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added some examples

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mhjensen
2019-10-24 13:59:10 +02:00
parent aecd18f3f7
commit 63659da7d8
40 changed files with 830 additions and 520 deletions
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doc/pub/DimRed/html/._DimRed-bs000.html
+15 -13
View File
@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -225,7 +227,7 @@ MathJax.Hub.Config({
<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-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs001.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs001.html
+15 -13
View File
@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -225,7 +227,7 @@ data.
<li><a href="._DimRed-bs009.html">10</a></li>
<li><a href="._DimRed-bs010.html">11</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs002.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs002.html
+15 -13
View File
@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -224,7 +226,7 @@ ensures that all features are exactly between \( 0 \) and \( 1 \). The
<li><a href="._DimRed-bs010.html">11</a></li>
<li><a href="._DimRed-bs011.html">12</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs003.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs003.html
+15 -13
View File
@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -227,7 +229,7 @@ techniques.
<li><a href="._DimRed-bs011.html">12</a></li>
<li><a href="._DimRed-bs012.html">13</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs004.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs004.html
+15 -13
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -302,7 +304,7 @@ svm<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
<li><a href="._DimRed-bs012.html">13</a></li>
<li><a href="._DimRed-bs013.html">14</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs005.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs005.html
+15 -13
View File
@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -252,7 +254,7 @@ svm<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
<li><a href="._DimRed-bs013.html">14</a></li>
<li><a href="._DimRed-bs014.html">15</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs006.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs006.html
+15 -13
View File
@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -231,7 +233,7 @@ logreg<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
<li><a href="._DimRed-bs014.html">15</a></li>
<li><a href="._DimRed-bs015.html">16</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs007.html">&raquo;</a></li>
</ul>
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doc/pub/DimRed/html/._DimRed-bs007.html
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
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('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -286,7 +288,7 @@ applications.
<li><a href="._DimRed-bs015.html">16</a></li>
<li><a href="._DimRed-bs016.html">17</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs008.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs008.html
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -216,7 +218,7 @@ We have a data set defined by a design/feature matrix \( \boldsymbol{X} \) (see
<li><a href="._DimRed-bs016.html">17</a></li>
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<li><a href="">...</a></li>
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<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs009.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs009.html
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
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('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -265,7 +267,7 @@ In the above example this is the function we constructed using <b>pandas</b>.
<li><a href="._DimRed-bs017.html">18</a></li>
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<li><a href="">...</a></li>
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<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs010.html">&raquo;</a></li>
</ul>
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doc/pub/DimRed/html/._DimRed-bs010.html
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -260,7 +262,7 @@ $$
<li><a href="._DimRed-bs018.html">19</a></li>
<li><a href="._DimRed-bs019.html">20</a></li>
<li><a href="">...</a></li>
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<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs011.html">&raquo;</a></li>
</ul>
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
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('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -248,7 +250,7 @@ C <span style="color: #666666">=</span> np<span style="color: #666666">.</span>c
<li><a href="._DimRed-bs019.html">20</a></li>
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<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs012.html">&raquo;</a></li>
</ul>
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doc/pub/DimRed/html/._DimRed-bs012.html
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
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('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -250,7 +252,7 @@ The above procedure with <b>numpy</b> can be made more compact if we use <b>pand
<li><a href="._DimRed-bs020.html">21</a></li>
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<li><a href="._DimRed-bs013.html">&raquo;</a></li>
</ul>
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
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@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -232,7 +234,7 @@ We expand this model to the Franke function discussed above.
<li><a href="._DimRed-bs021.html">22</a></li>
<li><a href="._DimRed-bs022.html">23</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs014.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs014.html
+15 -13
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
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('LLE', 2, None, '___sec28'),
('Other techniques', 2, None, '___sec29')]}
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<body>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -268,7 +270,7 @@ matrix.
<li><a href="._DimRed-bs022.html">23</a></li>
<li><a href="._DimRed-bs023.html">24</a></li>
<li><a href="">...</a></li>
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<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs015.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs015.html
+15 -13
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
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('LLE', 2, None, '___sec28'),
('Other techniques', 2, None, '___sec29')]}
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<body>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -248,7 +250,7 @@ It is easy to generalize this to a matrix \( \boldsymbol{X}\in {\mathbb{R}}^{n\t
<li><a href="._DimRed-bs023.html">24</a></li>
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<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs016.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs016.html
+15 -13
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
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<body>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -256,7 +258,7 @@ features/predictors.
