updating codes
This commit is contained in:
mhjensen
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
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('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
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('Other techniques', 2, None, '___sec12')]}
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||||
end of tocinfo -->
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<body>
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||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
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</li>
|
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@@ -170,7 +175,7 @@ MathJax.Hub.Config({
|
||||
<li><a href="._DimRed-bs008.html">9</a></li>
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<li><a href="._DimRed-bs009.html">10</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DimRed-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
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||||
</li>
|
||||
@@ -165,7 +170,7 @@ reduction techniques: the principal component analysis PCA, Kernel PCA, and Loca
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<li><a href="._DimRed-bs009.html">10</a></li>
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||||
<li><a href="._DimRed-bs010.html">11</a></li>
|
||||
<li><a href="">...</a></li>
|
||||
<li><a href="._DimRed-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs002.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
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||||
</li>
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||||
@@ -167,7 +172,7 @@ This scaling has the drawback that it does not ensure that we have a particular
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<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-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs003.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -245,6 +250,8 @@ svm<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<li><a href="._DimRed-bs010.html">11</a></li>
|
||||
<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-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs004.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -127,7 +132,7 @@ MathJax.Hub.Config({
|
||||
<a name="part0004"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec3" class="anchor">Simple preprocessing examples, breast cancer data and classification </h2>
|
||||
<h2 id="___sec3" class="anchor">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines </h2>
|
||||
|
||||
<p>
|
||||
We show here how we can use a simple regression case on the breast cancer data using support vector machine as algorithm for classification
|
||||
@@ -193,6 +198,7 @@ svm<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<li><a href="._DimRed-bs010.html">11</a></li>
|
||||
<li><a href="._DimRed-bs011.html">12</a></li>
|
||||
<li><a href="._DimRed-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs005.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -127,38 +132,57 @@ MathJax.Hub.Config({
|
||||
<a name="part0005"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec4" class="anchor">Principal Component Analysis </h2>
|
||||
<div class="panel panel-default">
|
||||
<div class="panel-body">
|
||||
<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
|
||||
Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
|
||||
First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.
|
||||
|
||||
<p>
|
||||
The following Python code uses NumPy’s <b>svd()</b> function to obtain all the principal components of the
|
||||
training set, then extracts the first two principal components
|
||||
<h2 id="___sec4" class="anchor">More on Cancer Data, now with Logistic Regression </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X_centered <span style="color: #666666">=</span> X <span style="color: #666666">-</span> X<span style="color: #666666">.</span>mean(axis<span style="color: #666666">=0</span>)
|
||||
U, s, V <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>svd(X_centered)
|
||||
c1 <span style="color: #666666">=</span> V<span style="color: #666666">.</span>T[:, <span style="color: #666666">0</span>]
|
||||
c2 <span style="color: #666666">=</span> V<span style="color: #666666">.</span>T[:, <span style="color: #666666">1</span>]
|
||||
</pre></div>
|
||||
<p>
|
||||
PCA assumes that the dataset is centered around the origin. Scikit-Learn’s PCA classes take care of centering
|
||||
the data for you. However, if you implement PCA yourself (as in the preceding example), or if you use other libraries, don’t
|
||||
forget to center the data first.
|
||||
<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()
|
||||
|
||||
<p>
|
||||
Once you have identified all the principal components, you can reduce the dimensionality of the dataset
|
||||
down to \( d \) dimensions by projecting it onto the hyperplane defined by the first \( d \) principal components.
|
||||
Selecting this hyperplane ensures that the projection will preserve as much variance as possible.
|
||||
<p>
|
||||
fig, axes <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(<span style="color: #666666">15</span>,<span style="color: #666666">2</span>,figsize<span style="color: #666666">=</span>(<span style="color: #666666">10</span>,<span style="color: #666666">20</span>))
|
||||
male <span style="color: #666666">=</span> cancer<span style="color: #666666">.</span>data[cancer<span style="color: #666666">.</span>target <span style="color: #666666">==</span> <span style="color: #666666">0</span>]
|
||||
bene <span style="color: #666666">=</span> cancer<span style="color: #666666">.</span>data[cancer<span style="color: #666666">.</span>target <span style="color: #666666">==</span> <span style="color: #666666">1</span>]
|
||||
ax <span style="color: #666666">=</span> axes<span style="color: #666666">.</span>ravel()
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "default" -->
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>W2 <span style="color: #666666">=</span> V<span style="color: #666666">.</span>T[:, :<span style="color: #666666">2</span>]
|
||||
X2D <span style="color: #666666">=</span> X_centered<span style="color: #666666">.</span>dot(W2)
