update book
This commit is contained in:
Morten Hjorth-Jensen
@@ -7,8 +7,8 @@
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1.0" />
|
||||
<title>11. Basic ideas of the Principal Component Analysis (PCA) — Applied Data Analysis and Machine Learning</title>
|
||||
|
||||
<link href="_static/css/theme.css" rel="stylesheet" />
|
||||
<link href="_static/css/index.c5995385ac14fb8791e8eb36b4908be2.css" rel="stylesheet" />
|
||||
<link href="_static/css/theme.css" rel="stylesheet">
|
||||
<link href="_static/css/index.ff1ffe594081f20da1ef19478df9384b.css" rel="stylesheet">
|
||||
|
||||
|
||||
<link rel="stylesheet"
|
||||
@@ -31,7 +31,7 @@
|
||||
<link rel="stylesheet" type="text/css" href="_static/panels-main.c949a650a448cc0ae9fd3441c0e17fb0.css" />
|
||||
<link rel="stylesheet" type="text/css" href="_static/panels-variables.06eb56fa6e07937060861dad626602ad.css" />
|
||||
|
||||
<link rel="preload" as="script" href="_static/js/index.1c5a1a01449ed65a7b51.js">
|
||||
<link rel="preload" as="script" href="_static/js/index.be7d3bbb2ef33a8344ce.js">
|
||||
|
||||
<script data-url_root="./" id="documentation_options" src="_static/documentation_options.js"></script>
|
||||
<script src="_static/jquery.js"></script>
|
||||
@@ -41,22 +41,24 @@
|
||||
<script src="_static/clipboard.min.js"></script>
|
||||
<script src="_static/copybutton.js"></script>
|
||||
<script>var togglebuttonSelector = '.toggle, .admonition.dropdown, .tag_hide_input div.cell_input, .tag_hide-input div.cell_input, .tag_hide_output div.cell_output, .tag_hide-output div.cell_output, .tag_hide_cell.cell, .tag_hide-cell.cell';</script>
|
||||
<script src="_static/sphinx-book-theme.12a9622fbb08dcb3a2a40b2c02b83a57.js"></script>
|
||||
<script async="async" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||||
<script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
|
||||
<script async="async" src="https://unpkg.com/thebe@0.5.1/lib/index.js"></script>
|
||||
<script>
|
||||
const thebe_selector = ".thebe"
|
||||
const thebe_selector_input = "pre"
|
||||
const thebe_selector_output = ".output"
|
||||
</script>
|
||||
<script src="_static/sphinx-book-theme.d59cb220de22ca1c485ebbdc042f0030.js"></script>
|
||||
<script>const THEBE_JS_URL = "https://unpkg.com/thebe@0.8.2/lib/index.js"
|
||||
const thebe_selector = ".thebe,.cell"
|
||||
const thebe_selector_input = "pre"
|
||||
const thebe_selector_output = ".output, .cell_output"
|
||||
</script>
|
||||
<script async="async" src="_static/sphinx-thebe.js"></script>
|
||||
<script defer="defer" src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js"></script>
|
||||
<script>window.MathJax = {"options": {"processHtmlClass": "tex2jax_process|mathjax_process|math|output_area"}}</script>
|
||||
<link rel="index" title="Index" href="genindex.html" />
|
||||
<link rel="search" title="Search" href="search.html" />
|
||||
<link rel="next" title="12. Neural networks" href="chapter9.html" />
|
||||
<link rel="next" title="12. Clustering and Unsupervised Learning" href="clustering.html" />
|
||||
<link rel="prev" title="10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods" href="chapter7.html" />
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||
<meta name="docsearch:language" content="en" />
|
||||
<meta name="docsearch:language" content="None">
|
||||
|
||||
|
||||
<!-- Google Analytics -->
|
||||
|
||||
</head>
|
||||
<body data-spy="scroll" data-target="#bd-toc-nav" data-offset="80">
|
||||
@@ -91,11 +93,11 @@
|
||||
<ul class="nav bd-sidenav">
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="intro.html">
|
||||
Applied Data Analysis and Machine Learning, FYS-STK3155/4155 at the University of Oslo, Norway
|
||||
Applied Data Analysis and Machine Learning
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p class="caption" role="heading">
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
About the course
|
||||
</span>
|
||||