<li><a href="._DimRed-bs024.html">25</a></li>
<li><a href="._DimRed-bs025.html">26</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs017.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs017.html
+15 -13
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
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('Other techniques', 2, None, '___sec29')]}
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<body>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
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@@ -239,7 +241,7 @@ After this we ask ourselves how do we prove the link between the maximum varianc
<li><a href="._DimRed-bs025.html">26</a></li>
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<li><a href="">...</a></li>
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<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs018.html">&raquo;</a></li>
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doc/pub/DimRed/html/._DimRed-bs018.html
+15 -13
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<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
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</li>
@@ -226,7 +228,7 @@ The PCA theorem states that minimizing the above reconstruction error correspond
<li><a href="._DimRed-bs026.html">27</a></li>
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="">...</a></li>
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<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs019.html">&raquo;</a></li>
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doc/pub/DimRed/html/._DimRed-bs019.html
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@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -228,7 +230,7 @@ where the vectors on the rhs are known.
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs020.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs020.html
+16 -12
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -242,6 +244,8 @@ We are almost there, we have obtained a relation between minimizing the reconstr
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="">...</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs021.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs021.html
+15 -12
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="#___sec20" style="font-size: 80%;">The final step</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs022.html#___sec21" style="font-size: 80%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -254,6 +256,7 @@ chapter 12.4 and discussion therein.
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs022.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs022.html
+15 -12
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- navigation toc: --> <li><a href="._DimRed-bs021.html#___sec20" style="font-size: 80%;">The final step</a></li>
<!-- navigation toc: --> <li><a href="#___sec21" style="font-size: 80%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -258,6 +260,7 @@ X2D <span style="color: #666666">=</span> X_centered<span style="color: #666666"
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs023.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs023.html
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -209,8 +211,7 @@ principal component is equal to
<p>
Another very useful piece of information is the explained variance ratio of each principal component,
available via the \( explained\_variance\_ratio \) variable. It indicates the proportion of the dataset&#8217;s
variance that lies along the axis of each principal component.
More material to come here.
variance that lies along the axis of each principal component.
<p>
<p>
@@ -234,6 +235,7 @@ More material to come here.
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs024.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs024.html
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -182,32 +184,43 @@ MathJax.Hub.Config({
<a name="part0024"></a>
<!-- !split -->
<h2 id="___sec23" class="anchor">More on the PCA </h2>
<p>
Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
choose the number of dimensions that add up to a sufficiently large portion of the variance (e.g., 95%).
Unless, of course, you are reducing dimensionality for data visualization &#8212; in that case you will
generally want to reduce the dimensionality down to 2 or 3.
The following code computes PCA without reducing dimensionality, then computes the minimum number
of dimensions required to preserve 95% of the training set&#8217;s variance:
<h2 id="___sec23" class="anchor">Back to the Cancer Data </h2>
We can now repeat the above but applied to real data, in this case our breat cancer data.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pca <span style="color: #666666">=</span> PCA()
pca<span style="color: #666666">.</span>fit(X)
cumsum <span style="color: #666666">=</span> np<span style="color: #666666">.</span>cumsum(pca<span style="color: #666666">.</span>explained_variance_ratio_)
d <span style="color: #666666">=</span> np<span style="color: #666666">.</span>argmax(cumsum <span style="color: #666666">&gt;=</span> <span style="color: #666666">0.95</span>) <span style="color: #666666">+</span> <span style="color: #666666">1</span>
</pre></div>
<p>
You could then set \( n\_components=d \) and run PCA again. However, there is a much better option: instead
of specifying the number of principal components you want to preserve, you can set \( n\_components \) to be
a float between 0.0 and 1.0, indicating the ratio of variance you wish to preserve:
<p>
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LogisticRegression
cancer <span style="color: #666666">=</span> load_breast_cancer()
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pca <span style="color: #666666">=</span> PCA(n_components<span style="color: #666666">=0.95</span>)
X_reduced <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>fit_transform(X)
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
<span style="color: #008000; font-weight: bold">print</span>(X_train<span style="color: #666666">.</span>shape)
<span style="color: #008000; font-weight: bold">print</span>(X_test<span style="color: #666666">.</span>shape)
logreg <span style="color: #666666">=</span> LogisticRegression()
logreg<span style="color: #666666">.</span>fit(X_train, y_train)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy from Logistic Regression: {:.2f}&quot;</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> MinMaxScaler, StandardScaler
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
logreg<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy scaled data: {:.2f}&quot;</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
<span style="color: #408080; font-style: italic">#thereafter we do a PCA with Scikit-learn</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.decomposition</span> <span style="color: #008000; font-weight: bold">import</span> PCA
pca <span style="color: #666666">=</span> PCA(n_components <span style="color: #666666">=</span> <span style="color: #666666">2</span>)
X2D_train <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>fit_transform(X_train_scaled)
X2D_test <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>fit_transform(X_test_scaled)
logreg<span style="color: #666666">.</span>fit(X2D_train,y_train)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy scaled data: {:.2f}&quot;</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X2D_test,y_test)))
</pre></div>
<p>
<p>
@@ -230,6 +243,7 @@ X_reduced <span style="color: #666666">=</span> pca<span style="color: #666666">
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs025.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs025.html
+39 -18
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</a></li>
<!-- navigation toc: --> <li><a href="#___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>
@@ -182,15 +184,33 @@ MathJax.Hub.Config({
<a name="part0025"></a>
<!-- !split -->
<h2 id="___sec24" class="anchor">Incremental PCA </h2>
<h2 id="___sec24" class="anchor">More on the PCA </h2>
<p>
One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have
been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch
at a time. This is useful for large training sets, and also to apply PCA online (i.e., on the fly, as new
instances arrive).
Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
choose the number of dimensions that add up to a sufficiently large portion of the variance (e.g., 95%).
Unless, of course, you are reducing dimensionality for data visualization &#8212; in that case you will
generally want to reduce the dimensionality down to 2 or 3.
The following code computes PCA without reducing dimensionality, then computes the minimum number
of dimensions required to preserve 95% of the training set&#8217;s variance:
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pca <span style="color: #666666">=</span> PCA()
pca<span style="color: #666666">.</span>fit(X)
cumsum <span style="color: #666666">=</span> np<span style="color: #666666">.</span>cumsum(pca<span style="color: #666666">.</span>explained_variance_ratio_)
d <span style="color: #666666">=</span> np<span style="color: #666666">.</span>argmax(cumsum <span style="color: #666666">&gt;=</span> <span style="color: #666666">0.95</span>) <span style="color: #666666">+</span> <span style="color: #666666">1</span>
</pre></div>
<p>
You could then set \( n\_components=d \) and run PCA again. However, there is a much better option: instead
of specifying the number of principal components you want to preserve, you can set \( n\_components \) to be
a float between 0.0 and 1.0, indicating the ratio of variance you wish to preserve:
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pca <span style="color: #666666">=</span> PCA(n_components<span style="color: #666666">=0.95</span>)
X_reduced <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>fit_transform(X)
</pre></div>
<p>
<p>
<!-- navigation buttons at the bottom of the page -->
@@ -211,6 +231,7 @@ instances arrive).
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs026.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs026.html
+21 -22
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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="#___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>
@@ -182,18 +184,14 @@ MathJax.Hub.Config({
<a name="part0026"></a>
<!-- !split -->
<h2 id="___sec25" class="anchor">Randomized PCA </h2>
<h2 id="___sec25" class="anchor">Incremental PCA </h2>
<p>
Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
algorithm that quickly finds an approximation of the first d principal components. Its computational
complexity is \( O(m \times d^2)+O(d^3) \), instead of \( O(m \times n^2) + O(n^3) \), so it is dramatically faster than the
previous algorithms when \( d \) is much smaller than \( n \).
<p>
</div>
</div>
One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have
been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch
at a time. This is useful for large training sets, and also to apply PCA online (i.e., on the fly, as new
instances arrive).
<p>
<p>
@@ -214,6 +212,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs027.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs027.html
+20 -31
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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="#___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>
@@ -182,28 +184,14 @@ MathJax.Hub.Config({
<a name="part0027"></a>
<!-- !split -->
<h2 id="___sec26" class="anchor">Kernel PCA </h2>
<div class="panel panel-default">
<div class="panel-body">
<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
<h2 id="___sec26" class="anchor">Randomized PCA </h2>
<p>
The kernel trick is a mathematical technique that implicitly maps instances into a
very high-dimensional space (called the feature space), enabling nonlinear classification and regression
with Support Vector Machines. Recall that a linear decision boundary in the high-dimensional feature
space corresponds to a complex nonlinear decision boundary in the original space.
It turns out that the same trick can be applied to PCA, making it possible to perform complex nonlinear
projections for dimensionality reduction. This is called Kernel PCA (kPCA). It is often good at
preserving clusters of instances after projection, or sometimes even unrolling datasets that lie close to a
twisted manifold.
For example, the following code uses Scikit-Learn&#8217;s KernelPCA class to perform kPCA with an
<p>
Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
algorithm that quickly finds an approximation of the first d principal components. Its computational
complexity is \( O(m \times d^2)+O(d^3) \), instead of \( O(m \times n^2) + O(n^3) \), so it is dramatically faster than the
previous algorithms when \( d \) is much smaller than \( n \).