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">30</span>):
|
||||
_, bins <span style="color: #666666">=</span> np<span style="color: #666666">.</span>histogram(cancer<span style="color: #666666">.</span>data[:,i], bins <span style="color: #666666">=50</span>)
|
||||
ax[i]<span style="color: #666666">.</span>hist(male[:,i], bins <span style="color: #666666">=</span> bins, alpha <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>)
|
||||
ax[i]<span style="color: #666666">.</span>hist(bene[:,i], bins <span style="color: #666666">=</span> bins, alpha <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>)
|
||||
ax[i]<span style="color: #666666">.</span>set_title(cancer<span style="color: #666666">.</span>feature_names[i])
|
||||
ax[i]<span style="color: #666666">.</span>set_yticks(())
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"Feature magnitude"</span>)
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"Frequency"</span>)
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>legend([<span style="color: #BA2121">"Male"</span>, <span style="color: #BA2121">"Bene"</span>], loc <span style="color: #666666">=</span><span style="color: #BA2121">"best"</span>)
|
||||
fig<span style="color: #666666">.</span>tight_layout()
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Set up training data</span>
|
||||
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: #408080; font-style: italic"># Perform Logistic Regression (replace with own code) </span>
|
||||
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">"Test set accuracy: {:.2f}"</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Scale data</span>
|
||||
<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> 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: #408080; font-style: italic">#svm.fit(X_train_scaled, y_train)</span>
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Test set accuracy scaled data: {:.2f}"</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"># Now add PCA</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>)
|
||||
pca<span style="color: #666666">.</span>fit(X_train_scaled)
|
||||
|
||||
X_pca <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>transform(X_train_scaled)
|
||||
</pre></div>
|
||||
<p>
|
||||
<p>
|
||||
@@ -178,6 +202,7 @@ X2D <span style="color: #666666">=</span> X_centered<span style="color: #666666"
|
||||
<li><a href="._DimRed-bs010.html">11</a></li>
|
||||
<li><a href="._DimRed-bs011.html">12</a></li>
|
||||
<li><a href="._DimRed-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs006.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -125,36 +130,41 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
|
||||
<a name="part0006"></a>
|
||||
<!-- !split -->
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec5" class="anchor">PCA and scikit-learn </h2>
|
||||
<h2 id="___sec5" class="anchor">Principal Component Analysis </h2>
|
||||
<div class="panel panel-default">
|
||||
<div class="panel-body">
|
||||
<p> <!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
|
||||
Principal Component Analysis (PCA) is by far the most popular dimensionality reduction algorithm.
|
||||
First it identifies the hyperplane that lies closest to the data, and then it projects the data onto it.
|
||||
|
||||
<p>
|
||||
Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The
|
||||
following code applies PCA to reduce the dimensionality of the dataset down to two dimensions (note
|
||||
that it automatically takes care of centering the data):
|
||||
The following Python code uses NumPy’s <b>svd()</b> function to obtain all the principal components of the
|
||||
training set, then extracts the first two principal components
|
||||
<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> PCA
|
||||
pca <span style="color: #666666">=</span> PCA(n_components <span style="color: #666666">=</span> <span style="color: #666666">2</span>)
|
||||
X2D <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>fit_transform(X)
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>X_centered <span style="color: #666666">=</span> X <span style="color: #666666">-</span> X<span style="color: #666666">.</span>mean(axis<span style="color: #666666">=0</span>)
|
||||
U, s, V <span style="color: #666666">=</span> np<span style="color: #666666">.</span>linalg<span style="color: #666666">.</span>svd(X_centered)
|
||||
c1 <span style="color: #666666">=</span> V<span style="color: #666666">.</span>T[:, <span style="color: #666666">0</span>]
|
||||
c2 <span style="color: #666666">=</span> V<span style="color: #666666">.</span>T[:, <span style="color: #666666">1</span>]
|
||||
</pre></div>
|
||||
<p>
|
||||
After fitting the PCA transformer to the dataset, you can access the principal components using the
|
||||
components variable (note that it contains the PCs as horizontal vectors, so, for example, the first
|
||||
principal component is equal to
|
||||
PCA assumes that the dataset is centered around the origin. Scikit-Learn’s PCA classes take care of centering
|
||||
the data for you. However, if you implement PCA yourself (as in the preceding example), or if you use other libraries, don’t
|
||||
forget to center the data first.
|
||||
|
||||
<p>
|
||||
Once you have identified all the principal components, you can reduce the dimensionality of the dataset
|
||||
down to \( d \) dimensions by projecting it onto the hyperplane defined by the first \( d \) principal components.
|
||||
Selecting this hyperplane ensures that the projection will preserve as much variance as possible.
|
||||
<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>components_<span style="color: #666666">.</span>T[:, <span style="color: #666666">0</span>])<span style="color: #666666">.</span>
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>W2 <span style="color: #666666">=</span> V<span style="color: #666666">.</span>T[:, :<span style="color: #666666">2</span>]
|
||||
X2D <span style="color: #666666">=</span> X_centered<span style="color: #666666">.</span>dot(W2)
|
||||
</pre></div>
|
||||
<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’s
|
||||
variance that lies along the axis of each principal component.
|
||||
More material to come here.
|
||||
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -173,6 +183,7 @@ More material to come here.