@@ -117,7 +119,7 @@
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p class="caption" role="heading">
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
Review of Statistics with Resampling Techniques and Linear Algebra
|
||||
</span>
|
||||
@@ -134,7 +136,7 @@
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p class="caption" role="heading">
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
From Regression to Support Vector Machines
|
||||
</span>
|
||||
@@ -171,7 +173,7 @@
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p class="caption" role="heading">
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
Decision Trees, Ensemble Methods and Boosting
|
||||
</span>
|
||||
@@ -188,7 +190,7 @@
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p class="caption" role="heading">
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
Dimensionality Reduction
|
||||
</span>
|
||||
@@ -199,8 +201,13 @@
|
||||
11. Basic ideas of the Principal Component Analysis (PCA)
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="clustering.html">
|
||||
12. Clustering and Unsupervised Learning
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
<p class="caption" role="heading">
|
||||
<p aria-level="2" class="caption" role="heading">
|
||||
<span class="caption-text">
|
||||
Deep Learning Methods
|
||||
</span>
|
||||
@@ -208,17 +215,27 @@
|
||||
<ul class="nav bd-sidenav">
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="chapter9.html">
|
||||
12. Neural networks
|
||||
13. Neural networks
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="chapter10.html">
|
||||
13. Building a Feed Forward Neural Network
|
||||
14. Building a Feed Forward Neural Network
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="chapter11.html">
|
||||
14. Solving Differential Equations with Deep Learning
|
||||
15. Solving Differential Equations with Deep Learning
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="chapter12.html">
|
||||
16. Convolutional Neural Networks
|
||||
</a>
|
||||
</li>
|
||||
<li class="toctree-l1">
|
||||
<a class="reference internal" href="chapter13.html">
|
||||
17. Recurrent neural networks: Overarching view
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
@@ -267,7 +284,7 @@
|
||||
data-placement="left">.ipynb</button></a>
|
||||
<!-- Download PDF via print -->
|
||||
<button type="button" id="download-print" class="btn btn-secondary topbarbtn" title="Print to PDF"
|
||||
onClick="window.print()" data-toggle="tooltip" data-placement="left">.pdf</button>
|
||||
onclick="printPdf(this)" data-toggle="tooltip" data-placement="left">.pdf</button>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
@@ -285,7 +302,7 @@
|
||||
</div>
|
||||
|
||||
<!-- Table of contents -->
|
||||
<div class="d-none d-md-block col-md-2 bd-toc show">
|
||||
<div class="d-none d-md-block col-md-2 bd-toc show noprint">
|
||||
|
||||
<div class="tocsection onthispage pt-5 pb-3">
|
||||
<i class="fas fa-list"></i> Contents
|
||||
@@ -374,7 +391,99 @@
|
||||
</div>
|
||||
<div id="main-content" class="row">
|
||||
<div class="col-12 col-md-9 pl-md-3 pr-md-0">
|
||||
|
||||
<!-- Table of contents that is only displayed when printing the page -->
|
||||
<div id="jb-print-docs-body" class="onlyprint">
|
||||
<h1>Basic ideas of the Principal Component Analysis (PCA)</h1>
|
||||
<!-- Table of contents -->
|
||||
<div id="print-main-content">
|
||||
<div id="jb-print-toc">
|
||||
|
||||
<div>
|
||||
<h2> Contents </h2>
|
||||
</div>
|
||||
<nav aria-label="Page">
|
||||
<ul class="visible nav section-nav flex-column">
|
||||
<li class="toc-h2 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#introducing-the-covariance-and-correlation-functions">
|
||||
11.1. Introducing the Covariance and Correlation functions
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h2 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#correlation-matrix">
