent color is darkblue.
|
||||
*
|
||||
* This theme is Copyright (C) 2012 Owen Versteeg, https://github.com/StereotypicalApps. It is MIT licensed.
|
||||
* reveal.js is Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
|
||||
* Center for Biomedical Computing theme made by Hans Petter Langtangen.
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: white;
|
||||
background-color: white; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Lato", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #404040; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: rgba(0, 0, 0, 0.99);
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #8a0808;
|
||||
font-family: "Helvetica", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #8a0808;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #ea0e0e;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #420404; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #404040;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #8a0808;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #8a0808; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #8a0808; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #8a0808; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #8a0808; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #ea0e0e; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #ea0e0e; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #ea0e0e; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #ea0e0e; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #8a0808;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #8a0808; }
|
||||
@@ -0,0 +1,153 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* Default theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url("../../lib/font/league_gothic-webfont.eot");
|
||||
src: url("../../lib/font/league_gothic-webfont.eot?#iefix") format("embedded-opentype"), url("../../lib/font/league_gothic-webfont.woff") format("woff"), url("../../lib/font/league_gothic-webfont.ttf") format("truetype"), url("../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular") format("svg");
|
||||
font-weight: normal;
|
||||
font-style: normal; }
|
||||
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #1c1e20;
|
||||
background: -moz-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: -webkit-gradient(radial, center center, 0px, center center, 100%, color-stop(0%, #555a5f), color-stop(100%, #1c1e20));
|
||||
background: -webkit-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: -o-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: -ms-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background-color: #2b2b2b; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Lato", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #eeeeee; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: #ff5e99;
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #eeeeee;
|
||||
font-family: "Helvetica", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0 1px 0 #cccccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbbbbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaaaaa, 0 6px 1px rgba(0, 0, 0, 0.1), 0 0 5px rgba(0, 0, 0, 0.1), 0 1px 3px rgba(0, 0, 0, 0.3), 0 3px 5px rgba(0, 0, 0, 0.2), 0 5px 10px rgba(0, 0, 0, 0.25), 0 20px 20px rgba(0, 0, 0, 0.15); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #13daec;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #71e9f4;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #0d99a5; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #eeeeee;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #13daec;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #13daec; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #13daec; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #13daec; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #13daec; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #71e9f4; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #71e9f4; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #71e9f4; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #71e9f4; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #13daec;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #13daec; }
|
||||
@@ -0,0 +1,153 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* Default theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url("../../lib/font/league_gothic-webfont.eot");
|
||||
src: url("../../lib/font/league_gothic-webfont.eot?#iefix") format("embedded-opentype"), url("../../lib/font/league_gothic-webfont.woff") format("woff"), url("../../lib/font/league_gothic-webfont.ttf") format("truetype"), url("../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular") format("svg");
|
||||
font-weight: normal;
|
||||
font-style: normal; }
|
||||
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #1c1e20;
|
||||
background: -moz-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: -webkit-gradient(radial, center center, 0px, center center, 100%, color-stop(0%, #555a5f), color-stop(100%, #1c1e20));
|
||||
background: -webkit-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: -o-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: -ms-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background-color: #2b2b2b; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Lato", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #eeeeee; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: #ff5e99;
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #eeeeee;
|
||||
font-family: "Helvetica", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0 1px 0 #cccccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbbbbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaaaaa, 0 6px 1px rgba(0, 0, 0, 0.1), 0 0 5px rgba(0, 0, 0, 0.1), 0 1px 3px rgba(0, 0, 0, 0.3), 0 3px 5px rgba(0, 0, 0, 0.2), 0 5px 10px rgba(0, 0, 0, 0.25), 0 20px 20px rgba(0, 0, 0, 0.15); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #13daec;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #71e9f4;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #0d99a5; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #eeeeee;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #13daec;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #13daec; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #13daec; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #13daec; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #13daec; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #71e9f4; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #71e9f4; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #71e9f4; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #71e9f4; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #13daec;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #13daec; }
|
||||
@@ -0,0 +1,279 @@
|
||||
@import url(../../lib/font/league-gothic/league-gothic.css);
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* League theme for reveal.js.
|
||||
*
|
||||
* This was the default theme pre-3.0.0.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #1c1e20;
|
||||
background: -moz-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: -webkit-gradient(radial, center center, 0px, center center, 100%, color-stop(0%, #555a5f), color-stop(100%, #1c1e20));
|
||||
background: -webkit-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: -o-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: -ms-radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background: radial-gradient(center, circle cover, #555a5f 0%, #1c1e20 100%);
|
||||
background-color: #2b2b2b; }
|
||||
|
||||
.reveal {
|
||||
font-family: 'Lato', sans-serif;
|
||||
font-size: 30px; /* changed by hpl from 36px */
|
||||
font-weight: normal;
|
||||
color: #eee; }
|
||||
|
||||
::selection {
|
||||
color: #fff;
|
||||
background: #FF5E99;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal .slides > section, .reveal .slides > section > section {
|
||||
/* removed by hpl: line-height: 1.3; */
|
||||
font-weight: inherit; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1, .reveal h2, .reveal h3, .reveal h4, .reveal h5, .reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #eee;
|
||||
font-family: 'Helvetica', Impact, sans-serif;
|
||||
font-weight: normal;
|
||||
line-height: 1.1em; /* changed by hpl from 1.2; */
|
||||
letter-spacing: normal;
|
||||
/* text-transform: uppercase; removed by hpl */
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2);
|
||||
word-wrap: break-word; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
}
|
||||
|
||||
/* removed by hpl:
|
||||
.reveal h1 {
|
||||
font-size: 3.77em; }
|
||||
|
||||
.reveal h2 {
|
||||
font-size: 2.11em; }
|
||||
|
||||
.reveal h3 {
|
||||
font-size: 1.55em; }
|
||||
|
||||
.reveal h4 {
|
||||
font-size: 1em; }
|
||||
*/
|
||||
|
||||
.reveal h1 {
|
||||
text-shadow: 0 1px 0 #ccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaa, 0 6px 1px rgba(0, 0, 0, 0.1), 0 0 5px rgba(0, 0, 0, 0.1), 0 1px 3px rgba(0, 0, 0, 0.3), 0 3px 5px rgba(0, 0, 0, 0.2), 0 5px 10px rgba(0, 0, 0, 0.25), 0 20px 20px rgba(0, 0, 0, 0.15); }
|
||||
|
||||
/*********************************************
|
||||
* OTHER
|
||||
*********************************************/
|
||||
.reveal p {
|
||||
margin: 20px 0;
|
||||
line-height: 1.3; }
|
||||
|
||||
/* Ensure certain elements are never larger than the slide itself */
|
||||
.reveal img, .reveal video, .reveal iframe {
|
||||
max-width: 95%;
|
||||
max-height: 95%; }
|
||||
|
||||
.reveal strong, .reveal b {
|
||||
font-weight: bold; }
|
||||
|
||||
.reveal em {
|
||||
font-style: italic; }
|
||||
|
||||
.reveal ol, .reveal dl, .reveal ul {
|
||||
display: inline-block;
|
||||
text-align: left;
|
||||
margin: 0 0 0 1em; }
|
||||
|
||||
.reveal ol {
|
||||
list-style-type: decimal; }
|
||||
|
||||
.reveal ul {
|
||||
list-style-type: disc; }
|
||||
|
||||
.reveal ul ul {
|
||||
list-style-type: square; }
|
||||
|
||||
.reveal ul ul ul {
|
||||
list-style-type: circle; }
|
||||
|
||||
.reveal ul ul, .reveal ul ol, .reveal ol ol, .reveal ol ul {
|
||||
display: block;
|
||||
margin-left: 40px; }
|
||||
|
||||
.reveal dt {
|
||||
font-weight: bold; }
|
||||
|
||||
.reveal dd {
|
||||
margin-left: 40px; }
|
||||
|
||||
.reveal q, .reveal blockquote {
|
||||
quotes: none; }
|
||||
|
||||
.reveal blockquote {
|
||||
display: block;
|
||||
position: relative;
|
||||
width: 70%;
|
||||
margin: 20px auto;
|
||||
padding: 5px;
|
||||
font-style: italic;
|
||||
background: rgba(255, 255, 255, 0.05);
|
||||
box-shadow: 0px 0px 2px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal blockquote p:first-child, .reveal blockquote p:last-child {
|
||||
display: inline-block; }
|
||||
|
||||
.reveal q {
|
||||
font-style: italic; }
|
||||
|
||||
.reveal pre {
|
||||
display: block;
|
||||
position: relative;
|
||||
width: 90%;
|
||||
margin: 20px auto;
|
||||
text-align: left;
|
||||
font-size: 0.55em;
|
||||
font-family: monospace;
|
||||
line-height: 1.2em;
|
||||
word-wrap: break-word;
|
||||
box-shadow: 0px 0px 6px rgba(0, 0, 0, 0.3); }
|
||||
|
||||
.reveal code {
|
||||
font-family: monospace; }
|
||||
|
||||
.reveal pre code {
|
||||
display: block;
|
||||
padding: 5px;
|
||||
overflow: auto;
|
||||
max-height: 400px;
|
||||
word-wrap: normal;
|
||||
background: #3F3F3F;
|
||||
color: #DCDCDC; }
|
||||
|
||||
.reveal table {
|
||||
margin: auto;
|
||||
border-collapse: collapse;
|
||||
border-spacing: 0; }
|
||||
|
||||
.reveal table th {
|
||||
font-weight: bold; }
|
||||
|
||||
.reveal table th, .reveal table td {
|
||||
/* text-align: left; */ /* hpl modification */
|
||||
padding: 0.2em 0.5em 0.2em 0.5em;
|
||||
border-bottom: 1px solid; }
|
||||
|
||||
.reveal table th[align="center"], .reveal table td[align="center"] {
|
||||
text-align: center; }
|
||||
|
||||
.reveal table th[align="right"], .reveal table td[align="right"] {
|
||||
text-align: right; }
|
||||
|
||||
.reveal table tr:last-child td {
|
||||
border-bottom: none; }
|
||||
|
||||
.reveal sup {
|
||||
vertical-align: super; }
|
||||
|
||||
.reveal sub {
|
||||
vertical-align: sub; }
|
||||
|
||||
.reveal small {
|
||||
display: inline-block;
|
||||
font-size: 0.6em;
|
||||
line-height: 1.2em;
|
||||
vertical-align: top; }
|
||||
|
||||
.reveal small * {
|
||||
vertical-align: top; }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a {
|
||||
color: #13DAEC;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color 0.15s ease;
|
||||
-moz-transition: color 0.15s ease;
|
||||
transition: color 0.15s ease; }
|
||||
|
||||
.reveal a:hover {
|
||||
color: #71ebf4;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #0d9ba5; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #eee;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15); }
|
||||
|
||||
.reveal a img {
|
||||
-webkit-transition: all 0.15s linear;
|
||||
-moz-transition: all 0.15s linear;
|
||||
transition: all 0.15s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #13DAEC;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left, .reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #13DAEC; }
|
||||
|
||||
.reveal .controls div.navigate-right, .reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #13DAEC; }
|
||||
|
||||
.reveal .controls div.navigate-up, .reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #13DAEC; }
|
||||
|
||||
.reveal .controls div.navigate-down, .reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #13DAEC; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #71ebf4; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #71ebf4; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #71ebf4; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #71ebf4; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #13DAEC;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #13DAEC; }
|
||||
@@ -0,0 +1,153 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* Solarized Dark theme for reveal.js.