|
||||
<li><a href="._DimRed-bs010.html">11</a></li>
|
||||
<li><a href="._DimRed-bs011.html">12</a></li>
|
||||
<li><a href="._DimRed-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs007.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -125,33 +130,36 @@ MathJax.Hub.Config({
|
||||
<p> </p><p> </p><p> </p> <!-- add vertical space -->
|
||||
|
||||
<a name="part0007"></a>
|
||||
<!-- !split -->
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec6" class="anchor">More on the PCA </h2>
|
||||
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 — 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’s variance:
|
||||
<h2 id="___sec6" class="anchor">PCA and scikit-learn </h2>
|
||||
|
||||
<p>
|
||||
Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The
|
||||
following code applies PCA to reduce the dimensionality of the dataset down to two dimensions (note
|
||||
that it automatically takes care of centering the 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">>=</span> <span style="color: #666666">0.95</span>) <span style="color: #666666">+</span> <span style="color: #666666">1</span>
|
||||
<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> PCA
|
||||
pca <span style="color: #666666">=</span> PCA(n_components <span style="color: #666666">=</span> <span style="color: #666666">2</span>)
|
||||
X2D <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>fit_transform(X)
|
||||
</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:
|
||||
After fitting the PCA transformer to the dataset, you can access the principal components using the
|
||||
components variable (note that it contains the PCs as horizontal vectors, so, for example, the first
|
||||
principal component is equal to
|
||||
<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)
|
||||
<div class="highlight" style="background: #f8f8f8"><pre style="line-height: 125%"><span></span>pca<span style="color: #666666">.</span>components_<span style="color: #666666">.</span>T[:, <span style="color: #666666">0</span>])<span style="color: #666666">.</span>
|
||||
</pre></div>
|
||||
<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’s
|
||||
variance that lies along the axis of each principal component.
|
||||
More material to come here.
|
||||
|
||||
<p>
|
||||
<p>
|
||||
<!-- navigation buttons at the bottom of the page -->
|
||||
@@ -170,6 +178,7 @@ X_reduced <span style="color: #666666">=</span> pca<span style="color: #666666">
|
||||
<li><a href="._DimRed-bs010.html">11</a></li>
|
||||
<li><a href="._DimRed-bs011.html">12</a></li>
|
||||
<li><a href="._DimRed-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs008.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -127,13 +132,31 @@ MathJax.Hub.Config({
|
||||
<a name="part0008"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec7" class="anchor">Incremental PCA </h2>
|
||||
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).
|
||||
<h2 id="___sec7" class="anchor">More on the PCA </h2>
|
||||
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 — 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’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">>=</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 -->
|
||||
@@ -152,6 +175,7 @@ instances arrive).
|
||||
<li><a href="._DimRed-bs010.html">11</a></li>
|
||||
<li><a href="._DimRed-bs011.html">12</a></li>
|
||||
<li><a href="._DimRed-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs009.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -127,18 +132,12 @@ MathJax.Hub.Config({
|
||||
<a name="part0009"></a>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec8" class="anchor">Randomized 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>
|
||||
|
||||
<h2 id="___sec8" class="anchor">Incremental PCA </h2>
|
||||
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>
|
||||
@@ -158,6 +157,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
|
||||
<li><a href="._DimRed-bs010.html">11</a></li>
|
||||
<li><a href="._DimRed-bs011.html">12</a></li>
|
||||
<li><a href="._DimRed-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs010.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -51,18 +51,22 @@ Automatically generated HTML file from DocOnce source
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -103,15 +107,16 @@ MathJax.Hub.Config({
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs001.html#___sec0" style="font-size: 80%;">Reducing the number of degrees of freedom, overarching view</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs002.html#___sec1" style="font-size: 80%;">Preprocessing our data</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs003.html#___sec2" style="font-size: 80%;">Simple preprocessing examples, Franke function and regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">Other techniques</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs004.html#___sec3" style="font-size: 80%;">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs005.html#___sec4" style="font-size: 80%;">More on Cancer Data, now with Logistic Regression</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs006.html#___sec5" style="font-size: 80%;">Principal Component Analysis</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs007.html#___sec6" style="font-size: 80%;">PCA and scikit-learn</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs008.html#___sec7" style="font-size: 80%;">More on the PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs009.html#___sec8" style="font-size: 80%;">Incremental PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs010.html#___sec9" style="font-size: 80%;">Randomized PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs011.html#___sec10" style="font-size: 80%;">Kernel PCA</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs012.html#___sec11" style="font-size: 80%;">LLE</a></li>