|
||||
11.2. Correlation Matrix
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h2 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#towards-the-pca-theorem">
|
||||
11.3. Towards the PCA theorem
|
||||
</a>
|
||||
<ul class="nav section-nav flex-column">
|
||||
<li class="toc-h3 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#the-algorithm-before-theorem">
|
||||
11.3.1. The Algorithm before theorem
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h3 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#writing-our-own-pca-code">
|
||||
11.3.2. Writing our own PCA code
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h3 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components">
|
||||
11.3.3. Diagonalize the sample covariance matrix to obtain the principal components
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-h2 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#classical-pca-theorem">
|
||||
11.4. Classical PCA Theorem
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h2 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#geometric-interpretation-and-link-with-singular-value-decomposition">
|
||||
11.5. Geometric Interpretation and link with Singular Value Decomposition
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h2 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#pca-and-scikit-learn">
|
||||
11.6. PCA and scikit-learn
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h2 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#back-to-the-cancer-data">
|
||||
11.7. Back to the Cancer Data
|
||||
</a>
|
||||
<ul class="nav section-nav flex-column">
|
||||
<li class="toc-h3 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#incremental-pca">
|
||||
11.7.1. Incremental PCA
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h3 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#randomized-pca">
|
||||
11.7.2. Randomized PCA
|
||||
</a>
|
||||
</li>
|
||||
<li class="toc-h3 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#kernel-pca">
|
||||
11.7.3. Kernel PCA
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
</li>
|
||||
<li class="toc-h2 nav-item toc-entry">
|
||||
<a class="reference internal nav-link" href="#other-techniques">
|
||||
11.8. Other techniques
|
||||
</a>
|
||||
</li>
|
||||
</ul>
|
||||
|
||||
</nav>
|
||||
</div>
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<div>
|
||||
|
||||
<div class="tex2jax_ignore mathjax_ignore section" id="basic-ideas-of-the-principal-component-analysis-pca">
|
||||
@@ -530,10 +639,10 @@ covariance matrix through the <strong>np.linalg.eig()</strong> function.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.0358909447132981
|
||||
4.176880142835407
|
||||
[[ 1.09297039 3.38901478]
|
||||
[ 3.38901478 11.48089797]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.03382304823545749
|
||||
4.021250026482402
|
||||
[[0.9252772 2.69061276]
|
||||
[2.69061276 8.90540529]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -573,10 +682,10 @@ a more brute force way. Here we scale the mean values for each column of the des
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.10044225464078282
|
||||
2.1586300629904382
|
||||
[[1. 0.72373129]
|
||||
[0.72373129 1. ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>0.08328216846752691
|
||||
2.094472507965532
|
||||
[[1. 0.67697934]
|
||||
[0.67697934 1. ]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -605,30 +714,30 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
</div>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[-0.50416731 -0.8962476 ]
|
||||
[-1.00198806 -2.48687342]
|
||||
[-0.14988578 -0.24485843]
|
||||
[ 1.33327369 3.92754397]
|
||||
[ 0.47531107 0.66818635]
|
||||
[-0.03278964 -1.08041015]
|
||||
[-0.32992274 1.59591979]
|
||||
[-1.06160438 -3.85324115]
|
||||
[ 0.4644244 1.36689784]
|
||||
[ 0.80734875 1.0030828 ]]
