From 63659da7d80a0a4caeb74d7ede73a349788e22d9 Mon Sep 17 00:00:00 2001 From: mhjensen Date: Thu, 24 Oct 2019 13:59:10 +0200 Subject: [PATCH] added some examples --- doc/pub/DimRed/html/._DimRed-bs000.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs001.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs002.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs003.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs004.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs005.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs006.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs007.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs008.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs009.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs010.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs011.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs012.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs013.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs014.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs015.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs016.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs017.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs018.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs019.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs020.html | 28 ++++--- doc/pub/DimRed/html/._DimRed-bs021.html | 27 +++--- doc/pub/DimRed/html/._DimRed-bs022.html | 27 +++--- doc/pub/DimRed/html/._DimRed-bs023.html | 30 +++---- doc/pub/DimRed/html/._DimRed-bs024.html | 82 +++++++++++-------- doc/pub/DimRed/html/._DimRed-bs025.html | 57 +++++++++---- doc/pub/DimRed/html/._DimRed-bs026.html | 43 +++++----- doc/pub/DimRed/html/._DimRed-bs027.html | 51 +++++------- doc/pub/DimRed/html/._DimRed-bs028.html | 57 +++++++++---- doc/pub/DimRed/html/._DimRed-bs029.html | 46 +++++------ doc/pub/DimRed/html/._DimRed-bs030.html | 12 +-- doc/pub/DimRed/html/DimRed-bs.html | 28 ++++--- doc/pub/DimRed/html/DimRed-reveal.html | 57 +++++++++++-- doc/pub/DimRed/html/DimRed-solarized.html | 69 ++++++++++++---- doc/pub/DimRed/html/DimRed.html | 69 ++++++++++++---- doc/pub/DimRed/ipynb/DimRed.ipynb | 57 ++++++++++++- doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz | Bin 191 -> 191 bytes doc/pub/DimRed/pdf/DimRed-minted.pdf | Bin 253120 -> 253275 bytes doc/src/DimRed/DimRed.do.txt | 40 ++++++++- doc/src/DimRed/PCAcancer.py | 10 ++- 40 files changed, 830 insertions(+), 520 deletions(-) diff --git a/doc/pub/DimRed/html/._DimRed-bs000.html b/doc/pub/DimRed/html/._DimRed-bs000.html index 396bd951a..bc9ba42c9 100644 --- a/doc/pub/DimRed/html/._DimRed-bs000.html +++ b/doc/pub/DimRed/html/._DimRed-bs000.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -225,7 +227,7 @@ MathJax.Hub.Config({
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs001.html b/doc/pub/DimRed/html/._DimRed-bs001.html index d9043ef27..5eacb11b3 100644 --- a/doc/pub/DimRed/html/._DimRed-bs001.html +++ b/doc/pub/DimRed/html/._DimRed-bs001.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -225,7 +227,7 @@ data.
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs002.html b/doc/pub/DimRed/html/._DimRed-bs002.html index cd7af24e6..1a1f68938 100644 --- a/doc/pub/DimRed/html/._DimRed-bs002.html +++ b/doc/pub/DimRed/html/._DimRed-bs002.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -224,7 +226,7 @@ ensures that all features are exactly between \( 0 \) and \( 1 \). The
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs003.html b/doc/pub/DimRed/html/._DimRed-bs003.html index 8da86d618..2d3bfbf9a 100644 --- a/doc/pub/DimRed/html/._DimRed-bs003.html +++ b/doc/pub/DimRed/html/._DimRed-bs003.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -227,7 +229,7 @@ techniques.
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs004.html b/doc/pub/DimRed/html/._DimRed-bs004.html index e8c8765cf..32a4b3df2 100644 --- a/doc/pub/DimRed/html/._DimRed-bs004.html +++ b/doc/pub/DimRed/html/._DimRed-bs004.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -302,7 +304,7 @@ svm.fit(X_train_scaled, y_train)
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs005.html b/doc/pub/DimRed/html/._DimRed-bs005.html index 4a94d8952..0f389a6c6 100644 --- a/doc/pub/DimRed/html/._DimRed-bs005.html +++ b/doc/pub/DimRed/html/._DimRed-bs005.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -252,7 +254,7 @@ svm.fit(X_train_scaled, y_train)
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs006.html b/doc/pub/DimRed/html/._DimRed-bs006.html index 6a971e73c..d5e29d62d 100644 --- a/doc/pub/DimRed/html/._DimRed-bs006.html +++ b/doc/pub/DimRed/html/._DimRed-bs006.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -231,7 +233,7 @@ logreg.fit(X_train_scaled, y_train)
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs007.html b/doc/pub/DimRed/html/._DimRed-bs007.html index 42caa2901..9a71aec08 100644 --- a/doc/pub/DimRed/html/._DimRed-bs007.html +++ b/doc/pub/DimRed/html/._DimRed-bs007.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -286,7 +288,7 @@ applications.