|
||||
* Author: Achim Staebler
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url("../../lib/font/league_gothic-webfont.eot");
|
||||
src: url("../../lib/font/league_gothic-webfont.eot?#iefix") format("embedded-opentype"), url("../../lib/font/league_gothic-webfont.woff") format("woff"), url("../../lib/font/league_gothic-webfont.ttf") format("truetype"), url("../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular") format("svg");
|
||||
font-weight: normal;
|
||||
font-style: normal; }
|
||||
|
||||
/**
|
||||
* Solarized colors by Ethan Schoonover
|
||||
*/
|
||||
html * {
|
||||
color-profile: sRGB;
|
||||
rendering-intent: auto; }
|
||||
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #002b36;
|
||||
background-color: #002b36; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Lato", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #93a1a1; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: #d33682;
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #eee8d5;
|
||||
font-family: "Helvetica", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #268bd2;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #78b9e6;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #1a6091; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #93a1a1;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #268bd2;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #268bd2; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #268bd2; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #268bd2; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #268bd2; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #78b9e6; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #78b9e6; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #78b9e6; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #78b9e6; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #268bd2;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #268bd2; }
|
||||
@@ -0,0 +1,141 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Montserrat:700);
|
||||
@import url(https://fonts.googleapis.com/css?family=Open+Sans:400,700,400italic,700italic);
|
||||
/**
|
||||
* Black theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #111111;
|
||||
background-color: #111111; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Open Sans", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #eeeeee; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: #e7ad52;
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #eeeeee;
|
||||
font-family: "Montserrat", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: -0.03em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #e7ad52;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #f3d7ac;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #d08a1d; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #eeeeee;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #e7ad52;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #e7ad52; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #e7ad52; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #e7ad52; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #e7ad52; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #f3d7ac; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #f3d7ac; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #f3d7ac; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #f3d7ac; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #e7ad52;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #e7ad52; }
|
||||
@@ -0,0 +1,143 @@
|
||||
/**
|
||||
* A simple theme for reveal.js presentations, similar
|
||||
* to the default theme. The accent color is brown.
|
||||
*
|
||||
* This theme is Copyright (C) 2012-2013 Owen Versteeg, http://owenversteeg.com - it is MIT licensed.
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
.reveal a:not(.image) {
|
||||
line-height: 1.3em; }
|
||||
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #f0f1eb;
|
||||
background-color: #f0f1eb; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Palatino Linotype", "Book Antiqua", Palatino, FreeSerif, serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: black; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: #26351c;
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #383d3d;
|
||||
font-family: "Palatino Linotype", "Book Antiqua", Palatino, FreeSerif, serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #51483d;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #8b7c69;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #25211c; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid black;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #51483d;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #51483d; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #51483d; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #51483d; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #51483d; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #8b7c69; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #8b7c69; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #8b7c69; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #8b7c69; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #51483d;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #51483d; }
|
||||
@@ -0,0 +1,144 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=News+Cycle:400,700);
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* A simple theme for reveal.js presentations, similar
|
||||
* to the default theme. The accent color is darkblue.
|
||||
*
|
||||
* This theme is Copyright (C) 2012 Owen Versteeg, https://github.com/StereotypicalApps. It is MIT licensed.
|
||||
* reveal.js is Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
/* changed (by hpl) from 'News Cycle', Impact, sans-serif; */
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: white;
|
||||
background-color: white; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Lato", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: black; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: rgba(0, 0, 0, 0.99);
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: black;
|
||||
font-family: "Helvetica", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: darkblue;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #0000f1;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #00003f; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid black;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: darkblue;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: darkblue; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: darkblue; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: darkblue; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: darkblue; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #0000f1; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #0000f1; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #0000f1; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #0000f1; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: darkblue;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: darkblue; }
|
||||
@@ -0,0 +1,144 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* A simple theme for reveal.js presentations, similar
|
||||
* to the default theme. The accent color is darkblue.
|
||||
*
|
||||
* This theme is Copyright (C) 2012 Owen Versteeg, https://github.com/StereotypicalApps. It is MIT licensed.
|
||||
* reveal.js is Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
|
||||
* Simula theme made by Hans Petter Langtangen.
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: white;
|
||||
background-color: white; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Lato", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #404040; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: rgba(0, 0, 0, 0.99);
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #ff8800;
|
||||
font-family: "Helvetica", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #ff8800;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #ffb866;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #b35f00; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #404040;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #ff8800;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #ff8800; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #ff8800; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #ff8800; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #ff8800; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #ffb866; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #ffb866; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #ffb866; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #ffb866; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #ff8800;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #ff8800; }
|
||||
@@ -0,0 +1,150 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Quicksand:400,700,400italic,700italic);
|
||||
@import url(https://fonts.googleapis.com/css?family=Open+Sans:400italic,700italic,400,700);
|
||||
/**
|
||||
* Sky theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
.reveal a:not(.image) {
|
||||
line-height: 1.3em; }
|
||||
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #add9e4;
|
||||
background: -moz-radial-gradient(center, circle cover, #f7fbfc 0%, #add9e4 100%);
|
||||
background: -webkit-gradient(radial, center center, 0px, center center, 100%, color-stop(0%, #f7fbfc), color-stop(100%, #add9e4));
|
||||
background: -webkit-radial-gradient(center, circle cover, #f7fbfc 0%, #add9e4 100%);
|
||||
background: -o-radial-gradient(center, circle cover, #f7fbfc 0%, #add9e4 100%);
|
||||
background: -ms-radial-gradient(center, circle cover, #f7fbfc 0%, #add9e4 100%);
|
||||
background: radial-gradient(center, circle cover, #f7fbfc 0%, #add9e4 100%);
|
||||
background-color: #f7fbfc; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Open Sans", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #333333; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: #134674;
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #333333;
|
||||
font-family: "Quicksand", sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: -0.08em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #3b759e;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #74a7cb;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #264c66; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #333333;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #3b759e;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #3b759e; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #3b759e; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #3b759e; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #3b759e; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #74a7cb; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #74a7cb; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #74a7cb; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #74a7cb; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #3b759e;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #3b759e; }
|
||||
@@ -0,0 +1,153 @@
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
/**
|
||||
* Solarized Light theme for reveal.js.
|
||||
* Author: Achim Staebler
|
||||
*/
|
||||
/* changed by hpl from 36px; */
|
||||
/* changed by hpl from 'League Gothic', Impact, sans-serif; */
|
||||
/* changed by hpl from uppercase; */
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url("../../lib/font/league_gothic-webfont.eot");
|
||||
src: url("../../lib/font/league_gothic-webfont.eot?#iefix") format("embedded-opentype"), url("../../lib/font/league_gothic-webfont.woff") format("woff"), url("../../lib/font/league_gothic-webfont.ttf") format("truetype"), url("../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular") format("svg");
|
||||
font-weight: normal;
|
||||
font-style: normal; }
|
||||
|
||||
/**
|
||||
* Solarized colors by Ethan Schoonover
|
||||
*/
|
||||
html * {
|
||||
color-profile: sRGB;
|
||||
rendering-intent: auto; }
|
||||
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #fdf6e3;
|
||||
background-color: #fdf6e3; }
|
||||
|
||||
.reveal {
|
||||
font-family: "Lato", sans-serif;
|
||||
font-size: 30px;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: #657b83; }
|
||||
|
||||
::selection {
|
||||
color: white;
|
||||
background: #d33682;
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #586e75;
|
||||
font-family: "Helvetica", Impact, sans-serif;
|
||||
line-height: 1.1em; /* changed (by hpl) from 0.9em */
|
||||
letter-spacing: 0.02em;
|
||||
text-transform: none;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
/* added by hpl */
|
||||
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a:not(.image) {
|
||||
color: #268bd2;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease; }
|
||||
|
||||
.reveal a:not(.image):hover {
|
||||
color: #78b9e6;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #1a6091; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #657b83;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #268bd2;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #268bd2; }
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #268bd2; }
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #268bd2; }
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #268bd2; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #78b9e6; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #78b9e6; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #78b9e6; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #78b9e6; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #268bd2;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #268bd2; }
|
||||
@@ -0,0 +1,50 @@
|
||||
/**
|
||||
* Beige theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url('../../lib/font/league_gothic-webfont.eot');
|
||||
src: url('../../lib/font/league_gothic-webfont.eot?#iefix') format('embedded-opentype'),
|
||||
url('../../lib/font/league_gothic-webfont.woff') format('woff'),
|
||||
url('../../lib/font/league_gothic-webfont.ttf') format('truetype'),
|
||||
url('../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular') format('svg');
|
||||
|
||||
font-weight: normal;
|
||||
font-style: normal;
|
||||
}
|
||||
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$mainColor: #333;
|
||||
$headingColor: #222; /* changed (by hpl) from #333; */
|
||||
$headingTextShadow: none;
|
||||
$backgroundColor: #f7f3de;
|
||||
$linkColor: #8b743d;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$selectionBackgroundColor: rgba(79, 64, 28, 0.99);
|
||||
$heading1TextShadow: 0 1px 0 #ccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaa, 0 6px 1px rgba(0,0,0,.1), 0 0 5px rgba(0,0,0,.1), 0 1px 3px rgba(0,0,0,.3), 0 3px 5px rgba(0,0,0,.2), 0 5px 10px rgba(0,0,0,.25), 0 20px 20px rgba(0,0,0,.15);
|
||||
|
||||
// Background generator
|
||||
@mixin bodyBackground() {
|
||||
@include radial-gradient( rgba(247,242,211,1), rgba(255,255,255,1) );
|
||||
}
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,51 @@
|
||||
/**
|
||||
* Beige theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url('../../lib/font/league_gothic-webfont.eot');
|
||||
src: url('../../lib/font/league_gothic-webfont.eot?#iefix') format('embedded-opentype'),
|
||||
url('../../lib/font/league_gothic-webfont.woff') format('woff'),
|
||||
url('../../lib/font/league_gothic-webfont.ttf') format('truetype'),
|
||||
url('../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular') format('svg');
|
||||
|
||||
font-weight: normal;
|
||||
font-style: normal;
|
||||
}
|
||||
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$mainColor: #333;
|
||||
$mainFontSize: 25px; /* added/changed by hpl */
|
||||
$headingColor: #222; /* changed (by hpl) from #333; */
|
||||
$headingTextShadow: none;
|
||||
$backgroundColor: #f7f3de;
|
||||
$linkColor: #8b743d;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$selectionBackgroundColor: rgba(79, 64, 28, 0.99);
|
||||
$heading1TextShadow: 0 1px 0 #ccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaa, 0 6px 1px rgba(0,0,0,.1), 0 0 5px rgba(0,0,0,.1), 0 1px 3px rgba(0,0,0,.3), 0 3px 5px rgba(0,0,0,.2), 0 5px 10px rgba(0,0,0,.25), 0 20px 20px rgba(0,0,0,.15);
|
||||
|
||||
// Background generator
|
||||
@mixin bodyBackground() {
|
||||
@include radial-gradient( rgba(247,242,211,1), rgba(255,255,255,1) );
|
||||
}
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,49 @@
|
||||
/**
|
||||
* Black theme for reveal.js. This is the opposite of the 'white' theme.