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.decomposition</span> <span style="color: #008000; font-weight: bold">import</span> KernelPCA
rbf_pca <span style="color: #666666">=</span> KernelPCA(n_components <span style="color: #666666">=</span> <span style="color: #666666">2</span>, kernel<span style="color: #666666">=</span><span style="color: #BA2121">&quot;rbf&quot;</span>, gamma<span style="color: #666666">=0.04</span>)
X_reduced <span style="color: #666666">=</span> rbf_pca<span style="color: #666666">.</span>fit_transform(X)
</pre></div>
<p>
</div>
</div>
@@ -227,6 +215,7 @@ X_reduced <span style="color: #666666">=</span> rbf_pca<span style="color: #6666
<li class="active"><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs028.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs028.html
+39 -18
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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="#___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>
@@ -182,14 +184,32 @@ MathJax.Hub.Config({
<a name="part0028"></a>
<!-- !split -->
<h2 id="___sec27" class="anchor">LLE </h2>
<h2 id="___sec27" class="anchor">Kernel PCA </h2>
<div class="panel panel-default">
<div class="panel-body">
<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
<p>
Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
(NLDR) technique. It is a Manifold Learning technique that does not rely on projections like the previous
algorithms. In a nutshell, LLE works by first measuring how each training instance linearly relates to its
closest neighbors (c.n.), and then looking for a low-dimensional representation of the training set where
these local relationships are best preserved (more details shortly).
The kernel trick is a mathematical technique that implicitly maps instances into a
very high-dimensional space (called the feature space), enabling nonlinear classification and regression
with Support Vector Machines. Recall that a linear decision boundary in the high-dimensional feature
space corresponds to a complex nonlinear decision boundary in the original space.
It turns out that the same trick can be applied to PCA, making it possible to perform complex nonlinear
projections for dimensionality reduction. This is called Kernel PCA (kPCA). It is often good at
preserving clusters of instances after projection, or sometimes even unrolling datasets that lie close to a
twisted manifold.
For example, the following code uses Scikit-Learn&#8217;s KernelPCA class to perform kPCA with an
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.decomposition</span> <span style="color: #008000; font-weight: bold">import</span> KernelPCA
rbf_pca <span style="color: #666666">=</span> KernelPCA(n_components <span style="color: #666666">=</span> <span style="color: #666666">2</span>, kernel<span style="color: #666666">=</span><span style="color: #BA2121">&quot;rbf&quot;</span>, gamma<span style="color: #666666">=0.04</span>)
X_reduced <span style="color: #666666">=</span> rbf_pca<span style="color: #666666">.</span>fit_transform(X)
</pre></div>
<p>
</div>
</div>
<p>
<p>
@@ -208,6 +228,7 @@ these local relationships are best preserved (more details shortly).
<li><a href="._DimRed-bs027.html">28</a></li>
<li class="active"><a href="._DimRed-bs028.html">29</a></li>
<li><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs029.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs029.html
+22 -24
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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="#___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>
@@ -182,22 +184,16 @@ MathJax.Hub.Config({
<a name="part0029"></a>
<!-- !split -->
<h2 id="___sec28" class="anchor">Other techniques </h2>
<h2 id="___sec28" class="anchor">LLE </h2>
<p>
There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
(NLDR) technique. It is a Manifold Learning technique that does not rely on projections like the previous
algorithms. In a nutshell, LLE works by first measuring how each training instance linearly relates to its
closest neighbors (c.n.), and then looking for a low-dimensional representation of the training set where
these local relationships are best preserved (more details shortly).
