updated schedule with video
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Morten Hjorth-Jensen
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<title>11. Basic ideas of the Principal Component Analysis (PCA) — Applied Data Analysis and Machine Learning</title>
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<p aria-level="2" class="caption" role="heading">
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<p class="caption" role="heading">
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<span class="caption-text">
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About the course
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<p aria-level="2" class="caption" role="heading">
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<p class="caption" role="heading">
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<span class="caption-text">
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Review of Statistics with Resampling Techniques and Linear Algebra
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</span>
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</a>
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<p aria-level="2" class="caption" role="heading">
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<p class="caption" role="heading">
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<span class="caption-text">
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From Regression to Support Vector Machines
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</span>
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</a>
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<p aria-level="2" class="caption" role="heading">
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<p class="caption" role="heading">
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<span class="caption-text">
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Decision Trees, Ensemble Methods and Boosting
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<p class="caption" role="heading">
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<span class="caption-text">
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Dimensionality Reduction
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<p aria-level="2" class="caption" role="heading">
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<p class="caption" role="heading">
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<span class="caption-text">
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Deep Learning Methods
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</span>
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data-placement="left">.ipynb</button></a>
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</div>
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<!-- Table of contents -->
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<div class="d-none d-md-block col-md-2 bd-toc show">
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<div class="tocsection onthispage pt-5 pb-3">
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<i class="fas fa-list"></i> Contents
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</div>
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<div id="main-content" class="row">
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<div class="col-12 col-md-9 pl-md-3 pr-md-0">
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<!-- Table of contents that is only displayed when printing the page -->
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<div id="jb-print-docs-body" class="onlyprint">
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<h1>Basic ideas of the Principal Component Analysis (PCA)</h1>
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<!-- Table of contents -->
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<div id="jb-print-toc">
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<div>
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<h2> Contents </h2>
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</div>
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<nav aria-label="Page">
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<ul class="visible nav section-nav flex-column">
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#introducing-the-covariance-and-correlation-functions">
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11.1. Introducing the Covariance and Correlation functions
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</a>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#correlation-matrix">
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11.2. Correlation Matrix
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</a>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#towards-the-pca-theorem">
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11.3. Towards the PCA theorem
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</a>
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<ul class="nav section-nav flex-column">
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<li class="toc-h3 nav-item toc-entry">
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<a class="reference internal nav-link" href="#the-algorithm-before-theorem">
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11.3.1. The Algorithm before theorem
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</a>
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</li>
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<li class="toc-h3 nav-item toc-entry">
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<a class="reference internal nav-link" href="#writing-our-own-pca-code">
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11.3.2. Writing our own PCA code
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</a>
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</li>
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<li class="toc-h3 nav-item toc-entry">
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<a class="reference internal nav-link" href="#diagonalize-the-sample-covariance-matrix-to-obtain-the-principal-components">
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11.3.3. Diagonalize the sample covariance matrix to obtain the principal components
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</a>
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</li>
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</ul>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#classical-pca-theorem">
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11.4. Classical PCA Theorem
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</a>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#geometric-interpretation-and-link-with-singular-value-decomposition">
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11.5. Geometric Interpretation and link with Singular Value Decomposition
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</a>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#pca-and-scikit-learn">
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11.6. PCA and scikit-learn
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</a>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#back-to-the-cancer-data">
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11.7. Back to the Cancer Data
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</a>
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<ul class="nav section-nav flex-column">
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<li class="toc-h3 nav-item toc-entry">
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<a class="reference internal nav-link" href="#incremental-pca">
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11.7.1. Incremental PCA
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</a>
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</li>
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<li class="toc-h3 nav-item toc-entry">
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<a class="reference internal nav-link" href="#randomized-pca">
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11.7.2. Randomized PCA
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</a>
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</li>
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<li class="toc-h3 nav-item toc-entry">
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<a class="reference internal nav-link" href="#kernel-pca">
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11.7.3. Kernel PCA
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</a>
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</li>
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</ul>
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</li>
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<li class="toc-h2 nav-item toc-entry">
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<a class="reference internal nav-link" href="#other-techniques">
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11.8. Other techniques
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</a>
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</li>
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</ul>
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</nav>
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</div>
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</div>
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</div>
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<div>
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<div class="tex2jax_ignore mathjax_ignore section" id="basic-ideas-of-the-principal-component-analysis-pca">
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</div>
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<p class="prev-next-subtitle">previous</p>
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<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>
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<p class="prev-next-title"><span class="section-number">12. </span>Clustering and Unsupervised Learning</p>
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<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>
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<p class="prevnext-title"><span class="section-number">12. </span>Clustering and Unsupervised Learning</p>
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By Morten Hjorth-Jensen<br/>
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© Copyright 2021.<br/>
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By Morten Hjorth-Jensen<br/>
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© Copyright 2021.<br/>
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