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took out pca from week 46

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Morten Hjorth-Jensen
2022-11-19 11:33:49 +01:00
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commit 243f1d2408
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@@ -8,8 +8,8 @@ doconce format html week46.do.txt --html_style=bootstrap --pygments_html_style=d
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="DocOnce: https://github.com/doconce/doconce/" />
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
<meta name="description" content="Week 46: Support Vector Machines and Project 3. Start Principal Component Analysis">
<title>Week 46: Support Vector Machines and Project 3. Start Principal Component Analysis</title>
<meta name="description" content="Week 46: Support Vector Machines and Project 3.">
<title>Week 46: Support Vector Machines and Project 3.</title>
<!-- Bootstrap style: bootstrap -->
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<link href="https://netdna.bootstrapcdn.com/bootstrap/3.1.1/css/bootstrap.min.css" rel="stylesheet">
@@ -94,63 +94,10 @@ doconce format html week46.do.txt --html_style=bootstrap --pygments_html_style=d
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('Basic ideas of the Principal Component Analysis (PCA)',
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('More on the PCA Theorem', 2, None, 'more-on-the-pca-theorem'),
('Writing our own PCA code', 2, None, 'writing-our-own-pca-code'),
('Implementing it', 2, None, 'implementing-it'),
('First Step', 2, None, 'first-step'),
('Scaling', 2, None, 'scaling'),
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('PCA and scikit-learn', 2, None, 'pca-and-scikit-learn'),
('Back to the Cancer Data', 2, None, 'back-to-the-cancer-data'),
('Incremental PCA', 2, None, 'incremental-pca'),
('Randomized PCA', 3, None, 'randomized-pca'),
('Kernel PCA', 3, None, 'kernel-pca'),
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<body>
@@ -178,72 +125,42 @@ MathJax.Hub.Config({
<span class="icon-bar"></span>
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<a class="navbar-brand" href="week46-bs.html">Week 46: Support Vector Machines and Project 3. Start Principal Component Analysis</a>
<a class="navbar-brand" href="week46-bs.html">Week 46: Support Vector Machines and Project 3.</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#overview-of-week-46" style="font-size: 80%;"><b>Overview of week 46</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs002.html#support-vector-machines-overarching-aims" style="font-size: 80%;"><b>Support Vector Machines, overarching aims</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs003.html#hyperplanes-and-all-that" style="font-size: 80%;"><b>Hyperplanes and all that</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs004.html#what-is-a-hyperplane" style="font-size: 80%;"><b>What is a hyperplane?</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs005.html#a-p-dimensional-space-of-features" style="font-size: 80%;"><b>A \( p \)-dimensional space of features</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs006.html#the-two-dimensional-case" style="font-size: 80%;"><b>The two-dimensional case</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs007.html#getting-into-the-details" style="font-size: 80%;"><b>Getting into the details</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs008.html#first-attempt-at-a-minimization-approach" style="font-size: 80%;"><b>First attempt at a minimization approach</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs009.html#solving-the-equations" style="font-size: 80%;"><b>Solving the equations</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs010.html#code-example" style="font-size: 80%;"><b>Code Example</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs011.html#problems-with-the-simpler-approach" style="font-size: 80%;"><b>Problems with the Simpler Approach</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs012.html#a-better-approach" style="font-size: 80%;"><b>A better approach</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs013.html#a-quick-reminder-on-lagrangian-multipliers" style="font-size: 80%;"><b>A quick Reminder on Lagrangian Multipliers</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs014.html#adding-the-multiplier" style="font-size: 80%;"><b>Adding the Multiplier</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs015.html#setting-up-the-problem" style="font-size: 80%;"><b>Setting up the Problem</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs022.html#the-problem-to-solve" style="font-size: 80%;"><b>The problem to solve</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs017.html#the-last-steps" style="font-size: 80%;"><b>The last steps</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs018.html#a-soft-classifier" style="font-size: 80%;"><b>A soft classifier</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs019.html#soft-optmization-problem" style="font-size: 80%;"><b>Soft optmization problem</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs020.html#kernels-and-non-linearity" style="font-size: 80%;"><b>Kernels and non-linearity</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs021.html#the-equations" style="font-size: 80%;"><b>The equations</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs022.html#the-problem-to-solve" style="font-size: 80%;"><b>The problem to solve</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs023.html#different-kernels-and-mercer-s-theorem" style="font-size: 80%;"><b>Different kernels and Mercer's theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs024.html#the-moons-example" style="font-size: 80%;"><b>The moons example</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs025.html#mathematical-optimization-of-convex-functions" style="font-size: 80%;"><b>Mathematical optimization of convex functions</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs026.html#how-do-we-solve-these-problems" style="font-size: 80%;"><b>How do we solve these problems?</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs027.html#a-simple-example" style="font-size: 80%;"><b>A simple example</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs028.html#back-to-the-more-realistic-cases" style="font-size: 80%;"><b>Back to the more realistic cases</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs029.html#basic-ideas-of-the-principal-component-analysis-pca" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs030.html#introducing-the-covariance-and-correlation-functions" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs031.html#more-on-the-covariance" style="font-size: 80%;"><b>More on the covariance</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs032.html#reminding-ourselves-about-linear-regression" style="font-size: 80%;"><b>Reminding ourselves about Linear Regression</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs033.html#simple-example" style="font-size: 80%;"><b>Simple Example</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs034.html#the-correlation-matrix" style="font-size: 80%;"><b>The Correlation Matrix</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs035.html#numpy-functionality" style="font-size: 80%;"><b>Numpy Functionality</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs036.html#correlation-matrix-again" style="font-size: 80%;"><b>Correlation Matrix again</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs037.html#using-pandas" style="font-size: 