<p>
Here are some of the most popular:
<ul>
<li> <b>Multidimensional Scaling (MDS)</b> reduces dimensionality while trying to preserve the distances between the instances.</li>
<li> <b>Isomap</b> creates a graph by connecting each instance to its nearest neighbors, then reduces dimensionality while trying to preserve the geodesic distances between the instances.</li>
<li> <b>t-Distributed Stochastic Neighbor Embedding</b> (t-SNE) reduces dimensionality while trying to keep similar instances close and dissimilar instances apart. It is mostly used for visualization, in particular to visualize clusters of instances in high-dimensional space (e.g., to visualize the MNIST images in 2D).</li>
<li> Linear Discriminant Analysis (LDA) is actually a classification algorithm, but during training it learns the most discriminative axes between the classes, and these axes can then be used to define a hyperplane onto which to project the data. The benefit is that the projection will keep classes as far apart as possible, so LDA is a good technique to reduce dimensionality before running another classification algorithm such as a Support Vector Machine (SVM) classifier discussed in the SVM lectures.</li>
</ul>
<p>
<!-- navigation buttons at the bottom of the page -->
<ul class="pagination">
@@ -213,6 +209,8 @@ Here are some of the most popular:
<li><a href="._DimRed-bs027.html">28</a></li>
<li><a href="._DimRed-bs028.html">29</a></li>
<li class="active"><a href="._DimRed-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs030.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/._DimRed-bs030.html
+6 -6
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@@ -93,9 +93,9 @@ Automatically generated HTML file from DocOnce source
('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'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('Back to the Cancer Data', 2, None, '___sec23'),
('More on the PCA', 2, None, '___sec24'),
('Incremental PCA', 2, None, '___sec25'),
('Randomized PCA', 2, None, '___sec26'),
@@ -160,9 +160,9 @@ MathJax.Hub.Config({
<!-- 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-bs022.html#___sec21" style="font-size: 80%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
doc/pub/DimRed/html/DimRed-bs.html
+15 -13
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@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
<!-- 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%;">Principal Component Analysis</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs023.html#___sec22" style="font-size: 80%;">PCA and scikit-learn</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">More on the PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs025.html#___sec24" style="font-size: 80%;">Incremental PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs026.html#___sec25" style="font-size: 80%;">Randomized PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs027.html#___sec26" style="font-size: 80%;">Kernel PCA</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs028.html#___sec27" style="font-size: 80%;">LLE</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs029.html#___sec28" style="font-size: 80%;">Other techniques</a></li>
<!-- navigation toc: --> <li><a href="._DimRed-bs024.html#___sec23" style="font-size: 80%;">Back to the Cancer Data</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>
@@ -225,7 +227,7 @@ MathJax.Hub.Config({
<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-bs029.html">30</a></li>
<li><a href="._DimRed-bs030.html">31</a></li>
<li><a href="._DimRed-bs001.html">&raquo;</a></li>
</ul>
<!-- ------------------- end of main content --------------- -->
doc/pub/DimRed/html/DimRed-reveal.html
+49 -8
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@@ -1232,13 +1232,54 @@ principal component is equal to
<p>
Another very useful piece of information is the explained variance ratio of each principal component,
available via the \( explained\_variance\_ratio \) variable. It indicates the proportion of the dataset&#8217;s
variance that lies along the axis of each principal component.
More material to come here.
variance that lies along the axis of each principal component.
</section>
<section>
<h2 id="___sec23">More on the PCA </h2>
<h2 id="___sec23">Back to the Cancer Data </h2>
We can now repeat the above but applied to real data, in this case our breat cancer data.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eeeedd"><pre style="font-size: 80%; line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> train_test_split
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.datasets</span> <span style="color: #8B008B; font-weight: bold">import</span> load_breast_cancer
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LogisticRegression
cancer = load_breast_cancer()
X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=<span style="color: #B452CD">0</span>)
<span style="color: #8B008B; font-weight: bold">print</span>(X_train.shape)
<span style="color: #8B008B; font-weight: bold">print</span>(X_test.shape)
logreg = LogisticRegression()
logreg.fit(X_train, y_train)
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&quot;Test set accuracy from Logistic Regression: {:.2f}&quot;</span>.format(logreg.score(X_test,y_test)))
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> MinMaxScaler, StandardScaler
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
logreg.fit(X_train_scaled, y_train)
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&quot;Test set accuracy scaled data: {:.2f}&quot;</span>.format(logreg.score(X_test_scaled,y_test)))
<span style="color: #228B22">#thereafter we do a PCA with Scikit-learn</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.decomposition</span> <span style="color: #8B008B; font-weight: bold">import</span> PCA
pca = PCA(n_components = <span style="color: #B452CD">2</span>)
X2D_train = pca.fit_transform(X_train_scaled)
X2D_test = pca.fit_transform(X_test_scaled)
logreg.fit(X2D_train,y_train)
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&quot;Test set accuracy scaled data: {:.2f}&quot;</span>.format(logreg.score(X2D_test,y_test)))
</pre></div>
</section>
<section>
<h2 id="___sec24">More on the PCA </h2>
<p>
Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
@@ -1269,7 +1310,7 @@ X_reduced = pca.fit_transform(X)
<section>
<h2 id="___sec24">Incremental PCA </h2>
<h2 id="___sec25">Incremental PCA </h2>
<p>
One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
@@ -1281,7 +1322,7 @@ instances arrive).
