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mhjensen 994e26c835 added code to pca
2019-12-30 15:13:28 +01:00

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<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;"><b>Reducing the number of degrees of freedom, overarching view</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;"><b>Preprocessing our data</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;"><b>More preprocessing</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;"><b>Simple preprocessing examples, Franke function and regression</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;"><b>Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;"><b>More on Cancer Data, now with Logistic Regression</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;"><b>Why should we think of reducing the dimensionality</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;"><b>Basic ideas of the Principal Component Analysis (PCA)</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;"><b>Introducing the Covariance and Correlation functions</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;"><b>Correlation Function and Design/Feature Matrix</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;"><b>Covariance Matrix Examples</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;"><b>Correlation Matrix</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;"><b>Correlation Matrix with Pandas</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs014.html#___sec13" style="font-size: 80%;"><b>Correlation Matrix with Pandas and the Franke function</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs015.html#___sec14" style="font-size: 80%;"><b>Rewriting the Covariance and/or Correlation Matrix</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs016.html#___sec15" style="font-size: 80%;"><b>Towards the PCA theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs017.html#___sec16" style="font-size: 80%;"><b>The Algorithm before the Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs018.html#___sec17" style="font-size: 80%;"><b>Writing our own PCA code</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs018.html#___sec18" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample mean and center the data</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs018.html#___sec19" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Compute the sample covariance</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs018.html#___sec20" style="font-size: 80%;">&nbsp;&nbsp;&nbsp;Diagonalize the sample covariance matrix to obtain the principal components</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs019.html#___sec21" style="font-size: 80%;"><b>Classical PCA Theorem</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs020.html#___sec22" style="font-size: 80%;"><b>Proof of the PCA Theorem</b></a></li>
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<!-- navigation toc: --> <li><a href="._DimRed-bs022.html#___sec24" style="font-size: 80%;"><b>The final step</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec25" style="font-size: 80%;"><b>Geometric Interpretation and link with Singular Value Decomposition</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec26" style="font-size: 80%;"><b>Principal Component Analysis</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec27" style="font-size: 80%;"><b>PCA and scikit-learn</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec28" style="font-size: 80%;"><b>Back to the Cancer Data</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec29" style="font-size: 80%;"><b>More on the PCA</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec30" style="font-size: 80%;"><b>Incremental PCA</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec31" style="font-size: 80%;"><b>Randomized PCA</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs030.html#___sec32" style="font-size: 80%;"><b>Kernel PCA</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs031.html#___sec33" style="font-size: 80%;"><b>LLE</b></a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs032.html#___sec34" style="font-size: 80%;"><b>Other techniques</b></a></li>
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<center><h1>Data Analysis and Machine Learning: Preprocessing and Dimensionality Reduction</h1></center> <!-- document title -->
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<b>Morten Hjorth-Jensen</b> [1, 2]
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<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>
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