|
||||
<!-- navigation toc: --> <li><a href="._DimRed-bs013.html#___sec12" style="font-size: 80%;">Other techniques</a></li>
|
||||
|
||||
</ul>
|
||||
</li>
|
||||
@@ -170,7 +175,7 @@ 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-bs012.html">13</a></li>
|
||||
<li><a href="._DimRed-bs013.html">14</a></li>
|
||||
<li><a href="._DimRed-bs001.html">»</a></li>
|
||||
</ul>
|
||||
<!-- ------------------- end of main content --------------- -->
|
||||
|
||||
@@ -304,7 +304,7 @@ svm.fit(X_train_scaled, y_train)
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec3">Simple preprocessing examples, breast cancer data and classification </h2>
|
||||
<h2 id="___sec3">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines </h2>
|
||||
|
||||
<p>
|
||||
We show here how we can use a simple regression case on the breast cancer data using support vector machine as algorithm for classification
|
||||
@@ -356,7 +356,63 @@ svm.fit(X_train_scaled, y_train)
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec4">Principal Component Analysis </h2>
|
||||
<h2 id="___sec4">More on Cancer Data, now with Logistic Regression </h2>
|
||||
<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()
|
||||
|
||||
fig, axes = plt.subplots(<span style="color: #B452CD">15</span>,<span style="color: #B452CD">2</span>,figsize=(<span style="color: #B452CD">10</span>,<span style="color: #B452CD">20</span>))
|
||||
male = cancer.data[cancer.target == <span style="color: #B452CD">0</span>]
|
||||
bene = cancer.data[cancer.target == <span style="color: #B452CD">1</span>]
|
||||
ax = axes.ravel()
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #B452CD">30</span>):
|
||||
_, bins = np.histogram(cancer.data[:,i], bins =<span style="color: #B452CD">50</span>)
|
||||
ax[i].hist(male[:,i], bins = bins, alpha = <span style="color: #B452CD">0.5</span>)
|
||||
ax[i].hist(bene[:,i], bins = bins, alpha = <span style="color: #B452CD">0.5</span>)
|
||||
ax[i].set_title(cancer.feature_names[i])
|
||||
ax[i].set_yticks(())
|
||||
ax[<span style="color: #B452CD">0</span>].set_xlabel(<span style="color: #CD5555">"Feature magnitude"</span>)
|
||||
ax[<span style="color: #B452CD">0</span>].set_ylabel(<span style="color: #CD5555">"Frequency"</span>)
|
||||
ax[<span style="color: #B452CD">0</span>].legend([<span style="color: #CD5555">"Male"</span>, <span style="color: #CD5555">"Bene"</span>], loc =<span style="color: #CD5555">"best"</span>)
|
||||
fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
<span style="color: #228B22"># Set up training data</span>
|
||||
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: #228B22"># Perform Logistic Regression (replace with own code) </span>
|
||||
logreg = LogisticRegression()
|
||||
logreg.fit(X_train, y_train)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test set accuracy: {:.2f}"</span>.format(logreg.score(X_test,y_test)))
|
||||
|
||||
<span style="color: #228B22"># Scale data</span>
|
||||
<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> 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: #228B22">#svm.fit(X_train_scaled, y_train)</span>
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test set accuracy scaled data: {:.2f}"</span>.format(logreg.score(X_test_scaled,y_test)))
|
||||
|
||||
<span style="color: #228B22"># Now add PCA</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>)
|
||||
pca.fit(X_train_scaled)
|
||||
|
||||
X_pca = pca.transform(X_train_scaled)
|
||||
</pre></div>
|
||||
</section>
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec5">Principal Component Analysis </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
@@ -393,7 +449,7 @@ X2D = X_centered.dot(W2)
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec5">PCA and scikit-learn </h2>
|
||||
<h2 id="___sec6">PCA and scikit-learn </h2>
|
||||
|
||||
<p>
|
||||
Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The
|
||||
@@ -424,7 +480,7 @@ More material to come here.
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec6">More on the PCA </h2>
|
||||
<h2 id="___sec7">More on the PCA </h2>
|
||||
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 — in that case you will
|
||||
@@ -453,7 +509,7 @@ X_reduced = pca.fit_transform(X)
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec7">Incremental PCA </h2>
|
||||
<h2 id="___sec8">Incremental PCA </h2>
|
||||
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
|
||||
@@ -463,7 +519,7 @@ instances arrive).
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec8">Randomized PCA </h2>
|
||||
<h2 id="___sec9">Randomized PCA </h2>
|
||||
|
||||
<p>
|
||||
Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
|
||||
@@ -477,7 +533,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec9">Kernel PCA </h2>
|
||||
<h2 id="___sec10">Kernel PCA </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
@@ -503,7 +559,7 @@ X_reduced = rbf_pca.fit_transform(X)
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec10">LLE </h2>
|
||||
<h2 id="___sec11">LLE </h2>
|
||||
|
||||
<p>
|
||||
Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
|
||||
@@ -515,7 +571,7 @@ these local relationships are best preserved (more details shortly).