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>[[ 2.38295101 5.51289697]
|
||||
[ 0.51803019 2.61399851]
|
||||
[-1.09849763 -1.02255619]
|
||||
[-0.54016188 -0.53794784]
|
||||
[ 0.28634473 1.32721178]
|
||||
[-1.66619972 -6.88017651]
|
||||
[ 1.52811546 4.29512284]
|
||||
[ 0.427017 2.43493232]
|
||||
[-0.80842254 -4.37964744]
|
||||
[-1.02917662 -3.36383443]]
|
||||
0 1
|
||||
0 -0.504167 -0.896248
|
||||
1 -1.001988 -2.486873
|
||||
2 -0.149886 -0.244858
|
||||
3 1.333274 3.927544
|
||||
4 0.475311 0.668186
|
||||
5 -0.032790 -1.080410
|
||||
6 -0.329923 1.595920
|
||||
7 -1.061604 -3.853241
|
||||
8 0.464424 1.366898
|
||||
9 0.807349 1.003083
|
||||
0 2.382951 5.512897
|
||||
1 0.518030 2.613999
|
||||
2 -1.098498 -1.022556
|
||||
3 -0.540162 -0.537948
|
||||
4 0.286345 1.327212
|
||||
5 -1.666200 -6.880177
|
||||
6 1.528115 4.295123
|
||||
7 0.427017 2.434932
|
||||
8 -0.808423 -4.379647
|
||||
9 -1.029177 -3.363834
|
||||
0 1
|
||||
0 1.000000 0.878297
|
||||
1 0.878297 1.000000
|
||||
0 1.000000 0.930583
|
||||
1 0.930583 1.000000
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -685,37 +794,37 @@ this matrix we easily see that it is a positive definite matrix.</p>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1 2 3 4 5 6 7 \
|
||||
0 0.0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.0 0.068937 0.073016 0.069091 0.070612 0.071705 0.061898 0.062451
|
||||
2 0.0 0.073016 0.079839 0.075573 0.078253 0.080256 0.068659 0.069754
|
||||
3 0.0 0.069091 0.075573 0.074488 0.077022 0.078911 0.069912 0.070911
|
||||
4 0.0 0.070612 0.078253 0.077022 0.080106 0.082451 0.072620 0.073907
|
||||
5 0.0 0.071705 0.080256 0.078911 0.082451 0.085185 0.074666 0.076204
|
||||
6 0.0 0.061898 0.068659 0.069912 0.072620 0.074666 0.067714 0.068809
|
||||
7 0.0 0.062451 0.069754 0.070911 0.073907 0.076204 0.068809 0.070071
|
||||
8 0.0 0.062884 0.070635 0.071698 0.074945 0.077467 0.069672 0.071086
|
||||
9 0.0 0.063250 0.071387 0.072348 0.075820 0.078548 0.070379 0.071935
|
||||
10 0.0 0.054585 0.060841 0.063657 0.066194 0.068120 0.063078 0.064108
|
||||
11 0.0 0.054785 0.061321 0.064052 0.066753 0.068831 0.063513 0.064648
|
||||
12 0.0 0.054963 0.061745 0.064384 0.067236 0.069455 0.063872 0.065106
|
||||
13 0.0 0.055137 0.062142 0.064681 0.067675 0.070028 0.064184 0.065514
|
||||
14 0.0 0.055320 0.062534 0.064964 0.068094 0.070576 0.064469 0.065892
|
||||
1 0.0 0.086074 0.080593 0.088526 0.083276 0.078269 0.081046 0.076604
|
||||
2 0.0 0.080593 0.076130 0.082896 0.078254 0.073810 0.076216 0.072216
|
||||
3 0.0 0.088526 0.082896 0.096472 0.091051 0.085879 0.091696 0.086956
|
||||
4 0.0 0.083276 0.078254 0.091051 0.086112 0.081388 0.086890 0.082536
|
||||
5 0.0 0.078269 0.073810 0.085879 0.081388 0.077083 0.082295 0.078299
|
||||
6 0.0 0.081046 0.076216 0.091696 0.086890 0.082295 0.089501 0.085163
|
||||
7 0.0 0.076604 0.072216 0.086956 0.082536 0.078299 0.085163 0.081144
|
||||
8 0.0 0.072442 0.068461 0.082503 0.078436 0.074530 0.081072 0.077349
|
||||
9 0.0 0.068538 0.064931 0.078314 0.074573 0.070972 0.077211 0.073761
|
||||
10 0.0 0.073062 0.069085 0.084862 0.080738 0.076780 0.084484 0.080647
|
||||
11 0.0 0.069275 0.065641 0.080706 0.076895 0.073230 0.080582 0.077013
|
||||
12 0.0 0.065730 0.062411 0.076804 0.073280 0.069884 0.076905 0.073583
|
||||
13 0.0 0.062409 0.059378 0.073136 0.069877 0.066729 0.073436 0.070343
|
||||
14 0.0 0.059294 0.056528 0.069685 0.066670 0.063752 0.070163 0.067282
|
||||
|
||||
8 9 10 11 12 13 14
|
||||
0 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
|
||||
1 0.062884 0.063250 0.054585 0.054785 0.054963 0.055137 0.055320
|
||||
2 0.070635 0.071387 0.060841 0.061321 0.061745 0.062142 0.062534
|
||||
3 0.071698 0.072348 0.063657 0.064052 0.064384 0.064681 0.064964
|
||||
4 0.074945 0.075820 0.066194 0.066753 0.067236 0.067675 0.068094
|
||||
5 0.077467 0.078548 0.068120 0.068831 0.069455 0.070028 0.070576
|
||||