<section>
<h2 id="___sec25">Randomized PCA </h2>
<h2 id="___sec26">Randomized PCA </h2>
<p>
Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
@@ -1295,7 +1336,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
<section>
<h2 id="___sec26">Kernel PCA </h2>
<h2 id="___sec27">Kernel PCA </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
@@ -1321,7 +1362,7 @@ X_reduced = rbf_pca.fit_transform(X)
<section>
<h2 id="___sec27">LLE </h2>
<h2 id="___sec28">LLE </h2>
<p>
Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
@@ -1333,7 +1374,7 @@ these local relationships are best preserved (more details shortly).
<section>
<h2 id="___sec28">Other techniques </h2>
<h2 id="___sec29">Other techniques </h2>
<p>
There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
doc/pub/DimRed/html/DimRed-solarized.html
+55 -14
View File
@@ -115,12 +115,13 @@ div { text-align: justify; text-justify: inter-word; }
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -1170,13 +1171,53 @@ principal component is equal to
<p>
Another very useful piece of information is the explained variance ratio of each principal component,
available via the \( explained\_variance\_ratio \) variable. It indicates the proportion of the dataset&#8217;s
variance that lies along the axis of each principal component.
More material to come here.
variance that lies along the axis of each principal component.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec23">More on the PCA </h2>
<h2 id="___sec23">Back to the Cancer Data </h2>
We can now repeat the above but applied to real data, in this case our breat cancer data.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
<div class="highlight" style="background: #eee8d5"><pre style="line-height: 125%"><span></span><span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">matplotlib.pyplot</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">plt</span>
<span style="color: #8B008B; font-weight: bold">import</span> <span style="color: #008b45; text-decoration: underline">numpy</span> <span style="color: #8B008B; font-weight: bold">as</span> <span style="color: #008b45; text-decoration: underline">np</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.model_selection</span> <span style="color: #8B008B; font-weight: bold">import</span> train_test_split
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.datasets</span> <span style="color: #8B008B; font-weight: bold">import</span> load_breast_cancer
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.linear_model</span> <span style="color: #8B008B; font-weight: bold">import</span> LogisticRegression
cancer = load_breast_cancer()
X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=<span style="color: #B452CD">0</span>)
<span style="color: #8B008B; font-weight: bold">print</span>(X_train.shape)
<span style="color: #8B008B; font-weight: bold">print</span>(X_test.shape)
logreg = LogisticRegression()
logreg.fit(X_train, y_train)
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&quot;Test set accuracy from Logistic Regression: {:.2f}&quot;</span>.format(logreg.score(X_test,y_test)))
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.preprocessing</span> <span style="color: #8B008B; font-weight: bold">import</span> MinMaxScaler, StandardScaler
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
logreg.fit(X_train_scaled, y_train)
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&quot;Test set accuracy scaled data: {:.2f}&quot;</span>.format(logreg.score(X_test_scaled,y_test)))
<span style="color: #228B22">#thereafter we do a PCA with Scikit-learn</span>
<span style="color: #8B008B; font-weight: bold">from</span> <span style="color: #008b45; text-decoration: underline">sklearn.decomposition</span> <span style="color: #8B008B; font-weight: bold">import</span> PCA
pca = PCA(n_components = <span style="color: #B452CD">2</span>)
X2D_train = pca.fit_transform(X_train_scaled)
X2D_test = pca.fit_transform(X_test_scaled)
logreg.fit(X2D_train,y_train)
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">&quot;Test set accuracy scaled data: {:.2f}&quot;</span>.format(logreg.score(X2D_test,y_test)))
</pre></div>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec24">More on the PCA </h2>
<p>
Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
@@ -1206,7 +1247,7 @@ X_reduced = pca.fit_transform(X)
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec24">Incremental PCA </h2>
<h2 id="___sec25">Incremental PCA </h2>
<p>
One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
@@ -1218,7 +1259,7 @@ instances arrive).
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec25">Randomized PCA </h2>
<h2 id="___sec26">Randomized PCA </h2>
<p>
Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
@@ -1233,7 +1274,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec26">Kernel PCA </h2>
<h2 id="___sec27">Kernel PCA </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
@@ -1262,7 +1303,7 @@ X_reduced = rbf_pca.fit_transform(X)
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec27">LLE </h2>
<h2 id="___sec28">LLE </h2>
<p>
Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
@@ -1274,7 +1315,7 @@ these local relationships are best preserved (more details shortly).