|
||||
*
|
||||
* Copyright (C) 2015 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@import url(../../lib/font/source-sans-pro/source-sans-pro.css);
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$backgroundColor: #222;
|
||||
|
||||
$mainColor: #fff;
|
||||
$headingColor: #fff;
|
||||
|
||||
$mainFontSize: 38px;
|
||||
$mainFont: 'Source Sans Pro', Helvetica, sans-serif;
|
||||
$headingFont: 'Source Sans Pro', Helvetica, sans-serif;
|
||||
$headingTextShadow: none;
|
||||
$headingLetterSpacing: normal;
|
||||
$headingTextTransform: uppercase;
|
||||
$headingFontWeight: 600;
|
||||
$linkColor: #42affa;
|
||||
$linkColorHover: lighten( $linkColor, 15% );
|
||||
$selectionBackgroundColor: lighten( $linkColor, 25% );
|
||||
|
||||
$heading1Size: 2.5em;
|
||||
$heading2Size: 1.6em;
|
||||
$heading3Size: 1.3em;
|
||||
$heading4Size: 1.0em;
|
||||
|
||||
section.has-light-background {
|
||||
&, h1, h2, h3, h4, h5, h6 {
|
||||
color: #222;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,91 @@
|
||||
/**
|
||||
* Blood theme for reveal.js
|
||||
* Author: Walther http://github.com/Walther
|
||||
*
|
||||
* Designed to be used with highlight.js theme
|
||||
* "monokai_sublime.css" available from
|
||||
* https://github.com/isagalaev/highlight.js/
|
||||
*
|
||||
* For other themes, change $codeBackground accordingly.
|
||||
*
|
||||
*/
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
// Include theme-specific fonts
|
||||
|
||||
@import url(https://fonts.googleapis.com/css?family=Ubuntu:300,700,300italic,700italic);
|
||||
|
||||
// Colors used in the theme
|
||||
$blood: #a23;
|
||||
$coal: #222;
|
||||
$codeBackground: #23241f;
|
||||
|
||||
// Main text
|
||||
$mainFont: Ubuntu, 'sans-serif';
|
||||
$mainFontSize: 30px;
|
||||
$mainColor: #eee;
|
||||
|
||||
// Headings
|
||||
$headingFont: Ubuntu, 'sans-serif';
|
||||
$headingTextShadow: 2px 2px 2px $coal;
|
||||
|
||||
// h1 shadow, borrowed humbly from
|
||||
// (c) Default theme by Hakim El Hattab
|
||||
$heading1TextShadow: 0 1px 0 #ccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaa, 0 6px 1px rgba(0,0,0,.1), 0 0 5px rgba(0,0,0,.1), 0 1px 3px rgba(0,0,0,.3), 0 3px 5px rgba(0,0,0,.2), 0 5px 10px rgba(0,0,0,.25), 0 20px 20px rgba(0,0,0,.15);
|
||||
|
||||
// Links
|
||||
$linkColor: $blood;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
|
||||
// Text selection
|
||||
$selectionBackgroundColor: $blood;
|
||||
$selectionColor: #fff;
|
||||
|
||||
// Background generator
|
||||
@mixin bodyBackground() {
|
||||
@include radial-gradient( $coal, lighten( $coal, 25% ) );
|
||||
}
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
|
||||
// some overrides after theme template import
|
||||
|
||||
.reveal p {
|
||||
font-weight: 300;
|
||||
text-shadow: 1px 1px $coal;
|
||||
}
|
||||
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
font-weight: 700;
|
||||
}
|
||||
|
||||
.reveal a:not(.image),
|
||||
.reveal a:not(.image):hover {
|
||||
text-shadow: 2px 2px 2px #000;
|
||||
}
|
||||
|
||||
.reveal small a:not(.image),
|
||||
.reveal small a:not(.image):hover {
|
||||
text-shadow: 1px 1px 1px #000;
|
||||
}
|
||||
|
||||
.reveal p code {
|
||||
background-color: $codeBackground;
|
||||
display: inline-block;
|
||||
border-radius: 7px;
|
||||
}
|
||||
|
||||
.reveal small code {
|
||||
vertical-align: baseline;
|
||||
}
|
||||
@@ -0,0 +1,39 @@
|
||||
/**
|
||||
* A simple theme for reveal.js presentations, similar
|
||||
* to the default theme. The accent color is darkblue.
|
||||
*
|
||||
* This theme is Copyright (C) 2012 Owen Versteeg, https://github.com/StereotypicalApps. It is MIT licensed.
|
||||
* reveal.js is Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
|
||||
* Center for Biomedical Computing theme made by Hans Petter Langtangen.
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$mainFont: 'Lato', sans-serif;
|
||||
$mainColor: #404040;
|
||||
$headingFont: 'Helvetica', Impact, sans-serif;
|
||||
$headingColor: #8A0808;
|
||||
$headingTextShadow: none;
|
||||
$headingTextTransform: none;
|
||||
$backgroundColor: #fff;
|
||||
$linkColor: #8A0808;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$selectionBackgroundColor: rgba(0, 0, 0, 0.99);
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,42 @@
|
||||
/**
|
||||
* Default theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url('../../lib/font/league_gothic-webfont.eot');
|
||||
src: url('../../lib/font/league_gothic-webfont.eot?#iefix') format('embedded-opentype'),
|
||||
url('../../lib/font/league_gothic-webfont.woff') format('woff'),
|
||||
url('../../lib/font/league_gothic-webfont.ttf') format('truetype'),
|
||||
url('../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular') format('svg');
|
||||
|
||||
font-weight: normal;
|
||||
font-style: normal;
|
||||
}
|
||||
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$heading1TextShadow: 0 1px 0 #ccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaa, 0 6px 1px rgba(0,0,0,.1), 0 0 5px rgba(0,0,0,.1), 0 1px 3px rgba(0,0,0,.3), 0 3px 5px rgba(0,0,0,.2), 0 5px 10px rgba(0,0,0,.25), 0 20px 20px rgba(0,0,0,.15);
|
||||
|
||||
// Background generator
|
||||
@mixin bodyBackground() {
|
||||
@include radial-gradient( rgba(28,30,32,1), rgba(85,90,95,1) );
|
||||
}
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,42 @@
|
||||
/**
|
||||
* Default theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url('../../lib/font/league_gothic-webfont.eot');
|
||||
src: url('../../lib/font/league_gothic-webfont.eot?#iefix') format('embedded-opentype'),
|
||||
url('../../lib/font/league_gothic-webfont.woff') format('woff'),
|
||||
url('../../lib/font/league_gothic-webfont.ttf') format('truetype'),
|
||||
url('../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular') format('svg');
|
||||
|
||||
font-weight: normal;
|
||||
font-style: normal;
|
||||
}
|
||||
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$heading1TextShadow: 0 1px 0 #ccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaa, 0 6px 1px rgba(0,0,0,.1), 0 0 5px rgba(0,0,0,.1), 0 1px 3px rgba(0,0,0,.3), 0 3px 5px rgba(0,0,0,.2), 0 5px 10px rgba(0,0,0,.25), 0 20px 20px rgba(0,0,0,.15);
|
||||
|
||||
// Background generator
|
||||
@mixin bodyBackground() {
|
||||
@include radial-gradient( rgba(28,30,32,1), rgba(85,90,95,1) );
|
||||
}
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,34 @@
|
||||
/**
|
||||
* League theme for reveal.js.
|
||||
*
|
||||
* This was the default theme pre-3.0.0.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@import url(../../lib/font/league-gothic/league-gothic.css);
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$headingTextShadow: 0px 0px 6px rgba(0,0,0,0.2);
|
||||
$heading1TextShadow: 0 1px 0 #ccc, 0 2px 0 #c9c9c9, 0 3px 0 #bbb, 0 4px 0 #b9b9b9, 0 5px 0 #aaa, 0 6px 1px rgba(0,0,0,.1), 0 0 5px rgba(0,0,0,.1), 0 1px 3px rgba(0,0,0,.3), 0 3px 5px rgba(0,0,0,.2), 0 5px 10px rgba(0,0,0,.25), 0 20px 20px rgba(0,0,0,.15);
|
||||
|
||||
// Background generator
|
||||
@mixin bodyBackground() {
|
||||
@include radial-gradient( rgba(28,30,32,1), rgba(85,90,95,1) );
|
||||
}
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,68 @@
|
||||
/**
|
||||
* Solarized Dark theme for reveal.js.