|
||||
|
||||
|
||||
<section>
|
||||
<h2 id="___sec11">Other techniques </h2>
|
||||
<h2 id="___sec12">Other techniques </h2>
|
||||
|
||||
<p>
|
||||
There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
|
||||
|
||||
@@ -71,18 +71,22 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -279,7 +283,7 @@ svm.fit(X_train_scaled, y_train)
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec3">Simple preprocessing examples, breast cancer data and classification </h2>
|
||||
<h2 id="___sec3">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines </h2>
|
||||
|
||||
<p>
|
||||
We show here how we can use a simple regression case on the breast cancer data using support vector machine as algorithm for classification
|
||||
@@ -330,7 +334,62 @@ svm.fit(X_train_scaled, y_train)
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec4">Principal Component Analysis </h2>
|
||||
<h2 id="___sec4">More on Cancer Data, now with Logistic Regression </h2>
|
||||
<p>
|
||||
|
||||
<!-- code=python (!bc pycod) typeset with pygments style "perldoc" -->
|
||||
<div class="highlight" style="background: #eeeedd"><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()
|
||||
|
||||
fig, axes = plt.subplots(<span style="color: #B452CD">15</span>,<span style="color: #B452CD">2</span>,figsize=(<span style="color: #B452CD">10</span>,<span style="color: #B452CD">20</span>))
|
||||
male = cancer.data[cancer.target == <span style="color: #B452CD">0</span>]
|
||||
bene = cancer.data[cancer.target == <span style="color: #B452CD">1</span>]
|
||||
ax = axes.ravel()
|
||||
|
||||
<span style="color: #8B008B; font-weight: bold">for</span> i <span style="color: #8B008B">in</span> <span style="color: #658b00">range</span>(<span style="color: #B452CD">30</span>):
|
||||
_, bins = np.histogram(cancer.data[:,i], bins =<span style="color: #B452CD">50</span>)
|
||||
ax[i].hist(male[:,i], bins = bins, alpha = <span style="color: #B452CD">0.5</span>)
|
||||
ax[i].hist(bene[:,i], bins = bins, alpha = <span style="color: #B452CD">0.5</span>)
|
||||
ax[i].set_title(cancer.feature_names[i])
|
||||
ax[i].set_yticks(())
|
||||
ax[<span style="color: #B452CD">0</span>].set_xlabel(<span style="color: #CD5555">"Feature magnitude"</span>)
|
||||
ax[<span style="color: #B452CD">0</span>].set_ylabel(<span style="color: #CD5555">"Frequency"</span>)
|
||||
ax[<span style="color: #B452CD">0</span>].legend([<span style="color: #CD5555">"Male"</span>, <span style="color: #CD5555">"Bene"</span>], loc =<span style="color: #CD5555">"best"</span>)
|
||||
fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
<span style="color: #228B22"># Set up training data</span>
|
||||
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: #228B22"># Perform Logistic Regression (replace with own code) </span>
|
||||
logreg = LogisticRegression()
|
||||
logreg.fit(X_train, y_train)
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test set accuracy: {:.2f}"</span>.format(logreg.score(X_test,y_test)))
|
||||
|
||||
<span style="color: #228B22"># Scale data</span>
|
||||
<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> 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: #228B22">#svm.fit(X_train_scaled, y_train)</span>
|
||||
<span style="color: #8B008B; font-weight: bold">print</span>(<span style="color: #CD5555">"Test set accuracy scaled data: {:.2f}"</span>.format(logreg.score(X_test_scaled,y_test)))
|
||||
|
||||
<span style="color: #228B22"># Now add PCA</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>)
|
||||
pca.fit(X_train_scaled)
|
||||
|
||||
X_pca = pca.transform(X_train_scaled)
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec5">Principal Component Analysis </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
@@ -366,7 +425,7 @@ X2D = X_centered.dot(W2)
|
||||
<p>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec5">PCA and scikit-learn </h2>
|
||||
<h2 id="___sec6">PCA and scikit-learn </h2>
|
||||
|
||||
<p>
|
||||
Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The
|
||||
@@ -397,7 +456,7 @@ More material to come here.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec6">More on the PCA </h2>
|
||||
<h2 id="___sec7">More on the PCA </h2>
|
||||
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 — in that case you will
|
||||
@@ -425,7 +484,7 @@ X_reduced = pca.fit_transform(X)
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec7">Incremental PCA </h2>
|
||||
<h2 id="___sec8">Incremental PCA </h2>
|
||||
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
|
||||
@@ -435,7 +494,7 @@ instances arrive).
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec8">Randomized PCA </h2>
|
||||
<h2 id="___sec9">Randomized PCA </h2>
|
||||
|
||||
<p>
|
||||
Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
|
||||
@@ -450,7 +509,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec9">Kernel PCA </h2>
|
||||
<h2 id="___sec10">Kernel PCA </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
@@ -479,7 +538,7 @@ X_reduced = rbf_pca.fit_transform(X)
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec10">LLE </h2>
|
||||
<h2 id="___sec11">LLE </h2>
|
||||
|
||||
<p>
|
||||
Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
|
||||
@@ -491,7 +550,7 @@ these local relationships are best preserved (more details shortly).