6 0.069672 0.070379 0.063078 0.063513 0.063872 0.064184 0.064469
|
||||
7 0.071086 0.071935 0.064108 0.064648 0.065106 0.065514 0.065892
|
||||
8 0.072242 0.073225 0.064918 0.065557 0.066110 0.066609 0.067079
|
||||
9 0.073225 0.074336 0.065575 0.066309 0.066954 0.067544 0.068103
|
||||
10 0.064918 0.065575 0.059783 0.060183 0.060507 0.060781 0.061025
|
||||
11 0.065557 0.066309 0.060183 0.060655 0.061048 0.061390 0.061701
|
||||
12 0.066110 0.066954 0.060507 0.061048 0.061509 0.061917 0.062294
|
||||
13 0.066609 0.067544 0.060781 0.061390 0.061917 0.062391 0.062834
|
||||
14 0.067079 0.068103 0.061025 0.061701 0.062294 0.062834 0.063343
|
||||
1 0.072442 0.068538 0.073062 0.069275 0.065730 0.062409 0.059294
|
||||
2 0.068461 0.064931 0.069085 0.065641 0.062411 0.059378 0.056528
|
||||
3 0.082503 0.078314 0.084862 0.080706 0.076804 0.073136 0.069685
|
||||
4 0.078436 0.074573 0.080738 0.076895 0.073280 0.069877 0.066670
|
||||
5 0.074530 0.070972 0.076780 0.073230 0.069884 0.066729 0.063752
|
||||
6 0.081072 0.077211 0.084484 0.080582 0.076905 0.073436 0.070163
|
||||
7 0.077349 0.073761 0.080647 0.077013 0.073583 0.070343 0.067282
|
||||
8 0.073827 0.070492 0.077015 0.073629 0.070429 0.067402 0.064538
|
||||
9 0.070492 0.067392 0.073575 0.070419 0.067432 0.064604 0.061923
|
||||
10 0.077015 0.073575 0.080984 0.077452 0.074111 0.070950 0.067956
|
||||
11 0.073629 0.070419 0.077452 0.074149 0.071022 0.068059 0.065249
|
||||
12 0.070429 0.067432 0.074111 0.071022 0.068093 0.065314 0.062676
|
||||
13 0.067402 0.064604 0.070950 0.068059 0.065314 0.062706 0.060228
|
||||
14 0.064538 0.061923 0.067956 0.065249 0.062676 0.060228 0.057899
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -904,10 +1013,10 @@ We can write our own code or simply use either the functionaly of <strong>numpy<
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span> 0 1
|
||||
0 3.947903 1.993972
|
||||
1 1.993972 1.993535
|
||||
[[3.94790323 1.99397245]
|
||||
[1.99397245 1.99353454]]
|
||||
0 4.038506 2.027865
|
||||
1 2.027865 2.037559
|
||||
[[4.03850557 2.02786488]
|
||||
[2.02786488 2.03755944]]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -934,8 +1043,8 @@ Our own code here is not very elegant and asks for obvious improvements. It is t
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Centered covariance using own code
|
||||
[[3.94790323 1.99397245]
|
||||
[1.99397245 1.99353454]]
|
||||
[[4.03850557 2.02786488]
|
||||
[2.02786488 2.03755944]]
|
||||
</pre></div>
|
||||
</div>
|
||||
<img alt="_images/chapter8_65_1.png" src="_images/chapter8_65_1.png" />
|
||||
@@ -995,16 +1104,16 @@ questions.</p>
|
||||
</div>
|
||||
<div class="cell_output docutils container">
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvalues of Covariance matrix
|
||||
5.191262820314401
|
||||
0.7501749450963715
|
||||
5.299267190588216
|
||||
0.7767978193240488
|
||||
First eigenvector
|
||||
[0.84854738 0.52911941]
|
||||
[0.84924834 0.52799362]
|
||||
Second eigenvector
|
||||
[-0.52911941 0.84854738]
|
||||
[-0.52799362 0.84924834]
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stream highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>Eigenvector of largest eigenvalue
|
||||
[-0.84854738 -0.52911941]
|
||||
[0.84924834 0.52799362]
|
||||
</pre></div>
|
||||
</div>
|
||||
</div>
|
||||
@@ -1349,7 +1458,7 @@ Train set accuracy scaled data: 0.99
|
||||
Train set accuracy scaled and PCA data: 0.96
|
||||
</pre></div>
|
||||
</div>
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/MortenImac/anaconda3/lib/python3.8/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
|
||||
<div class="output stderr highlight-myst-ansi notranslate"><div class="highlight"><pre><span></span>/Users/mhjensen/miniforge3/envs/myenv/lib/python3.9/site-packages/sklearn/linear_model/_logistic.py:814: ConvergenceWarning: lbfgs failed to converge (status=1):
|
||||
STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.