|
||||
* Author: Achim Staebler
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url('../../lib/font/league_gothic-webfont.eot');
|
||||
src: url('../../lib/font/league_gothic-webfont.eot?#iefix') format('embedded-opentype'),
|
||||
url('../../lib/font/league_gothic-webfont.woff') format('woff'),
|
||||
url('../../lib/font/league_gothic-webfont.ttf') format('truetype'),
|
||||
url('../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular') format('svg');
|
||||
|
||||
font-weight: normal;
|
||||
font-style: normal;
|
||||
}
|
||||
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
/**
|
||||
* Solarized colors by Ethan Schoonover
|
||||
*/
|
||||
html * {
|
||||
color-profile: sRGB;
|
||||
rendering-intent: auto;
|
||||
}
|
||||
|
||||
// Solarized colors
|
||||
$base03: #002b36;
|
||||
$base02: #073642;
|
||||
$base01: #586e75;
|
||||
$base00: #657b83;
|
||||
$base0: #839496;
|
||||
$base1: #93a1a1;
|
||||
$base2: #eee8d5;
|
||||
$base3: #fdf6e3;
|
||||
$yellow: #b58900;
|
||||
$orange: #cb4b16;
|
||||
$red: #dc322f;
|
||||
$magenta: #d33682;
|
||||
$violet: #6c71c4;
|
||||
$blue: #268bd2;
|
||||
$cyan: #2aa198;
|
||||
$green: #859900;
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$mainColor: $base1;
|
||||
$headingColor: $base2;
|
||||
$headingTextShadow: none;
|
||||
$backgroundColor: $base03;
|
||||
$linkColor: $blue;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$selectionBackgroundColor: $magenta;
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,35 @@
|
||||
/**
|
||||
* Black theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@import url(https://fonts.googleapis.com/css?family=Montserrat:700);
|
||||
@import url(https://fonts.googleapis.com/css?family=Open+Sans:400,700,400italic,700italic);
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$backgroundColor: #111;
|
||||
|
||||
$mainFont: 'Open Sans', sans-serif;
|
||||
$linkColor: #e7ad52;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$headingFont: 'Montserrat', Impact, sans-serif;
|
||||
$headingTextShadow: none;
|
||||
$headingLetterSpacing: -0.03em;
|
||||
$headingTextTransform: none;
|
||||
$selectionBackgroundColor: #e7ad52;
|
||||
$mainFontSize: 30px;
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,35 @@
|
||||
/**
|
||||
* A simple theme for reveal.js presentations, similar
|
||||
* to the default theme. The accent color is brown.
|
||||
*
|
||||
* This theme is Copyright (C) 2012-2013 Owen Versteeg, http://owenversteeg.com - it is MIT licensed.
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$mainFont: 'Palatino Linotype', 'Book Antiqua', Palatino, FreeSerif, serif;
|
||||
$mainColor: #000;
|
||||
$headingFont: 'Palatino Linotype', 'Book Antiqua', Palatino, FreeSerif, serif;
|
||||
$headingColor: #383D3D;
|
||||
$headingTextShadow: none;
|
||||
$headingTextTransform: none;
|
||||
$backgroundColor: #F0F1EB;
|
||||
$linkColor: #51483D;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$selectionBackgroundColor: #26351C;
|
||||
|
||||
.reveal a:not(.image) {
|
||||
line-height: 1.3em;
|
||||
}
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,38 @@
|
||||
/**
|
||||
* A simple theme for reveal.js presentations, similar
|
||||
* to the default theme. The accent color is darkblue.
|
||||
*
|
||||
* This theme is Copyright (C) 2012 Owen Versteeg, https://github.com/StereotypicalApps. It is MIT licensed.
|
||||
* reveal.js is Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@import url(https://fonts.googleapis.com/css?family=News+Cycle:400,700);
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$mainFont: 'Lato', sans-serif;
|
||||
$mainColor: #000;
|
||||
$headingFont: 'Helvetica', Impact, sans-serif; /* changed (by hpl) from 'News Cycle', Impact, sans-serif; */
|
||||
$headingColor: #000;
|
||||
$headingTextShadow: none;
|
||||
$headingTextTransform: none;
|
||||
$backgroundColor: #fff;
|
||||
$linkColor: #00008B;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$selectionBackgroundColor: rgba(0, 0, 0, 0.99);
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,39 @@
|
||||
/**
|
||||
* A simple theme for reveal.js presentations, similar
|
||||
* to the default theme. The accent color is darkblue.
|
||||
*
|
||||
* This theme is Copyright (C) 2012 Owen Versteeg, https://github.com/StereotypicalApps. It is MIT licensed.
|
||||
* reveal.js is Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
|
||||
* Simula theme made by Hans Petter Langtangen.
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$mainFont: 'Lato', sans-serif;
|
||||
$mainColor: #404040;
|
||||
$headingFont: 'Helvetica', Impact, sans-serif;
|
||||
$headingColor: #ff8800;
|
||||
$headingTextShadow: none;
|
||||
$headingTextTransform: none;
|
||||
$backgroundColor: #fff;
|
||||
$linkColor: #ff8800;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$selectionBackgroundColor: rgba(0, 0, 0, 0.99);
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,46 @@
|
||||
/**
|
||||
* Sky theme for reveal.js.
|
||||
*
|
||||
* Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@import url(https://fonts.googleapis.com/css?family=Quicksand:400,700,400italic,700italic);
|
||||
@import url(https://fonts.googleapis.com/css?family=Open+Sans:400italic,700italic,400,700);
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$mainFont: 'Open Sans', sans-serif;
|
||||
$mainColor: #333;
|
||||
$headingFont: 'Quicksand', sans-serif;
|
||||
$headingColor: #333;
|
||||
$headingLetterSpacing: -0.08em;
|
||||
$headingTextShadow: none;
|
||||
$backgroundColor: #f7fbfc;
|
||||
$linkColor: #3b759e;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$selectionBackgroundColor: #134674;
|
||||
|
||||
// Fix links so they are not cut off
|
||||
.reveal a:not(.image) {
|
||||
line-height: 1.3em;
|
||||
}
|
||||
|
||||
// Background generator
|
||||
@mixin bodyBackground() {
|
||||
@include radial-gradient( #add9e4, #f7fbfc );
|
||||
}
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,74 @@
|
||||
/**
|
||||
* Solarized Light theme for reveal.js.
|
||||
* Author: Achim Staebler
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url('../../lib/font/league_gothic-webfont.eot');
|
||||
src: url('../../lib/font/league_gothic-webfont.eot?#iefix') format('embedded-opentype'),
|
||||
url('../../lib/font/league_gothic-webfont.woff') format('woff'),
|
||||
url('../../lib/font/league_gothic-webfont.ttf') format('truetype'),
|
||||
url('../../lib/font/league_gothic-webfont.svg#LeagueGothicRegular') format('svg');
|
||||
|
||||
font-weight: normal;
|
||||
font-style: normal;
|
||||
}
|
||||
|
||||
@import url(https://fonts.googleapis.com/css?family=Lato:400,700,400italic,700italic);
|
||||
|
||||
|
||||
/**
|
||||
* Solarized colors by Ethan Schoonover
|
||||
*/
|
||||
html * {
|
||||
color-profile: sRGB;
|
||||
rendering-intent: auto;
|
||||
}
|
||||
|
||||
// Solarized colors
|
||||
$base03: #002b36;
|
||||
$base02: #073642;
|
||||
$base01: #586e75;
|
||||
$base00: #657b83;
|
||||
$base0: #839496;
|
||||
$base1: #93a1a1;
|
||||
$base2: #eee8d5;
|
||||
$base3: #fdf6e3;
|
||||
$yellow: #b58900;
|
||||
$orange: #cb4b16;
|
||||
$red: #dc322f;
|
||||
$magenta: #d33682;
|
||||
$violet: #6c71c4;
|
||||
$blue: #268bd2;
|
||||
$cyan: #2aa198;
|
||||
$green: #859900;
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$mainColor: $base00;
|
||||
$headingColor: $base01;
|
||||
$headingTextShadow: none;
|
||||
$backgroundColor: $base3;
|
||||
$linkColor: $blue;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
$selectionBackgroundColor: $magenta;
|
||||
|
||||
// Background generator
|
||||
// @mixin bodyBackground() {
|
||||
// @include radial-gradient( rgba($base3,1), rgba(lighten($base3, 20%),1) );
|
||||
// }
|
||||
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,49 @@
|
||||
/**
|
||||
* White theme for reveal.js. This is the opposite of the 'black' theme.