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec28">Other techniques </h2>
<h2 id="___sec29">Other techniques </h2>
<p>
There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
doc/pub/DimRed/html/DimRed.html
+55 -14
View File
@@ -120,12 +120,13 @@ div { text-align: justify; text-justify: inter-word; }
('The final step', 2, None, '___sec20'),
('Principal Component Analysis', 2, None, '___sec21'),
('PCA and scikit-learn', 2, None, '___sec22'),
('More on the PCA', 2, None, '___sec23'),
('Incremental PCA', 2, None, '___sec24'),
('Randomized PCA', 2, None, '___sec25'),
('Kernel PCA', 2, None, '___sec26'),
('LLE', 2, None, '___sec27'),
('Other techniques', 2, None, '___sec28')]}
('Back to the Cancer Data', 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>
@@ -1175,13 +1176,53 @@ principal component is equal to
<p>
Another very useful piece of information is the explained variance ratio of each principal component,
available via the \( explained\_variance\_ratio \) variable. It indicates the proportion of the dataset&#8217;s
variance that lies along the axis of each principal component.
More material to come here.
variance that lies along the axis of each principal component.
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec23">More on the PCA </h2>
<h2 id="___sec23">Back to the Cancer Data </h2>
We can now repeat the above but applied to real data, in this case our breat cancer data.
<p>
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">matplotlib.pyplot</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">plt</span>
<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_breast_cancer
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.linear_model</span> <span style="color: #008000; font-weight: bold">import</span> LogisticRegression
cancer <span style="color: #666666">=</span> load_breast_cancer()
X_train, X_test, y_train, y_test <span style="color: #666666">=</span> train_test_split(cancer<span style="color: #666666">.</span>data,cancer<span style="color: #666666">.</span>target,random_state<span style="color: #666666">=0</span>)
<span style="color: #008000; font-weight: bold">print</span>(X_train<span style="color: #666666">.</span>shape)
<span style="color: #008000; font-weight: bold">print</span>(X_test<span style="color: #666666">.</span>shape)
logreg <span style="color: #666666">=</span> LogisticRegression()
logreg<span style="color: #666666">.</span>fit(X_train, y_train)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy from Logistic Regression: {:.2f}&quot;</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> MinMaxScaler, StandardScaler
scaler <span style="color: #666666">=</span> StandardScaler()
scaler<span style="color: #666666">.</span>fit(X_train)
X_train_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_train)
X_test_scaled <span style="color: #666666">=</span> scaler<span style="color: #666666">.</span>transform(X_test)
logreg<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy scaled data: {:.2f}&quot;</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test_scaled,y_test)))
<span style="color: #408080; font-style: italic">#thereafter we do a PCA with Scikit-learn</span>
<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.decomposition</span> <span style="color: #008000; font-weight: bold">import</span> PCA
pca <span style="color: #666666">=</span> PCA(n_components <span style="color: #666666">=</span> <span style="color: #666666">2</span>)
X2D_train <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>fit_transform(X_train_scaled)
X2D_test <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>fit_transform(X_test_scaled)
logreg<span style="color: #666666">.</span>fit(X2D_train,y_train)
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">&quot;Test set accuracy scaled data: {:.2f}&quot;</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X2D_test,y_test)))
</pre></div>
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec24">More on the PCA </h2>
<p>
Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
@@ -1211,7 +1252,7 @@ X_reduced <span style="color: #666666">=</span> pca<span style="color: #666666">
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec24">Incremental PCA </h2>
<h2 id="___sec25">Incremental PCA </h2>
<p>
One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
@@ -1223,7 +1264,7 @@ instances arrive).
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec25">Randomized PCA </h2>
<h2 id="___sec26">Randomized PCA </h2>
<p>
Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
@@ -1238,7 +1279,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec26">Kernel PCA </h2>
<h2 id="___sec27">Kernel PCA </h2>
<div class="alert alert-block alert-block alert-text-normal">
<b></b>
<p>
@@ -1267,7 +1308,7 @@ X_reduced <span style="color: #666666">=</span> rbf_pca<span style="color: #6666
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec27">LLE </h2>
<h2 id="___sec28">LLE </h2>
<p>
Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
@@ -1279,7 +1320,7 @@ these local relationships are best preserved (more details shortly).
<p>
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
<h2 id="___sec28">Other techniques </h2>
<h2 id="___sec29">Other techniques </h2>
<p>
There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
doc/pub/DimRed/ipynb/DimRed.ipynb
+53 -4
View File
@@ -1431,8 +1431,57 @@
"Another very useful piece of information is the explained variance ratio of each principal component,\n",
"available via the $explained\\_variance\\_ratio$ variable. It indicates the proportion of the dataset’s\n",
"variance that lies along the axis of each principal component. \n",
"More material to come here.\n",
"\n",
"## Back to the Cancer Data\n",
"We can now repeat the above but applied to real data, in this case our breat cancer data."