80%;"><b>Using Pandas</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs038.html#and-then-the-franke-function" style="font-size: 80%;"><b>And then the Franke Function</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs039.html#links-with-the-design-matrix" style="font-size: 80%;"><b>Links with the Design Matrix</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs040.html#computing-the-expectation-values" style="font-size: 80%;"><b>Computing the Expectation Values</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs041.html#towards-the-pca-theorem" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs042.html#more-on-the-pca-theorem" style="font-size: 80%;"><b>More on the PCA Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs043.html#writing-our-own-pca-code" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs044.html#implementing-it" style="font-size: 80%;"><b>Implementing it</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs045.html#first-step" style="font-size: 80%;"><b>First Step</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs046.html#scaling" style="font-size: 80%;"><b>Scaling</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs047.html#centered-data" style="font-size: 80%;"><b>Centered Data</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs048.html#exploring" style="font-size: 80%;"><b>Exploring</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs049.html#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components" style="font-size: 80%;"><b>Diagonalize the sample covariance matrix to obtain the principal components</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs050.html#collecting-all-steps" style="font-size: 80%;"><b>Collecting all Steps</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs051.html#classical-pca-theorem" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs052.html#the-pca-theorem" style="font-size: 80%;"><b>The PCA Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs053.html#geometric-interpretation-and-link-with-singular-value-decomposition" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs054.html#pca-and-scikit-learn" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs055.html#back-to-the-cancer-data" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs056.html#incremental-pca" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs056.html#randomized-pca" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs056.html#kernel-pca" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs057.html#other-techniques" style="font-size: 80%;"><b>Other techniques</b></a></li>
<!-- navigation toc: --> <li><a href="._week46-bs001.html#overview-of-week-46" style="font-size: 80%;">Overview of week 46</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs002.html#support-vector-machines-overarching-aims" style="font-size: 80%;">Support Vector Machines, overarching aims</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs003.html#hyperplanes-and-all-that" style="font-size: 80%;">Hyperplanes and all that</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs004.html#what-is-a-hyperplane" style="font-size: 80%;">What is a hyperplane?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs005.html#a-p-dimensional-space-of-features" style="font-size: 80%;">A \( p \)-dimensional space of features</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs006.html#the-two-dimensional-case" style="font-size: 80%;">The two-dimensional case</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs007.html#getting-into-the-details" style="font-size: 80%;">Getting into the details</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs008.html#first-attempt-at-a-minimization-approach" style="font-size: 80%;">First attempt at a minimization approach</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs009.html#solving-the-equations" style="font-size: 80%;">Solving the equations</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs010.html#code-example" style="font-size: 80%;">Code Example</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs011.html#problems-with-the-simpler-approach" style="font-size: 80%;">Problems with the Simpler Approach</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs012.html#a-better-approach" style="font-size: 80%;">A better approach</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs013.html#a-quick-reminder-on-lagrangian-multipliers" style="font-size: 80%;">A quick Reminder on Lagrangian Multipliers</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs014.html#adding-the-multiplier" style="font-size: 80%;">Adding the Multiplier</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs015.html#setting-up-the-problem" style="font-size: 80%;">Setting up the Problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs022.html#the-problem-to-solve" style="font-size: 80%;">The problem to solve</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs017.html#the-last-steps" style="font-size: 80%;">The last steps</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs018.html#a-soft-classifier" style="font-size: 80%;">A soft classifier</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs019.html#soft-optmization-problem" style="font-size: 80%;">Soft optmization problem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs020.html#kernels-and-non-linearity" style="font-size: 80%;">Kernels and non-linearity</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs021.html#the-equations" style="font-size: 80%;">The equations</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs022.html#the-problem-to-solve" style="font-size: 80%;">The problem to solve</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs023.html#different-kernels-and-mercer-s-theorem" style="font-size: 80%;">Different kernels and Mercer's theorem</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs024.html#the-moons-example" style="font-size: 80%;">The moons example</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs025.html#mathematical-optimization-of-convex-functions" style="font-size: 80%;">Mathematical optimization of convex functions</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs026.html#how-do-we-solve-these-problems" style="font-size: 80%;">How do we solve these problems?</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs027.html#a-simple-example" style="font-size: 80%;">A simple example</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs028.html#back-to-the-more-realistic-cases" style="font-size: 80%;">Back to the more realistic cases</a></li>
<!-- navigation toc: --> <li><a href="._week46-bs029.html#support-vector-machines-for-regression" style="font-size: 80%;">Support vector machines for regression</a></li>
</ul>
</li>
@@ -257,7 +174,7 @@ MathJax.Hub.Config({
<!-- ------------------- main content ---------------------- -->
<div class="jumbotron">
<center>
<h1>Week 46: Support Vector Machines and Project 3. Start Principal Component Analysis</h1>
<h1>Week 46: Support Vector Machines and Project 3. </h1>
</center> <!-- document title -->
<!-- author(s): Morten Hjorth-Jensen -->
@@ -273,7 +190,7 @@ MathJax.Hub.Config({
</center>
<br>
<center>
<h4>Nov 18, 2022</h4>
<h4>Nov 19, 2022</h4>
</center> <!-- date -->
<br>
@@ -298,7 +215,7 @@ MathJax.Hub.Config({
<li><a href="._week46-bs008.html">9</a></li>
<li><a href="._week46-bs009.html">10</a></li>
<li><a href="">...</a></li>
<li><a href="._week46-bs057.html">58</a></li>
<li><a href="._week46-bs029.html">30</a></li>
<li><a href="._week46-bs001.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->