|
||||
*
|
||||
* Copyright (C) 2015 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
|
||||
|
||||
// Default mixins and settings -----------------
|
||||
@import "../template/mixins";
|
||||
@import "../template/settings";
|
||||
// ---------------------------------------------
|
||||
|
||||
|
||||
// Include theme-specific fonts
|
||||
@import url(../../lib/font/source-sans-pro/source-sans-pro.css);
|
||||
|
||||
|
||||
// Override theme settings (see ../template/settings.scss)
|
||||
$backgroundColor: #fff;
|
||||
|
||||
$mainColor: #222;
|
||||
$headingColor: #222;
|
||||
|
||||
$mainFontSize: 38px;
|
||||
$mainFont: 'Source Sans Pro', Helvetica, sans-serif;
|
||||
$headingFont: 'Source Sans Pro', Helvetica, sans-serif;
|
||||
$headingTextShadow: none;
|
||||
$headingLetterSpacing: normal;
|
||||
$headingTextTransform: uppercase;
|
||||
$headingFontWeight: 600;
|
||||
$linkColor: #2a76dd;
|
||||
$linkColorHover: lighten( $linkColor, 15% );
|
||||
$selectionBackgroundColor: lighten( $linkColor, 25% );
|
||||
|
||||
$heading1Size: 2.5em;
|
||||
$heading2Size: 1.6em;
|
||||
$heading3Size: 1.3em;
|
||||
$heading4Size: 1.0em;
|
||||
|
||||
section.has-dark-background {
|
||||
&, h1, h2, h3, h4, h5, h6 {
|
||||
color: #fff;
|
||||
}
|
||||
}
|
||||
|
||||
|
||||
// Theme template ------------------------------
|
||||
@import "../template/theme";
|
||||
// ---------------------------------------------
|
||||
@@ -0,0 +1,29 @@
|
||||
@mixin vertical-gradient( $top, $bottom ) {
|
||||
background: $top;
|
||||
background: -moz-linear-gradient( top, $top 0%, $bottom 100% );
|
||||
background: -webkit-gradient( linear, left top, left bottom, color-stop(0%,$top), color-stop(100%,$bottom) );
|
||||
background: -webkit-linear-gradient( top, $top 0%, $bottom 100% );
|
||||
background: -o-linear-gradient( top, $top 0%, $bottom 100% );
|
||||
background: -ms-linear-gradient( top, $top 0%, $bottom 100% );
|
||||
background: linear-gradient( top, $top 0%, $bottom 100% );
|
||||
}
|
||||
|
||||
@mixin horizontal-gradient( $top, $bottom ) {
|
||||
background: $top;
|
||||
background: -moz-linear-gradient( left, $top 0%, $bottom 100% );
|
||||
background: -webkit-gradient( linear, left top, right top, color-stop(0%,$top), color-stop(100%,$bottom) );
|
||||
background: -webkit-linear-gradient( left, $top 0%, $bottom 100% );
|
||||
background: -o-linear-gradient( left, $top 0%, $bottom 100% );
|
||||
background: -ms-linear-gradient( left, $top 0%, $bottom 100% );
|
||||
background: linear-gradient( left, $top 0%, $bottom 100% );
|
||||
}
|
||||
|
||||
@mixin radial-gradient( $outer, $inner, $type: circle ) {
|
||||
background: $outer;
|
||||
background: -moz-radial-gradient( center, $type cover, $inner 0%, $outer 100% );
|
||||
background: -webkit-gradient( radial, center center, 0px, center center, 100%, color-stop(0%,$inner), color-stop(100%,$outer) );
|
||||
background: -webkit-radial-gradient( center, $type cover, $inner 0%, $outer 100% );
|
||||
background: -o-radial-gradient( center, $type cover, $inner 0%, $outer 100% );
|
||||
background: -ms-radial-gradient( center, $type cover, $inner 0%, $outer 100% );
|
||||
background: radial-gradient( center, $type cover, $inner 0%, $outer 100% );
|
||||
}
|
||||
@@ -0,0 +1,34 @@
|
||||
// Base settings for all themes that can optionally be
|
||||
// overridden by the super-theme
|
||||
|
||||
// Background of the presentation
|
||||
$backgroundColor: #2b2b2b;
|
||||
|
||||
// Primary/body text
|
||||
$mainFont: 'Lato', sans-serif;
|
||||
$mainFontSize: 30px; /* changed (by hpl) from 36px; */
|
||||
$mainColor: #eee;
|
||||
|
||||
// Headings
|
||||
$headingMargin: 0 0 20px 0;
|
||||
$headingFont: 'League Gothic', Impact, sans-serif;
|
||||
$headingColor: #eee;
|
||||
$headingLineHeight: 0.9em;
|
||||
$headingLetterSpacing: 0.02em;
|
||||
$headingTextTransform: none; /* changed (by hpl) from uppercase; */
|
||||
$headingTextShadow: 0px 0px 6px rgba(0,0,0,0.2);
|
||||
$heading1TextShadow: $headingTextShadow;
|
||||
|
||||
// Links and actions
|
||||
$linkColor: #13DAEC;
|
||||
$linkColorHover: lighten( $linkColor, 20% );
|
||||
|
||||
// Text selection
|
||||
$selectionBackgroundColor: #FF5E99;
|
||||
$selectionColor: #fff;
|
||||
|
||||
// Generates the presentation background, can be overridden
|
||||
// to return a background image or gradient
|
||||
@mixin bodyBackground() {
|
||||
background: $backgroundColor;
|
||||
}
|
||||
@@ -0,0 +1,171 @@
|
||||
// Base theme template for reveal.js
|
||||
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
|
||||
body {
|
||||
@include bodyBackground();
|
||||
background-color: $backgroundColor;
|
||||
}
|
||||
|
||||
.reveal {
|
||||
font-family: $mainFont;
|
||||
font-size: $mainFontSize;
|
||||
font-weight: normal;
|
||||
letter-spacing: -0.02em;
|
||||
color: $mainColor;
|
||||
}
|
||||
|
||||
::selection {
|
||||
color: $selectionColor;
|
||||
background: $selectionBackgroundColor;
|
||||
text-shadow: none;
|
||||
}
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
|
||||
.reveal h1,
|
||||
.reveal h2,
|
||||
.reveal h3,
|
||||
.reveal h4,
|
||||
.reveal h5,
|
||||
.reveal h6 {
|
||||
margin: $headingMargin;
|
||||
color: $headingColor;
|
||||
|
||||
font-family: $headingFont;
|
||||
line-height: $headingLineHeight;
|
||||
letter-spacing: $headingLetterSpacing;
|
||||
|
||||
text-transform: $headingTextTransform;
|
||||
text-shadow: $headingTextShadow;
|
||||
}
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em; /* added by hpl */
|
||||
text-shadow: $heading1TextShadow;
|
||||
}
|
||||
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
|
||||
.reveal a:not(.image) {
|
||||
color: $linkColor;
|
||||
text-decoration: none;
|
||||
|
||||
-webkit-transition: color .15s ease;
|
||||
-moz-transition: color .15s ease;
|
||||
-ms-transition: color .15s ease;
|
||||
-o-transition: color .15s ease;
|
||||
transition: color .15s ease;
|
||||
}
|
||||
.reveal a:not(.image):hover {
|
||||
color: $linkColorHover;
|
||||
|
||||
text-shadow: none;
|
||||
border: none;
|
||||
}
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: darken( $linkColor, 15% );
|
||||
}
|
||||
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255,255,255,0.12);
|
||||
border: 4px solid $mainColor;
|
||||
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
|
||||
|
||||
-webkit-transition: all .2s linear;
|
||||
-moz-transition: all .2s linear;
|
||||
-ms-transition: all .2s linear;
|
||||
-o-transition: all .2s linear;
|
||||
transition: all .2s linear;
|
||||
}
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255,255,255,0.2);
|
||||
border-color: $linkColor;
|
||||
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55);
|
||||
}
|
||||
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
|
||||
.reveal .controls div.navigate-left,
|
||||
.reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: $linkColor;
|
||||
}
|
||||
|
||||
.reveal .controls div.navigate-right,
|
||||
.reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: $linkColor;
|
||||
}
|
||||
|
||||
.reveal .controls div.navigate-up,
|
||||
.reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: $linkColor;
|
||||
}
|
||||
|
||||
.reveal .controls div.navigate-down,
|
||||
.reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: $linkColor;
|
||||
}
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: $linkColorHover;
|
||||
}
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: $linkColorHover;
|
||||
}
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: $linkColorHover;
|
||||
}
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: $linkColorHover;
|
||||
}
|
||||
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
|
||||
.reveal .progress {
|
||||
background: rgba(0,0,0,0.2);
|
||||
}
|
||||
.reveal .progress span {
|
||||
background: $linkColor;
|
||||
|
||||
-webkit-transition: width 800ms cubic-bezier(0.260, 0.860, 0.440, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.260, 0.860, 0.440, 0.985);
|
||||
-ms-transition: width 800ms cubic-bezier(0.260, 0.860, 0.440, 0.985);
|
||||
-o-transition: width 800ms cubic-bezier(0.260, 0.860, 0.440, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.260, 0.860, 0.440, 0.985);
|
||||
}
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: $linkColor;
|
||||
}
|
||||
|
||||
|
||||
@@ -0,0 +1,273 @@
|
||||
@import url(../../lib/font/source-sans-pro/source-sans-pro.css);
|
||||
/**
|
||||
* White theme for reveal.js. This is the opposite of the 'black' theme.
|
||||
*
|
||||
* Copyright (C) 2015 Hakim El Hattab, http://hakim.se
|
||||
*/
|
||||
section.has-dark-background, section.has-dark-background h1, section.has-dark-background h2, section.has-dark-background h3, section.has-dark-background h4, section.has-dark-background h5, section.has-dark-background h6 {
|
||||
color: #fff; }
|
||||
|
||||
/*********************************************
|
||||
* GLOBAL STYLES
|
||||
*********************************************/
|
||||
body {
|
||||
background: #fff;
|
||||
background-color: #fff; }
|
||||
|
||||
.reveal {
|
||||
font-family: 'Source Sans Pro', Helvetica, sans-serif;
|
||||
font-size: 30px; /* changed by hpl from 38px */
|
||||
font-weight: normal;
|
||||
color: #222; }
|
||||
|
||||
::selection {
|
||||
color: #fff;
|
||||
background: #98bdef;
|
||||
text-shadow: none; }
|
||||
|
||||
.reveal .slides > section, .reveal .slides > section > section {
|
||||
line-height: 1.1em; /* changed by hpl from 1.2; */
|
||||
font-weight: inherit; }
|
||||
|
||||
/*********************************************
|
||||
* HEADERS
|
||||
*********************************************/
|
||||
.reveal h1, .reveal h2, .reveal h3, .reveal h4, .reveal h5, .reveal h6 {
|
||||
margin: 0 0 20px 0;
|
||||
color: #222;
|
||||
font-family: 'Source Sans Pro', Helvetica, sans-serif;
|
||||
font-weight: 600;
|
||||
line-height: 1.1em; /* changed by hpl from 1.2; */
|
||||
letter-spacing: normal;
|
||||
/* text-transform: uppercase; removed by hpl */
|
||||
text-shadow: none;
|
||||
word-wrap: break-word; }
|
||||
|
||||
.reveal h1 {
|
||||
line-height: 1.2em;
|
||||
}
|
||||
|
||||
/* removed by hpl
|
||||
.reveal h1 {
|
||||
font-size: 2.5em; }
|
||||
|
||||
.reveal h2 {
|
||||
font-size: 1.6em; }
|
||||
|
||||
.reveal h3 {
|
||||
font-size: 1.3em; }
|
||||
|
||||
.reveal h4 {
|
||||
font-size: 1em; }
|
||||
*/
|
||||
|
||||
.reveal h1 {
|
||||
text-shadow: none; }