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec11">Other techniques </h2>
|
||||
<h2 id="___sec12">Other techniques </h2>
|
||||
|
||||
<p>
|
||||
There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
|
||||
|
||||
@@ -76,18 +76,22 @@ div { text-align: justify; text-justify: inter-word; }
|
||||
None,
|
||||
'___sec2'),
|
||||
('Simple preprocessing examples, breast cancer data and '
|
||||
'classification',
|
||||
'classification, Support Vector Machines',
|
||||
2,
|
||||
None,
|
||||
'___sec3'),
|
||||
('Principal Component Analysis', 2, None, '___sec4'),
|
||||
('PCA and scikit-learn', 2, None, '___sec5'),
|
||||
('More on the PCA', 2, None, '___sec6'),
|
||||
('Incremental PCA', 2, None, '___sec7'),
|
||||
('Randomized PCA', 2, None, '___sec8'),
|
||||
('Kernel PCA', 2, None, '___sec9'),
|
||||
('LLE', 2, None, '___sec10'),
|
||||
('Other techniques', 2, None, '___sec11')]}
|
||||
('More on Cancer Data, now with Logistic Regression',
|
||||
2,
|
||||
None,
|
||||
'___sec4'),
|
||||
('Principal Component Analysis', 2, None, '___sec5'),
|
||||
('PCA and scikit-learn', 2, None, '___sec6'),
|
||||
('More on the PCA', 2, None, '___sec7'),
|
||||
('Incremental PCA', 2, None, '___sec8'),
|
||||
('Randomized PCA', 2, None, '___sec9'),
|
||||
('Kernel PCA', 2, None, '___sec10'),
|
||||
('LLE', 2, None, '___sec11'),
|
||||
('Other techniques', 2, None, '___sec12')]}
|
||||
end of tocinfo -->
|
||||
|
||||
<body>
|
||||
@@ -284,7 +288,7 @@ svm<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec3">Simple preprocessing examples, breast cancer data and classification </h2>
|
||||
<h2 id="___sec3">Simple preprocessing examples, breast cancer data and classification, Support Vector Machines </h2>
|
||||
|
||||
<p>
|
||||
We show here how we can use a simple regression case on the breast cancer data using support vector machine as algorithm for classification
|
||||
@@ -335,7 +339,62 @@ svm<span style="color: #666666">.</span>fit(X_train_scaled, y_train)
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec4">Principal Component Analysis </h2>
|
||||
<h2 id="___sec4">More on Cancer Data, now with Logistic Regression </h2>
|
||||
<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()
|
||||
|
||||
fig, axes <span style="color: #666666">=</span> plt<span style="color: #666666">.</span>subplots(<span style="color: #666666">15</span>,<span style="color: #666666">2</span>,figsize<span style="color: #666666">=</span>(<span style="color: #666666">10</span>,<span style="color: #666666">20</span>))
|
||||
male <span style="color: #666666">=</span> cancer<span style="color: #666666">.</span>data[cancer<span style="color: #666666">.</span>target <span style="color: #666666">==</span> <span style="color: #666666">0</span>]
|
||||
bene <span style="color: #666666">=</span> cancer<span style="color: #666666">.</span>data[cancer<span style="color: #666666">.</span>target <span style="color: #666666">==</span> <span style="color: #666666">1</span>]
|
||||
ax <span style="color: #666666">=</span> axes<span style="color: #666666">.</span>ravel()
|
||||
|
||||
<span style="color: #008000; font-weight: bold">for</span> i <span style="color: #AA22FF; font-weight: bold">in</span> <span style="color: #008000">range</span>(<span style="color: #666666">30</span>):
|
||||
_, bins <span style="color: #666666">=</span> np<span style="color: #666666">.</span>histogram(cancer<span style="color: #666666">.</span>data[:,i], bins <span style="color: #666666">=50</span>)
|
||||
ax[i]<span style="color: #666666">.</span>hist(male[:,i], bins <span style="color: #666666">=</span> bins, alpha <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>)
|
||||
ax[i]<span style="color: #666666">.</span>hist(bene[:,i], bins <span style="color: #666666">=</span> bins, alpha <span style="color: #666666">=</span> <span style="color: #666666">0.5</span>)
|
||||
ax[i]<span style="color: #666666">.</span>set_title(cancer<span style="color: #666666">.</span>feature_names[i])
|
||||
ax[i]<span style="color: #666666">.</span>set_yticks(())
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>set_xlabel(<span style="color: #BA2121">"Feature magnitude"</span>)
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>set_ylabel(<span style="color: #BA2121">"Frequency"</span>)
|
||||
ax[<span style="color: #666666">0</span>]<span style="color: #666666">.</span>legend([<span style="color: #BA2121">"Male"</span>, <span style="color: #BA2121">"Bene"</span>], loc <span style="color: #666666">=</span><span style="color: #BA2121">"best"</span>)
|
||||
fig<span style="color: #666666">.</span>tight_layout()
|
||||
plt<span style="color: #666666">.</span>show()
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Set up training data</span>
|
||||
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: #408080; font-style: italic"># Perform Logistic Regression (replace with own code) </span>
|
||||
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">"Test set accuracy: {:.2f}"</span><span style="color: #666666">.</span>format(logreg<span style="color: #666666">.</span>score(X_test,y_test)))
|
||||
|
||||
<span style="color: #408080; font-style: italic"># Scale data</span>
|
||||
<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> 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: #408080; font-style: italic">#svm.fit(X_train_scaled, y_train)</span>
|
||||
<span style="color: #008000; font-weight: bold">print</span>(<span style="color: #BA2121">"Test set accuracy scaled data: {:.2f}"</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"># Now add PCA</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>)
|
||||
pca<span style="color: #666666">.</span>fit(X_train_scaled)
|
||||
|
||||
X_pca <span style="color: #666666">=</span> pca<span style="color: #666666">.</span>transform(X_train_scaled)
|
||||
</pre></div>
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec5">Principal Component Analysis </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
@@ -371,7 +430,7 @@ X2D <span style="color: #666666">=</span> X_centered<span style="color: #666666"
|
||||
<p>
|
||||
<!-- !split -->
|
||||
|
||||
<h2 id="___sec5">PCA and scikit-learn </h2>
|
||||
<h2 id="___sec6">PCA and scikit-learn </h2>
|
||||
|
||||
<p>
|
||||
Scikit-Learn’s PCA class implements PCA using SVD decomposition just like we did before. The
|
||||
@@ -402,7 +461,7 @@ More material to come here.
