mhjensen
256 lines
11 KiB
HTML
256 lines
11 KiB
HTML
<!--
|
|
Automatically generated HTML file from DocOnce source
|
|
(https://github.com/hplgit/doconce/)
|
|
-->
|
|
<html>
|
|
<head>
|
|
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
|
|
<meta name="generator" content="DocOnce: https://github.com/hplgit/doconce/" />
|
|
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
|
|
<meta name="description" content="Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction">
|
|
|
|
<title>Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction</title>
|
|
|
|
<!-- Bootstrap style: bootstrap -->
|
|
<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
|
|
<!-- not necessary
|
|
<link href="https://netdna.bootstrapcdn.com/font-awesome/4.0.3/css/font-awesome.css" rel="stylesheet">
|
|
-->
|
|
|
|
<style type="text/css">
|
|
|
|
/* Add scrollbar to dropdown menus in bootstrap navigation bar */
|
|
.dropdown-menu {
|
|
height: auto;
|
|
max-height: 400px;
|
|
overflow-x: hidden;
|
|
}
|
|
|
|
/* Adds an invisible element before each target to offset for the navigation
|
|
bar */
|
|
.anchor::before {
|
|
content:"";
|
|
display:block;
|
|
height:50px; /* fixed header height for style bootstrap */
|
|
margin:-50px 0 0; /* negative fixed header height */
|
|
}
|
|
</style>
|
|
|
|
|
|
</head>
|
|
|
|
<!-- tocinfo
|
|
{'highest level': 2,
|
|
'sections': [('Reducing the number of degrees of freedom, overarching view',
|
|
2,
|
|
None,
|
|
'___sec0'),
|
|
('Preprocessing our data', 2, None, '___sec1'),
|
|
('More preprocessing', 2, None, '___sec2'),
|
|
('Simple preprocessing examples, Franke function and regression',
|
|
2,
|
|
None,
|
|
'___sec3'),
|
|
('Simple preprocessing examples, breast cancer data and '
|
|
'classification, Support Vector Machines',
|
|
2,
|
|
None,
|
|
'___sec4'),
|
|
('More on Cancer Data, now with Logistic Regression',
|
|
2,
|
|
None,
|
|
'___sec5'),
|
|
('Why should we think of reducing the dimensionality',
|
|
2,
|
|
None,
|
|
'___sec6'),
|
|
('Basic ideas of the Principal Component Analysis (PCA)',
|
|
2,
|
|
None,
|
|
'___sec7'),
|
|
('Introducing the Covariance and Correlation functions',
|
|
2,
|
|
None,
|
|
'___sec8'),
|
|
('Correlation Function and Design/Feature Matrix',
|
|
2,
|
|
None,
|
|
'___sec9'),
|
|
('Covariance Matrix Examples', 2, None, '___sec10'),
|
|
('Correlation Matrix', 2, None, '___sec11'),
|
|
('Correlation Matrix with Pandas', 2, None, '___sec12'),
|
|
('Correlation Matrix with Pandas and the Franke function',
|
|
2,
|
|
None,
|
|
'___sec13'),
|
|
('Rewriting the Covariance and/or Correlation Matrix',
|
|
2,
|
|
None,
|
|
'___sec14'),
|
|
('Towards the PCA theorem', 2, None, '___sec15'),
|
|
('The Algorithm before the Theorem', 2, None, '___sec16'),
|
|
('Classical PCA Theorem', 2, None, '___sec17'),
|
|
('Proof of the PCA Theorem', 2, None, '___sec18'),
|
|
('PCA Proof continued', 2, None, '___sec19'),
|
|
('The final step', 2, None, '___sec20'),
|
|
('PCA and Scikit-Learn Functionality', 2, None, '___sec21'),
|
|
('Principal Component Analysis', 2, None, '___sec22'),
|
|
('PCA and scikit-learn', 2, None, '___sec23'),
|
|
('More on the PCA', 2, None, '___sec24'),
|
|
('Incremental PCA', 2, None, '___sec25'),
|
|
('Randomized PCA', 2, None, '___sec26'),
|
|
('Kernel PCA', 2, None, '___sec27'),
|
|
('LLE', 2, None, '___sec28'),
|
|
('Other techniques', 2, None, '___sec29')]}
|
|