|
||||
|
||||
/*********************************************
|
||||
* OTHER
|
||||
*********************************************/
|
||||
.reveal p {
|
||||
margin: 20px 0;
|
||||
line-height: 1.3; }
|
||||
|
||||
/* Ensure certain elements are never larger than the slide itself */
|
||||
.reveal img, .reveal video, .reveal iframe {
|
||||
max-width: 95%;
|
||||
max-height: 95%; }
|
||||
|
||||
.reveal strong, .reveal b {
|
||||
font-weight: bold; }
|
||||
|
||||
.reveal em {
|
||||
font-style: italic; }
|
||||
|
||||
.reveal ol, .reveal dl, .reveal ul {
|
||||
display: inline-block;
|
||||
text-align: left;
|
||||
margin: 0 0 0 1em; }
|
||||
|
||||
.reveal ol {
|
||||
list-style-type: decimal; }
|
||||
|
||||
.reveal ul {
|
||||
list-style-type: disc; }
|
||||
|
||||
.reveal ul ul {
|
||||
list-style-type: square; }
|
||||
|
||||
.reveal ul ul ul {
|
||||
list-style-type: circle; }
|
||||
|
||||
.reveal ul ul, .reveal ul ol, .reveal ol ol, .reveal ol ul {
|
||||
display: block;
|
||||
margin-left: 40px; }
|
||||
|
||||
.reveal dt {
|
||||
font-weight: bold; }
|
||||
|
||||
.reveal dd {
|
||||
margin-left: 40px; }
|
||||
|
||||
.reveal q, .reveal blockquote {
|
||||
quotes: none; }
|
||||
|
||||
.reveal blockquote {
|
||||
display: block;
|
||||
position: relative;
|
||||
width: 70%;
|
||||
margin: 20px auto;
|
||||
padding: 5px;
|
||||
font-style: italic;
|
||||
background: rgba(255, 255, 255, 0.05);
|
||||
box-shadow: 0px 0px 2px rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal blockquote p:first-child, .reveal blockquote p:last-child {
|
||||
display: inline-block; }
|
||||
|
||||
.reveal q {
|
||||
font-style: italic; }
|
||||
|
||||
.reveal pre {
|
||||
display: block;
|
||||
position: relative;
|
||||
width: 90%;
|
||||
margin: 20px auto;
|
||||
text-align: left;
|
||||
font-size: 0.55em;
|
||||
font-family: monospace;
|
||||
line-height: 1.2em;
|
||||
word-wrap: break-word;
|
||||
box-shadow: 0px 0px 6px rgba(0, 0, 0, 0.3); }
|
||||
|
||||
.reveal code {
|
||||
font-family: monospace; }
|
||||
|
||||
.reveal pre code {
|
||||
display: block;
|
||||
padding: 5px;
|
||||
overflow: auto;
|
||||
max-height: 400px;
|
||||
word-wrap: normal;
|
||||
background: #3F3F3F;
|
||||
color: #DCDCDC; }
|
||||
|
||||
.reveal table {
|
||||
margin: auto;
|
||||
border-collapse: collapse;
|
||||
border-spacing: 0; }
|
||||
|
||||
.reveal table th {
|
||||
font-weight: bold; }
|
||||
|
||||
.reveal table th, .reveal table td {
|
||||
/* text-align: left; */ /* hpl modification */
|
||||
padding: 0.2em 0.5em 0.2em 0.5em;
|
||||
border-bottom: 1px solid; }
|
||||
|
||||
.reveal table th[align="center"], .reveal table td[align="center"] {
|
||||
text-align: center; }
|
||||
|
||||
.reveal table th[align="right"], .reveal table td[align="right"] {
|
||||
text-align: right; }
|
||||
|
||||
.reveal table tr:last-child td {
|
||||
border-bottom: none; }
|
||||
|
||||
.reveal sup {
|
||||
vertical-align: super; }
|
||||
|
||||
.reveal sub {
|
||||
vertical-align: sub; }
|
||||
|
||||
.reveal small {
|
||||
display: inline-block;
|
||||
font-size: 0.6em;
|
||||
line-height: 1.2em;
|
||||
vertical-align: top; }
|
||||
|
||||
.reveal small * {
|
||||
vertical-align: top; }
|
||||
|
||||
/*********************************************
|
||||
* LINKS
|
||||
*********************************************/
|
||||
.reveal a {
|
||||
color: #2a76dd;
|
||||
text-decoration: none;
|
||||
-webkit-transition: color 0.15s ease;
|
||||
-moz-transition: color 0.15s ease;
|
||||
transition: color 0.15s ease; }
|
||||
|
||||
.reveal a:hover {
|
||||
color: #6ca2e8;
|
||||
text-shadow: none;
|
||||
border: none; }
|
||||
|
||||
.reveal .roll span:after {
|
||||
color: #fff;
|
||||
background: #1a54a1; }
|
||||
|
||||
/*********************************************
|
||||
* IMAGES
|
||||
*********************************************/
|
||||
.reveal section img {
|
||||
margin: 15px 0px;
|
||||
background: rgba(255, 255, 255, 0.12);
|
||||
border: 4px solid #222;
|
||||
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15); }
|
||||
|
||||
.reveal a img {
|
||||
-webkit-transition: all 0.15s linear;
|
||||
-moz-transition: all 0.15s linear;
|
||||
transition: all 0.15s linear; }
|
||||
|
||||
.reveal a:hover img {
|
||||
background: rgba(255, 255, 255, 0.2);
|
||||
border-color: #2a76dd;
|
||||
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
|
||||
|
||||
/*********************************************
|
||||
* NAVIGATION CONTROLS
|
||||
*********************************************/
|
||||
.reveal .controls div.navigate-left, .reveal .controls div.navigate-left.enabled {
|
||||
border-right-color: #2a76dd; }
|
||||
|
||||
.reveal .controls div.navigate-right, .reveal .controls div.navigate-right.enabled {
|
||||
border-left-color: #2a76dd; }
|
||||
|
||||
.reveal .controls div.navigate-up, .reveal .controls div.navigate-up.enabled {
|
||||
border-bottom-color: #2a76dd; }
|
||||
|
||||
.reveal .controls div.navigate-down, .reveal .controls div.navigate-down.enabled {
|
||||
border-top-color: #2a76dd; }
|
||||
|
||||
.reveal .controls div.navigate-left.enabled:hover {
|
||||
border-right-color: #6ca2e8; }
|
||||
|
||||
.reveal .controls div.navigate-right.enabled:hover {
|
||||
border-left-color: #6ca2e8; }
|
||||
|
||||
.reveal .controls div.navigate-up.enabled:hover {
|
||||
border-bottom-color: #6ca2e8; }
|
||||
|
||||
.reveal .controls div.navigate-down.enabled:hover {
|
||||
border-top-color: #6ca2e8; }
|
||||
|
||||
/*********************************************
|
||||
* PROGRESS BAR
|
||||
*********************************************/
|
||||
.reveal .progress {
|
||||
background: rgba(0, 0, 0, 0.2); }
|
||||
|
||||
.reveal .progress span {
|
||||
background: #2a76dd;
|
||||
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
|
||||
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
|
||||
|
||||
/*********************************************
|
||||
* SLIDE NUMBER
|
||||
*********************************************/
|
||||
.reveal .slide-number {
|
||||
color: #2a76dd; }
|
||||
@@ -0,0 +1,411 @@
|
||||
<!doctype html>
|
||||
<html lang="en">
|
||||
|
||||
<head>
|
||||
<meta charset="utf-8">
|
||||
|
||||
<title>reveal.js - The HTML Presentation Framework</title>
|
||||
|
||||
<meta name="description" content="A framework for easily creating beautiful presentations using HTML">
|
||||
<meta name="author" content="Hakim El Hattab">
|
||||
|
||||
<meta name="apple-mobile-web-app-capable" content="yes" />
|
||||
<meta name="apple-mobile-web-app-status-bar-style" content="black-translucent" />
|
||||
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1.0, maximum-scale=1.0, user-scalable=no, minimal-ui">
|
||||
|
||||
<link rel="stylesheet" href="css/reveal.css">
|
||||
<link rel="stylesheet" href="css/theme/black.css" id="theme">
|
||||
|
||||
<!-- Code syntax highlighting -->
|
||||
<link rel="stylesheet" href="lib/css/zenburn.css">
|
||||
|
||||
<!-- Printing and PDF exports -->
|
||||
<script>
|
||||
var link = document.createElement( 'link' );
|
||||
link.rel = 'stylesheet';
|
||||
link.type = 'text/css';
|
||||
link.href = window.location.search.match( /print-pdf/gi ) ? 'css/print/pdf.css' : 'css/print/paper.css';
|
||||
document.getElementsByTagName( 'head' )[0].appendChild( link );
|
||||
</script>
|
||||
|
||||
<!--[if lt IE 9]>
|
||||
<script src="lib/js/html5shiv.js"></script>
|
||||
<![endif]-->
|
||||
</head>
|
||||
|
||||
<body>
|
||||
|
||||
<div class="reveal">
|
||||
|
||||
<!-- Any section element inside of this container is displayed as a slide -->
|
||||
<div class="slides">
|
||||
<section>
|
||||
<h1>Reveal.js</h1>
|
||||
<h3>The HTML Presentation Framework</h3>
|
||||
<p>
|
||||
<small>Created by <a href="http://hakim.se">Hakim El Hattab</a> / <a href="http://twitter.com/hakimel">@hakimel</a></small>
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Hello There</h2>
|
||||
<p>
|
||||
reveal.js enables you to create beautiful interactive slide decks using HTML. This presentation will show you examples of what it can do.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<!-- Example of nested vertical slides -->
|
||||
<section>
|
||||
<section>
|
||||
<h2>Vertical Slides</h2>
|
||||
<p>Slides can be nested inside of each other.</p>
|
||||
<p>Use the <em>Space</em> key to navigate through all slides.</p>
|
||||
<br>
|
||||
<a href="#" class="navigate-down">
|
||||
<img width="178" height="238" data-src="https://s3.amazonaws.com/hakim-static/reveal-js/arrow.png" alt="Down arrow">
|
||||
</a>
|
||||
</section>
|
||||
<section>
|
||||
<h2>Basement Level 1</h2>
|
||||
<p>Nested slides are useful for adding additional detail underneath a high level horizontal slide.</p>
|
||||
</section>
|
||||
<section>
|
||||
<h2>Basement Level 2</h2>
|
||||
<p>That's it, time to go back up.</p>
|
||||
<br>
|
||||
<a href="#/2">
|
||||
<img width="178" height="238" data-src="https://s3.amazonaws.com/hakim-static/reveal-js/arrow.png" alt="Up arrow" style="transform: rotate(180deg); -webkit-transform: rotate(180deg);">
|
||||
</a>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Slides</h2>
|
||||
<p>
|
||||
Not a coder? Not a problem. There's a fully-featured visual editor for authoring these, try it out at <a href="http://slides.com" target="_blank">http://slides.com</a>.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Point of View</h2>
|
||||
<p>
|
||||
Press <strong>ESC</strong> to enter the slide overview.
|
||||
</p>
|
||||
<p>
|
||||
Hold down alt and click on any element to zoom in on it using <a href="http://lab.hakim.se/zoom-js">zoom.js</a>. Alt + click anywhere to zoom back out.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Touch Optimized</h2>
|
||||
<p>
|
||||
Presentations look great on touch devices, like mobile phones and tablets. Simply swipe through your slides.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section data-markdown>
|
||||
<script type="text/template">
|
||||
## Markdown support
|
||||
|
||||
Write content using inline or external Markdown.
|
||||
Instructions and more info available in the [readme](https://github.com/hakimel/reveal.js#markdown).
|
||||
|
||||
```
|
||||
<section data-markdown>
|
||||
## Markdown support
|
||||
|
||||
Write content using inline or external Markdown.
|
||||
Instructions and more info available in the [readme](https://github.com/hakimel/reveal.js#markdown).