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec6">More on the PCA </h2>
|
||||
<h2 id="___sec7">More on the PCA </h2>
|
||||
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 — in that case you will
|
||||
@@ -430,7 +489,7 @@ 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="___sec7">Incremental PCA </h2>
|
||||
<h2 id="___sec8">Incremental PCA </h2>
|
||||
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
|
||||
@@ -440,7 +499,7 @@ instances arrive).
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec8">Randomized PCA </h2>
|
||||
<h2 id="___sec9">Randomized PCA </h2>
|
||||
|
||||
<p>
|
||||
Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic
|
||||
@@ -455,7 +514,7 @@ previous algorithms when \( d \) is much smaller than \( n \).
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec9">Kernel PCA </h2>
|
||||
<h2 id="___sec10">Kernel PCA </h2>
|
||||
<div class="alert alert-block alert-block alert-text-normal">
|
||||
<b></b>
|
||||
<p>
|
||||
@@ -484,7 +543,7 @@ 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="___sec10">LLE </h2>
|
||||
<h2 id="___sec11">LLE </h2>
|
||||
|
||||
<p>
|
||||
Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction
|
||||
@@ -496,7 +555,7 @@ these local relationships are best preserved (more details shortly).
|
||||
<p>
|
||||
<!-- !split --><br><br><br><br><br><br><br><br><br><br>
|
||||
|
||||
<h2 id="___sec11">Other techniques </h2>
|
||||
<h2 id="___sec12">Other techniques </h2>
|
||||
|
||||
<p>
|
||||
There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn.
|
||||
|
||||
@@ -158,7 +158,7 @@
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## Simple preprocessing examples, breast cancer data and classification\n",
|
||||
"## Simple preprocessing examples, breast cancer data and classification, Support Vector Machines\n",
|
||||
"\n",
|
||||
"We show here how we can use a simple regression case on the breast cancer data using support vector machine as algorithm for classification"
|
||||
]
|
||||
@@ -212,6 +212,70 @@
|
||||
"print(\"Test set accuracy scaled data: {:.2f}\".format(svm.score(X_test_scaled,y_test)))"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
"source": [
|
||||
"## More on Cancer Data, now with Logistic Regression"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"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",
|
||||
"fig, axes = plt.subplots(15,2,figsize=(10,20))\n",
|
||||
"male = cancer.data[cancer.target == 0]\n",
|
||||
"bene = cancer.data[cancer.target == 1]\n",
|
||||
"ax = axes.ravel()\n",
|
||||
"\n",
|
||||
"for i in range(30):\n",
|
||||
" _, bins = np.histogram(cancer.data[:,i], bins =50)\n",
|
||||
" ax[i].hist(male[:,i], bins = bins, alpha = 0.5)\n",
|
||||
" ax[i].hist(bene[:,i], bins = bins, alpha = 0.5)\n",
|
||||
" ax[i].set_title(cancer.feature_names[i])\n",
|
||||
" ax[i].set_yticks(())\n",
|
||||
"ax[0].set_xlabel(\"Feature magnitude\")\n",
|
||||
"ax[0].set_ylabel(\"Frequency\")\n",
|
||||
"ax[0].legend([\"Male\", \"Bene\"], loc =\"best\")\n",
|
||||
"fig.tight_layout()\n",
|
||||
"plt.show()\n",
|
||||
"\n",
|
||||
"# Set up training data\n",
|
||||
"X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n",
|
||||
"# Perform Logistic Regression (replace with own code) \n",
|
||||
"logreg = LogisticRegression()\n",
|
||||
"logreg.fit(X_train, y_train)\n",
|
||||
"print(\"Test set accuracy: {:.2f}\".format(logreg.score(X_test,y_test)))\n",
|
||||
"\n",
|
||||
"# Scale data\n",
|
||||
"from sklearn.preprocessing import 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",
|
||||
"logreg.fit(X_train_scaled, y_train)\n",
|
||||
"#svm.fit(X_train_scaled, y_train)\n",
|
||||
"print(\"Test set accuracy scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n",
|
||||
"\n",
|
||||
"# Now add PCA\n",
|
||||
"from sklearn.decomposition import PCA\n",
|
||||
"pca = PCA(n_components = 2)\n",
|
||||
"pca.fit(X_train_scaled)\n",
|
||||
"\n",
|
||||
"X_pca = pca.transform(X_train_scaled)"
|
||||
]
|
||||
},
|
||||
{
|
||||
"cell_type": "markdown",
|
||||
"metadata": {},
|
||||
@@ -226,7 +290,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 3,
|
||||
"execution_count": 4,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -253,7 +317,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 4,
|
||||
"execution_count": 5,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -277,7 +341,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 5,
|
||||
"execution_count": 6,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -299,7 +363,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 6,
|
||||
"execution_count": 7,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -328,7 +392,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 7,
|
||||
"execution_count": 8,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -351,7 +415,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 8,
|
||||
"execution_count": 9,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
@@ -397,7 +461,7 @@
|
||||
},
|
||||
{
|
||||
"cell_type": "code",
|
||||
"execution_count": 9,
|
||||
"execution_count": 10,
|
||||
"metadata": {
|
||||
"collapsed": false
|
||||
},
|
||||
|
||||
Binary file not shown.