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="DimRed-bs.html">Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction</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="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">More preprocessing</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">Why should we think of reducing the dimensionality</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Basic ideas of the Principal Component Analysis (PCA)</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Introducing the Covariance and Correlation functions</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Correlation Function and Design/Feature Matrix</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Covariance Matrix Examples</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Correlation Matrix</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Correlation Matrix with Pandas</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs014.html#___sec13" style="font-size: 80%;">Correlation Matrix with Pandas and the Franke function</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs015.html#___sec14" style="font-size: 80%;">Rewriting the Covariance and/or Correlation Matrix</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs016.html#___sec15" style="font-size: 80%;">Towards the PCA theorem</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs017.html#___sec16" style="font-size: 80%;">The Algorithm before the Theorem</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs018.html#___sec17" style="font-size: 80%;">Classical PCA Theorem</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs019.html#___sec18" style="font-size: 80%;">Proof of the PCA Theorem</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs020.html#___sec19" style="font-size: 80%;">PCA Proof continued</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs021.html#___sec20" style="font-size: 80%;">The final step</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs022.html#___sec21" style="font-size: 80%;">PCA and Scikit-Learn Functionality</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">Principal Component Analysis</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">More on the PCA</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Incremental PCA</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Randomized PCA</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">Kernel PCA</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">LLE</a></li>
|
|
<!-- navigation toc: --> <li><a href="._DimRed-bs030.html#___sec29" style="font-size: 80%;">Other techniques</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="part0000"></a>
|
|
<!-- ------------------- main content ---------------------- -->
|
|
|
|
|
|
|
|
<div class="jumbotron">
|
|
<center><h1>Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction</h1></center> <!-- document title -->
|
|
|
|
<p>
|
|
<!-- author(s): Morten Hjorth-Jensen -->
|
|
|
|
<center>
|
|
<b>Morten Hjorth-Jensen</b> [1, 2]
|
|
</center>
|
|
|
|
<p>
|
|
<!-- institution(s) -->
|
|
|
|
<center>[1] <b>Department of Physics, University of Oslo</b></center>
|
|
<center>[2] <b>Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory, Michigan State University</b></center>
|
|
<br>
|
|
<p>
|
|
<center><h4>Oct 24, 2019</h4></center> <!-- date -->
|
|
<br>
|
|
<p>
|
|
|
|
|
|
<p><a href="._DimRed-bs001.html" class="btn btn-primary btn-lg">Read »</a></p>
|
|
|
|
|
|
</div> <!-- end jumbotron -->
|
|
|
|
<p>
|
|
<!-- navigation buttons at the bottom of the page -->
|
|
<ul class="pagination">
|
|
<li class="active"><a href="._DimRed-bs000.html">1</a></li>
|
|
<li><a href="._DimRed-bs001.html">2</a></li>
|
|
<li><a href="._DimRed-bs002.html">3</a></li>
|
|
<li><a href="._DimRed-bs003.html">4</a></li>
|
|
<li><a href="._DimRed-bs004.html">5</a></li>
|
|
<li><a href="._DimRed-bs005.html">6</a></li>
|
|
<li><a href="._DimRed-bs006.html">7</a></li>
|
|
<li><a href="._DimRed-bs007.html">8</a></li>
|
|
<li><a href="._DimRed-bs008.html">9</a></li>
|
|
<li><a href="._DimRed-bs009.html">10</a></li>
|
|
<li><a href="">...</a></li>
|
|
<li><a href="._DimRed-bs030.html">31</a></li>
|
|
<li><a href="._DimRed-bs001.html">»</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 --> © 1999-2019, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license
|
|
</center>
|
|
|
|
|
|
</body>
|
|
</html>
|
|
|
|
|