|
||||
</section>
|
||||
```
|
||||
</script>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section id="fragments">
|
||||
<h2>Fragments</h2>
|
||||
<p>Hit the next arrow...</p>
|
||||
<p class="fragment">... to step through ...</p>
|
||||
<p><span class="fragment">... a</span> <span class="fragment">fragmented</span> <span class="fragment">slide.</span></p>
|
||||
|
||||
<aside class="notes">
|
||||
This slide has fragments which are also stepped through in the notes window.
|
||||
</aside>
|
||||
</section>
|
||||
<section>
|
||||
<h2>Fragment Styles</h2>
|
||||
<p>There's different types of fragments, like:</p>
|
||||
<p class="fragment grow">grow</p>
|
||||
<p class="fragment shrink">shrink</p>
|
||||
<p class="fragment fade-out">fade-out</p>
|
||||
<p class="fragment current-visible">current-visible</p>
|
||||
<p class="fragment highlight-red">highlight-red</p>
|
||||
<p class="fragment highlight-blue">highlight-blue</p>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section id="transitions">
|
||||
<h2>Transition Styles</h2>
|
||||
<p>
|
||||
You can select from different transitions, like: <br>
|
||||
<a href="?transition=none#/transitions">None</a> -
|
||||
<a href="?transition=fade#/transitions">Fade</a> -
|
||||
<a href="?transition=slide#/transitions">Slide</a> -
|
||||
<a href="?transition=convex#/transitions">Convex</a> -
|
||||
<a href="?transition=concave#/transitions">Concave</a> -
|
||||
<a href="?transition=zoom#/transitions">Zoom</a>
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section id="themes">
|
||||
<h2>Themes</h2>
|
||||
<p>
|
||||
reveal.js comes with a few themes built in: <br>
|
||||
<!-- Hacks to swap themes after the page has loaded. Not flexible and only intended for the reveal.js demo deck. -->
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/black.css'); return false;">Black (default)</a> -
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/white.css'); return false;">White</a> -
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/league.css'); return false;">League</a> -
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/sky.css'); return false;">Sky</a> -
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/beige.css'); return false;">Beige</a> -
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/simple.css'); return false;">Simple</a> <br>
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/serif.css'); return false;">Serif</a> -
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/blood.css'); return false;">Blood</a> -
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/night.css'); return false;">Night</a> -
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/moon.css'); return false;">Moon</a> -
|
||||
<a href="#" onclick="document.getElementById('theme').setAttribute('href','css/theme/solarized.css'); return false;">Solarized</a>
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<section data-background="#dddddd">
|
||||
<h2>Slide Backgrounds</h2>
|
||||
<p>
|
||||
Set <code>data-background="#dddddd"</code> on a slide to change the background color. All CSS color formats are supported.
|
||||
</p>
|
||||
<a href="#" class="navigate-down">
|
||||
<img width="178" height="238" data-src="https://s3.amazonaws.com/hakim-static/reveal-js/arrow.png" alt="Down arrow">
|
||||
</a>
|
||||
</section>
|
||||
<section data-background="https://s3.amazonaws.com/hakim-static/reveal-js/image-placeholder.png">
|
||||
<h2>Image Backgrounds</h2>
|
||||
<pre><code><section data-background="image.png"></code></pre>
|
||||
</section>
|
||||
<section data-background="https://s3.amazonaws.com/hakim-static/reveal-js/image-placeholder.png" data-background-repeat="repeat" data-background-size="100px">
|
||||
<h2>Tiled Backgrounds</h2>
|
||||
<pre><code style="word-wrap: break-word;"><section data-background="image.png" data-background-repeat="repeat" data-background-size="100px"></code></pre>
|
||||
</section>
|
||||
<section data-background-video="https://s3.amazonaws.com/static.slid.es/site/homepage/v1/homepage-video-editor.mp4,https://s3.amazonaws.com/static.slid.es/site/homepage/v1/homepage-video-editor.webm" data-background-color="#000000">
|
||||
<div style="background-color: rgba(0, 0, 0, 0.9); color: #fff; padding: 20px;">
|
||||
<h2>Video Backgrounds</h2>
|
||||
<pre><code style="word-wrap: break-word;"><section data-background-video="video.mp4,video.webm"></code></pre>
|
||||
</div>
|
||||
</section>
|
||||
<section data-background="http://i.giphy.com/90F8aUepslB84.gif">
|
||||
<h2>... and GIFs!</h2>
|
||||
</section>
|
||||
</section>
|
||||
|
||||
<section data-transition="slide" data-background="#4d7e65" data-background-transition="zoom">
|
||||
<h2>Background Transitions</h2>
|
||||
<p>
|
||||
Different background transitions are available via the backgroundTransition option. This one's called "zoom".
|
||||
</p>
|
||||
<pre><code>Reveal.configure({ backgroundTransition: 'zoom' })</code></pre>
|
||||
</section>
|
||||
|
||||
<section data-transition="slide" data-background="#b5533c" data-background-transition="zoom">
|
||||
<h2>Background Transitions</h2>
|
||||
<p>
|
||||
You can override background transitions per-slide.
|
||||
</p>
|
||||
<pre><code style="word-wrap: break-word;"><section data-background-transition="zoom"></code></pre>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Pretty Code</h2>
|
||||
<pre><code data-trim contenteditable>
|
||||
function linkify( selector ) {
|
||||
if( supports3DTransforms ) {
|
||||
|
||||
var nodes = document.querySelectorAll( selector );
|
||||
|
||||
for( var i = 0, len = nodes.length; i < len; i++ ) {
|
||||
var node = nodes[i];
|
||||
|
||||
if( !node.className ) {
|
||||
node.className += ' roll';
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
</code></pre>
|
||||
<p>Code syntax highlighting courtesy of <a href="http://softwaremaniacs.org/soft/highlight/en/description/">highlight.js</a>.</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Marvelous List</h2>
|
||||
<ul>
|
||||
<li>No order here</li>
|
||||
<li>Or here</li>
|
||||
<li>Or here</li>
|
||||
<li>Or here</li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Fantastic Ordered List</h2>
|
||||
<ol>
|
||||
<li>One is smaller than...</li>
|
||||
<li>Two is smaller than...</li>
|
||||
<li>Three!</li>
|
||||
</ol>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Tabular Tables</h2>
|
||||
<table>
|
||||
<thead>
|
||||
<tr>
|
||||
<th>Item</th>
|
||||
<th>Value</th>
|
||||
<th>Quantity</th>
|
||||
</tr>
|
||||
</thead>
|
||||
<tbody>
|
||||
<tr>
|
||||
<td>Apples</td>
|
||||
<td>$1</td>
|
||||
<td>7</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Lemonade</td>
|
||||
<td>$2</td>
|
||||
<td>18</td>
|
||||
</tr>
|
||||
<tr>
|
||||
<td>Bread</td>
|
||||
<td>$3</td>
|
||||
<td>2</td>
|
||||
</tr>
|
||||
</tbody>
|
||||
</table>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Clever Quotes</h2>
|
||||
<p>
|
||||
These guys come in two forms, inline: <q cite="http://searchservervirtualization.techtarget.com/definition/Our-Favorite-Technology-Quotations">
|
||||
“The nice thing about standards is that there are so many to choose from”</q> and block:
|
||||
</p>
|
||||
<blockquote cite="http://searchservervirtualization.techtarget.com/definition/Our-Favorite-Technology-Quotations">
|
||||
“For years there has been a theory that millions of monkeys typing at random on millions of typewriters would
|
||||
reproduce the entire works of Shakespeare. The Internet has proven this theory to be untrue.”
|
||||
</blockquote>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Intergalactic Interconnections</h2>
|
||||
<p>
|
||||
You can link between slides internally,
|
||||
<a href="#/2/3">like this</a>.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Speaker View</h2>
|
||||
<p>There's a <a href="https://github.com/hakimel/reveal.js#speaker-notes">speaker view</a>. It includes a timer, preview of the upcoming slide as well as your speaker notes.</p>
|
||||
<p>Press the <em>S</em> key to try it out.</p>
|
||||
|
||||
<aside class="notes">
|
||||
Oh hey, these are some notes. They'll be hidden in your presentation, but you can see them if you open the speaker notes window (hit 's' on your keyboard).
|
||||
</aside>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Export to PDF</h2>
|
||||
<p>Presentations can be <a href="https://github.com/hakimel/reveal.js#pdf-export">exported to PDF</a>, here's an example:</p>
|
||||
<iframe src="//www.slideshare.net/slideshow/embed_code/42840540" width="445" height="355" frameborder="0" marginwidth="0" marginheight="0" scrolling="no" style="border:3px solid #666; margin-bottom:5px; max-width: 100%;" allowfullscreen> </iframe>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Global State</h2>
|
||||
<p>
|
||||
Set <code>data-state="something"</code> on a slide and <code>"something"</code>
|
||||
will be added as a class to the document element when the slide is open. This lets you
|
||||
apply broader style changes, like switching the page background.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section data-state="customevent">
|
||||
<h2>State Events</h2>
|
||||
<p>
|
||||
Additionally custom events can be triggered on a per slide basis by binding to the <code>data-state</code> name.
|
||||
</p>
|
||||
<pre><code class="javascript" data-trim contenteditable style="font-size: 18px;">
|
||||
Reveal.addEventListener( 'customevent', function() {
|
||||
console.log( '"customevent" has fired' );
|
||||
} );
|
||||
</code></pre>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Take a Moment</h2>
|
||||
<p>
|
||||
Press B or . on your keyboard to pause the presentation. This is helpful when you're on stage and want to take distracting slides off the screen.