|
||||
|
||||
Increase the number of iterations (max_iter) or scale the data as shown in:
|
||||
@@ -1461,54 +1570,42 @@ For example, the following code uses Scikit-Learn’s KernelPCA class to perform
|
||||
|
||||
</div>
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
<div class='prev-next-bottom'>
|
||||
|
||||
<div id="prev">
|
||||
<a class="left-prev" href="chapter7.html" title="previous page">
|
||||
<i class="prevnext-label fas fa-angle-left"></i>
|
||||
<div class="prevnext-info">
|
||||
<p class="prevnext-label">previous</p>
|
||||
<p class="prevnext-title"><span class="section-number">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</p>
|
||||
</div>
|
||||
</a>
|
||||
<!-- Previous / next buttons -->
|
||||
<div class='prev-next-area'>
|
||||
<a class='left-prev' id="prev-link" href="chapter7.html" title="previous page">
|
||||
<i class="fas fa-angle-left"></i>
|
||||
<div class="prev-next-info">
|
||||
<p class="prev-next-subtitle">previous</p>
|
||||
<p class="prev-next-title"><span class="section-number">10. </span>Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods</p>
|
||||
</div>
|
||||
</a>
|
||||
<a class='right-next' id="next-link" href="clustering.html" title="next page">
|
||||
<div class="prev-next-info">
|
||||
<p class="prev-next-subtitle">next</p>
|
||||
<p class="prev-next-title"><span class="section-number">12. </span>Clustering and Unsupervised Learning</p>
|
||||
</div>
|
||||
<div id="next">
|
||||
<a class="right-next" href="chapter9.html" title="next page">
|
||||
<div class="prevnext-info">
|
||||
<p class="prevnext-label">next</p>
|
||||
<p class="prevnext-title"><span class="section-number">12. </span>Neural networks</p>
|
||||
</div>
|
||||
<i class="prevnext-label fas fa-angle-right"></i>
|
||||
</a>
|
||||
</div>
|
||||
|
||||
<i class="fas fa-angle-right"></i>
|
||||
</a>
|
||||
</div>
|
||||
|
||||
|
||||
</div>
|
||||
</div>
|
||||
<footer class="footer">
|
||||
<div class="container">
|
||||
<p>
|
||||
|
||||
By Morten Hjorth-Jensen<br/>
|
||||
|
||||
© Copyright 2021.<br/>
|
||||
</p>
|
||||
</div>
|
||||
</footer>
|
||||
<p>
|
||||
|
||||
By Morten Hjorth-Jensen<br/>
|
||||
|
||||
© Copyright 2021.<br/>
|
||||
</p>
|
||||
</footer>
|
||||
</main>
|
||||
|
||||
|
||||
</div>
|
||||
</div>
|
||||
|
||||
<script src="_static/js/index.1c5a1a01449ed65a7b51.js"></script>
|
||||
<script src="_static/js/index.be7d3bbb2ef33a8344ce.js"></script>
|
||||
|
||||
|
||||
</body>
|
||||
</html>
|
||||
Reference in New Issue
Block a user