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from sklearn.model_selection import train_test_split \n",
"from sklearn.datasets import load_breast_cancer\n",
"from sklearn.linear_model import LogisticRegression\n",
"cancer = load_breast_cancer()\n",
"\n",
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
"print(X_train.shape)\n",
"print(X_test.shape)\n",
"\n",
"logreg = LogisticRegression()\n",
"logreg.fit(X_train, y_train)\n",
"print(\"Test set accuracy from Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
"\n",
"from sklearn.preprocessing import MinMaxScaler, StandardScaler\n",
"scaler = StandardScaler()\n",
"scaler.fit(X_train)\n",
"X_train_scaled = scaler.transform(X_train)\n",
"X_test_scaled = scaler.transform(X_test)\n",
"\n",
"logreg.fit(X_train_scaled, y_train)\n",
"print(\"Test set accuracy scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
"\n",
"#thereafter we do a PCA with Scikit-learn\n",
"from sklearn.decomposition import PCA\n",
"pca = PCA(n_components = 2)\n",
"X2D_train = pca.fit_transform(X_train_scaled)\n",
"X2D_test = pca.fit_transform(X_test_scaled)\n",
"\n",
"logreg.fit(X2D_train,y_train)\n",
"print(\"Test set accuracy scaled data: {:.2f}\".format(logreg.score(X2D_test,y_test)))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## More on the PCA\n",
"\n",
"Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to\n",
@@ -1445,7 +1494,7 @@
},
{
"cell_type": "code",
"execution_count": 15,
"execution_count": 16,
"metadata": {
"collapsed": false
},
@@ -1468,7 +1517,7 @@
},
{
"cell_type": "code",
"execution_count": 16,
"execution_count": 17,
"metadata": {
"collapsed": false
},
@@ -1515,7 +1564,7 @@
},
{
"cell_type": "code",
"execution_count": 17,
"execution_count": 18,
"metadata": {
"collapsed": false
},
doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz
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doc/pub/DimRed/pdf/DimRed-minted.pdf
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doc/src/DimRed/DimRed.do.txt
+39 -1
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@@ -948,7 +948,45 @@ pca.components_.T[:, 0].
Another very useful piece of information is the explained variance ratio of each principal component,
available via the $explained\_variance\_ratio$ variable. It indicates the proportion of the dataset’s
variance that lies along the axis of each principal component.
More material to come here.
!split
===== Back to the Cancer Data =====
We can now repeat the above but applied to real data, in this case our breat cancer data.
!bc pycod
import matplotlib.pyplot as plt
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.datasets import load_breast_cancer
from sklearn.linear_model import LogisticRegression
cancer = load_breast_cancer()
X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
print(X_train.shape)
print(X_test.shape)
logreg = LogisticRegression()
logreg.fit(X_train, y_train)
print("Test set accuracy from Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
from sklearn.preprocessing import MinMaxScaler, StandardScaler
scaler = StandardScaler()
scaler.fit(X_train)
X_train_scaled = scaler.transform(X_train)
X_test_scaled = scaler.transform(X_test)
logreg.fit(X_train_scaled, y_train)
print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
#thereafter we do a PCA with Scikit-learn
from sklearn.decomposition import PCA
pca = PCA(n_components = 2)
X2D_train = pca.fit_transform(X_train_scaled)
X2D_test = pca.fit_transform(X_test_scaled)
logreg.fit(X2D_train,y_train)
print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X2D_test,y_test)))
!ec
!split
===== More on the PCA =====
doc/src/DimRed/PCAcancer.py
+7 -3
View File
@@ -14,7 +14,6 @@ correlation_matrix = cancerpd.corr().round(1)
# use the heatmap function from seaborn to plot the correlation matrix
# annot = True to print the values inside the square
sns.heatmap(data=correlation_matrix, annot=True)
plt.show()
EigValues, EigVectors = np.linalg.eig(correlation_matrix)
print(EigValues)
@@ -35,6 +34,11 @@ X_test_scaled = scaler.transform(X_test)
logreg.fit(X_train_scaled, y_train)
print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
#thereafter we do a PCA with Scikit-learn
from sklearn.decomposition import PCA
pca = PCA(n_components = 2)
X2D_train = pca.fit_transform(X_train_scaled)
X2D_test = pca.fit_transform(X_test_scaled)
logreg.fit(X2D_train,y_train)
print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X2D_test,y_test)))