|
||||
</p>
|
||||
</section>
|
||||
|
||||
<section>
|
||||
<h2>Much more</h2>
|
||||
<ul>
|
||||
<li>Right-to-left support</li>
|
||||
<li><a href="https://github.com/hakimel/reveal.js#api">Extensive JavaScript API</a></li>
|
||||
<li><a href="https://github.com/hakimel/reveal.js#auto-sliding">Auto-progression</a></li>
|
||||
<li><a href="https://github.com/hakimel/reveal.js#parallax-background">Parallax backgrounds</a></li>
|
||||
<li><a href="https://github.com/hakimel/reveal.js#keyboard-bindings">Custom keyboard bindings</a></li>
|
||||
</ul>
|
||||
</section>
|
||||
|
||||
<section style="text-align: left;">
|
||||
<h1>THE END</h1>
|
||||
<p>
|
||||
- <a href="http://slides.com">Try the online editor</a> <br>
|
||||
- <a href="https://github.com/hakimel/reveal.js">Source code & documentation</a>
|
||||
</p>
|
||||
</section>
|
||||
|
||||
</div>
|
||||
|
||||
</div>
|
||||
|
||||
<script src="lib/js/head.min.js"></script>
|
||||
<script src="js/reveal.js"></script>
|
||||
|
||||
<script>
|
||||
|
||||
// Full list of configuration options available at:
|
||||
// https://github.com/hakimel/reveal.js#configuration
|
||||
Reveal.initialize({
|
||||
controls: true,
|
||||
progress: true,
|
||||
history: true,
|
||||
center: true,
|
||||
|
||||
transition: 'slide', // none/fade/slide/convex/concave/zoom
|
||||
|
||||
// Optional reveal.js plugins
|
||||
dependencies: [
|
||||
{ src: 'lib/js/classList.js', condition: function() { return !document.body.classList; } },
|
||||
{ src: 'plugin/markdown/marked.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
|
||||
{ src: 'plugin/markdown/markdown.js', condition: function() { return !!document.querySelector( '[data-markdown]' ); } },
|
||||
{ src: 'plugin/highlight/highlight.js', async: true, condition: function() { return !!document.querySelector( 'pre code' ); }, callback: function() { hljs.initHighlightingOnLoad(); } },
|
||||
{ src: 'plugin/zoom-js/zoom.js', async: true },
|
||||
{ src: 'plugin/notes/notes.js', async: true }
|
||||
]
|
||||
});
|
||||
|
||||
</script>
|
||||
|
||||
</body>
|
||||
</html>
|
||||
File diff suppressed because it is too large
Load Diff
@@ -0,0 +1,117 @@
|
||||
/*
|
||||
|
||||
Zenburn style from voldmar.ru (c) Vladimir Epifanov <voldmar@voldmar.ru>
|
||||
based on dark.css by Ivan Sagalaev
|
||||
|
||||
*/
|
||||
|
||||
.hljs {
|
||||
display: block; padding: 0.5em;
|
||||
background: #3F3F3F;
|
||||
color: #DCDCDC;
|
||||
}
|
||||
|
||||
.hljs-keyword,
|
||||
.hljs-tag,
|
||||
.css .hljs-class,
|
||||
.css .hljs-id,
|
||||
.lisp .hljs-title,
|
||||
.nginx .hljs-title,
|
||||
.hljs-request,
|
||||
.hljs-status,
|
||||
.clojure .hljs-attribute {
|
||||
color: #E3CEAB;
|
||||
}
|
||||
|
||||
.django .hljs-template_tag,
|
||||
.django .hljs-variable,
|
||||
.django .hljs-filter .hljs-argument {
|
||||
color: #DCDCDC;
|
||||
}
|
||||
|
||||
.hljs-number,
|
||||
.hljs-date {
|
||||
color: #8CD0D3;
|
||||
}
|
||||
|
||||
.dos .hljs-envvar,
|
||||
.dos .hljs-stream,
|
||||
.hljs-variable,
|
||||
.apache .hljs-sqbracket {
|
||||
color: #EFDCBC;
|
||||
}
|
||||
|
||||
.dos .hljs-flow,
|
||||
.diff .hljs-change,
|
||||
.python .exception,
|
||||
.python .hljs-built_in,
|
||||
.hljs-literal,
|
||||
.tex .hljs-special {
|
||||
color: #EFEFAF;
|
||||
}
|
||||
|
||||
.diff .hljs-chunk,
|
||||
.hljs-subst {
|
||||
color: #8F8F8F;
|
||||
}
|
||||
|
||||
.dos .hljs-keyword,
|
||||
.python .hljs-decorator,
|
||||
.hljs-title,
|
||||
.haskell .hljs-type,
|
||||
.diff .hljs-header,
|
||||
.ruby .hljs-class .hljs-parent,
|
||||
.apache .hljs-tag,
|
||||
.nginx .hljs-built_in,
|
||||
.tex .hljs-command,
|
||||
.hljs-prompt {
|
||||
color: #efef8f;
|
||||
}
|
||||
|
||||
.dos .hljs-winutils,
|
||||
.ruby .hljs-symbol,
|
||||
.ruby .hljs-symbol .hljs-string,
|
||||
.ruby .hljs-string {
|
||||
color: #DCA3A3;
|
||||
}
|
||||
|
||||
.diff .hljs-deletion,
|
||||
.hljs-string,
|
||||
.hljs-tag .hljs-value,
|
||||
.hljs-preprocessor,
|
||||
.hljs-pragma,
|
||||
.hljs-built_in,
|
||||
.sql .hljs-aggregate,
|
||||
.hljs-javadoc,
|
||||
.smalltalk .hljs-class,
|
||||
.smalltalk .hljs-localvars,
|
||||
.smalltalk .hljs-array,
|
||||
.css .hljs-rules .hljs-value,
|
||||
.hljs-attr_selector,
|
||||
.hljs-pseudo,
|
||||
.apache .hljs-cbracket,
|
||||
.tex .hljs-formula,
|
||||
.coffeescript .hljs-attribute {
|
||||
color: #CC9393;
|
||||
}
|
||||
|
||||
.hljs-shebang,
|
||||
.diff .hljs-addition,
|
||||
.hljs-comment,
|
||||
.java .hljs-annotation,
|
||||
.hljs-template_comment,
|
||||
.hljs-pi,
|
||||
.hljs-doctype {
|
||||
color: #7F9F7F;
|
||||
}
|
||||
|
||||
.coffeescript .javascript,
|
||||
.javascript .xml,
|
||||
.tex .hljs-formula,
|
||||
.xml .javascript,
|
||||
.xml .vbscript,
|
||||
.xml .css,
|
||||
.xml .hljs-cdata {
|
||||
opacity: 0.5;
|
||||
}
|
||||
|
||||
@@ -0,0 +1,2 @@
|
||||
SIL Open Font License (OFL)
|
||||
http://scripts.sil.org/cms/scripts/page.php?site_id=nrsi&id=OFL
|
||||
@@ -0,0 +1,10 @@
|
||||
@font-face {
|
||||
font-family: 'League Gothic';
|
||||
src: url('league-gothic.eot');
|
||||
src: url('league-gothic.eot?#iefix') format('embedded-opentype'),
|
||||
url('league-gothic.woff') format('woff'),
|
||||
url('league-gothic.ttf') format('truetype');
|
||||
|
||||
font-weight: normal;
|
||||
font-style: normal;
|
||||
}
|
||||
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@@ -0,0 +1,45 @@
|
||||
SIL Open Font License
|
||||
|
||||
Copyright 2010, 2012 Adobe Systems Incorporated (http://www.adobe.com/), with Reserved Font Name ‘Source’. All Rights Reserved. Source is a trademark of Adobe Systems Incorporated in the United States and/or other countries.
|
||||
|
||||
This Font Software is licensed under the SIL Open Font License, Version 1.1.
|
||||
This license is copied below, and is also available with a FAQ at: http://scripts.sil.org/OFL
|
||||
|
||||
—————————————————————————————-
|
||||
SIL OPEN FONT LICENSE Version 1.1 - 26 February 2007
|
||||
—————————————————————————————-
|
||||
|
||||
PREAMBLE
|
||||
The goals of the Open Font License (OFL) are to stimulate worldwide development of collaborative font projects, to support the font creation efforts of academic and linguistic communities, and to provide a free and open framework in which fonts may be shared and improved in partnership with others.
|
||||
|
||||
The OFL allows the licensed fonts to be used, studied, modified and redistributed freely as long as they are not sold by themselves. The fonts, including any derivative works, can be bundled, embedded, redistributed and/or sold with any software provided that any reserved names are not used by derivative works. The fonts and derivatives, however, cannot be released under any other type of license. The requirement for fonts to remain under this license does not apply to any document created using the fonts or their derivatives.
|
||||
|
||||
DEFINITIONS
|
||||
“Font Software” refers to the set of files released by the Copyright Holder(s) under this license and clearly marked as such. This may include source files, build scripts and documentation.
|
||||
|
||||
“Reserved Font Name” refers to any names specified as such after the copyright statement(s).
|
||||
|
||||
“Original Version” refers to the collection of Font Software components as distributed by the Copyright Holder(s).
|
||||
|
||||
“Modified Version” refers to any derivative made by adding to, deleting, or substituting—in part or in whole—any of the components of the Original Version, by changing formats or by porting the Font Software to a new environment.
|
||||
|
||||
“Author” refers to any designer, engineer, programmer, technical writer or other person who contributed to the Font Software.
|
||||
|
||||
PERMISSION & CONDITIONS
|
||||
Permission is hereby granted, free of charge, to any person obtaining a copy of the Font Software, to use, study, copy, merge, embed, modify, redistribute, and sell modified and unmodified copies of the Font Software, subject to the following conditions:
|
||||
|
||||
1) Neither the Font Software nor any of its individual components, in Original or Modified Versions, may be sold by itself.
|
||||
|
||||
2) Original or Modified Versions of the Font Software may be bundled, redistributed and/or sold with any software, provided that each copy contains the above copyright notice and this license. These can be included either as stand-alone text files, human-readable headers or in the appropriate machine-readable metadata fields within text or binary files as long as those fields can be easily viewed by the user.
|
||||
|
||||
3) No Modified Version of the Font Software may use the Reserved Font Name(s) unless explicit written permission is granted by the corresponding Copyright Holder. This restriction only applies to the primary font name as presented to the users.
|
||||
|
||||
4) The name(s) of the Copyright Holder(s) or the Author(s) of the Font Software shall not be used to promote, endorse or advertise any Modified Version, except to acknowledge the contribution(s) of the Copyright Holder(s) and the Author(s) or with their explicit written permission.
|
||||
|
||||
5) The Font Software, modified or unmodified, in part or in whole, must be distributed entirely under this license, and must not be distributed under any other license. The requirement for fonts to remain under this license does not apply to any document created using the Font Software.
|
||||
|
||||
TERMINATION
|
||||
This license becomes null and void if any of the above conditions are not met.
|
||||
|
||||
DISCLAIMER
|
||||
THE FONT SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO ANY WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT OF COPYRIGHT, PATENT, TRADEMARK, OR OTHER RIGHT. IN NO EVENT SHALL THE COPYRIGHT HOLDER BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, INCLUDING ANY GENERAL, SPECIAL, INDIRECT, INCIDENTAL, OR CONSEQUENTIAL DAMAGES, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF THE USE OR INABILITY TO USE THE FONT SOFTWARE OR FROM OTHER DEALINGS IN THE FONT SOFTWARE.
|
||||
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Some files were not shown because too many files have changed in this diff Show More
Reference in New Issue
Block a user