Binary file not shown.
@@ -139,7 +139,7 @@ print("R2 score for scaled data: {:.2f}".format(svm.score(X_test_scaled,y_test)
|
||||
|
||||
|
||||
!split
|
||||
===== Simple preprocessing examples, breast cancer data and classification =====
|
||||
===== Simple preprocessing examples, breast cancer data and classification, Support Vector Machines =====
|
||||
|
||||
We show here how we can use a simple regression case on the breast cancer data using support vector machine as algorithm for classification
|
||||
|
||||
@@ -188,6 +188,59 @@ print("Test set accuracy scaled data: {:.2f}".format(svm.score(X_test_scaled,y_t
|
||||
!ec
|
||||
|
||||
|
||||
!split
|
||||
===== More on Cancer Data, now with Logistic Regression =====
|
||||
!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()
|
||||
|
||||
fig, axes = plt.subplots(15,2,figsize=(10,20))
|
||||
male = cancer.data[cancer.target == 0]
|
||||
bene = cancer.data[cancer.target == 1]
|
||||
ax = axes.ravel()
|
||||
|
||||
for i in range(30):
|
||||
_, bins = np.histogram(cancer.data[:,i], bins =50)
|
||||
ax[i].hist(male[:,i], bins = bins, alpha = 0.5)
|
||||
ax[i].hist(bene[:,i], bins = bins, alpha = 0.5)
|
||||
ax[i].set_title(cancer.feature_names[i])
|
||||
ax[i].set_yticks(())
|
||||
ax[0].set_xlabel("Feature magnitude")
|
||||
ax[0].set_ylabel("Frequency")
|
||||
ax[0].legend(["Male", "Bene"], loc ="best")
|
||||
fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
# Set up training data
|
||||
X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
|
||||
# Perform Logistic Regression (replace with own code)
|
||||
logreg = LogisticRegression()
|
||||
logreg.fit(X_train, y_train)
|
||||
print("Test set accuracy: {:.2f}".format(logreg.score(X_test,y_test)))
|
||||
|
||||
# Scale data
|
||||
from sklearn.preprocessing import 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)
|
||||
#svm.fit(X_train_scaled, y_train)
|
||||
print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
|
||||
|
||||
# Now add PCA
|
||||
from sklearn.decomposition import PCA
|
||||
pca = PCA(n_components = 2)
|
||||
pca.fit(X_train_scaled)
|
||||
|
||||
X_pca = pca.transform(X_train_scaled)
|
||||
|
||||
|
||||
!ec
|
||||
|
||||
!split
|
||||
===== Principal Component Analysis =====
|
||||
|
||||
@@ -0,0 +1,43 @@
|
||||
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.svm import SVC
|
||||
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)
|
||||
|
||||
#svm = SVC(C=100)
|
||||
#svm.fit(X_train, y_train)
|
||||
print("Test set accuracy: {:.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)
|
||||
|
||||
print("Feature min values before scaling:\n {}".format(X_train.min(axis=0)))
|
||||
print("Feature max values before scaling:\n {}".format(X_train.max(axis=0)))
|
||||
|
||||
print("Feature min values before scaling:\n {}".format(X_train_scaled.min(axis=0)))
|
||||
print("Feature max values before scaling:\n {}".format(X_train_scaled.max(axis=0)))
|
||||
|
||||
logreg.fit(X_train_scaled, y_train)
|
||||
#svm.fit(X_train_scaled, y_train)
|
||||
print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
|
||||
|
||||
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)
|
||||
#svm.fit(X_train_scaled, y_train)
|
||||
print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
|
||||
@@ -0,0 +1,40 @@
|
||||
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()
|
||||
|
||||
fig, axes = plt.subplots(15,2,figsize=(10,20))
|
||||
malignant = cancer.data[cancer.target == 0]
|
||||
benign = cancer.data[cancer.target == 1]
|
||||
ax = axes.ravel()
|
||||
|
||||
for i in range(30):
|
||||
_, bins = np.histogram(cancer.data[:,i], bins =50)
|
||||
ax[i].hist(malignant[:,i], bins = bins, alpha = 0.5)
|
||||
ax[i].hist(benign[:,i], bins = bins, alpha = 0.5)
|
||||
ax[i].set_title(cancer.feature_names[i])
|
||||
ax[i].set_yticks(())
|
||||
ax[0].set_xlabel("Feature magnitude")
|
||||
ax[0].set_ylabel("Frequency")
|
||||
ax[0].legend(["Malignant", "Benign"], loc ="best")
|
||||
fig.tight_layout()
|
||||
plt.show()
|
||||
|
||||
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)))
|
||||
Reference in New Issue
Block a user