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs008.html b/doc/pub/DimRed/html/._DimRed-bs008.html index e21955283..c2a86cade 100644 --- a/doc/pub/DimRed/html/._DimRed-bs008.html +++ b/doc/pub/DimRed/html/._DimRed-bs008.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -216,7 +218,7 @@ We have a data set defined by a design/feature matrix \( \boldsymbol{X} \) (see
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs009.html b/doc/pub/DimRed/html/._DimRed-bs009.html index d59b62820..710178b2e 100644 --- a/doc/pub/DimRed/html/._DimRed-bs009.html +++ b/doc/pub/DimRed/html/._DimRed-bs009.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -265,7 +267,7 @@ In the above example this is the function we constructed using pandas.
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs010.html b/doc/pub/DimRed/html/._DimRed-bs010.html index 0499b414b..126d5627c 100644 --- a/doc/pub/DimRed/html/._DimRed-bs010.html +++ b/doc/pub/DimRed/html/._DimRed-bs010.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -260,7 +262,7 @@ $$
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs011.html b/doc/pub/DimRed/html/._DimRed-bs011.html index 997227329..0b8212479 100644 --- a/doc/pub/DimRed/html/._DimRed-bs011.html +++ b/doc/pub/DimRed/html/._DimRed-bs011.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -248,7 +250,7 @@ C = np.c
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs012.html b/doc/pub/DimRed/html/._DimRed-bs012.html index 2c5be19cc..b8c4a9bf3 100644 --- a/doc/pub/DimRed/html/._DimRed-bs012.html +++ b/doc/pub/DimRed/html/._DimRed-bs012.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -250,7 +252,7 @@ The above procedure with numpy can be made more compact if we use pand
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs013.html b/doc/pub/DimRed/html/._DimRed-bs013.html index 14ec6ffb6..3e0982c2d 100644 --- a/doc/pub/DimRed/html/._DimRed-bs013.html +++ b/doc/pub/DimRed/html/._DimRed-bs013.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -232,7 +234,7 @@ We expand this model to the Franke function discussed above.
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs014.html b/doc/pub/DimRed/html/._DimRed-bs014.html index a95f8dbbd..77882c670 100644 --- a/doc/pub/DimRed/html/._DimRed-bs014.html +++ b/doc/pub/DimRed/html/._DimRed-bs014.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -268,7 +270,7 @@ matrix.
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs015.html b/doc/pub/DimRed/html/._DimRed-bs015.html index e66cf4e66..2339a6d61 100644 --- a/doc/pub/DimRed/html/._DimRed-bs015.html +++ b/doc/pub/DimRed/html/._DimRed-bs015.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -248,7 +250,7 @@ It is easy to generalize this to a matrix \( \boldsymbol{X}\in {\mathbb{R}}^{n\t
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs016.html b/doc/pub/DimRed/html/._DimRed-bs016.html index 3ed9f1660..c1988b0b0 100644 --- a/doc/pub/DimRed/html/._DimRed-bs016.html +++ b/doc/pub/DimRed/html/._DimRed-bs016.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -256,7 +258,7 @@ features/predictors.
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs017.html b/doc/pub/DimRed/html/._DimRed-bs017.html index 4ab4a0339..73aecf9a2 100644 --- a/doc/pub/DimRed/html/._DimRed-bs017.html +++ b/doc/pub/DimRed/html/._DimRed-bs017.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -239,7 +241,7 @@ After this we ask ourselves how do we prove the link between the maximum varianc
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs018.html b/doc/pub/DimRed/html/._DimRed-bs018.html index c29620553..95d449567 100644 --- a/doc/pub/DimRed/html/._DimRed-bs018.html +++ b/doc/pub/DimRed/html/._DimRed-bs018.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -226,7 +228,7 @@ The PCA theorem states that minimizing the above reconstruction error correspond
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs019.html b/doc/pub/DimRed/html/._DimRed-bs019.html index 63ee497dc..a6e981422 100644 --- a/doc/pub/DimRed/html/._DimRed-bs019.html +++ b/doc/pub/DimRed/html/._DimRed-bs019.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -228,7 +230,7 @@ where the vectors on the rhs are known.
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs020.html b/doc/pub/DimRed/html/._DimRed-bs020.html index b41d42150..d1e36909d 100644 --- a/doc/pub/DimRed/html/._DimRed-bs020.html +++ b/doc/pub/DimRed/html/._DimRed-bs020.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -242,6 +244,8 @@ We are almost there, we have obtained a relation between minimizing the reconstr
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs021.html b/doc/pub/DimRed/html/._DimRed-bs021.html index 5a04c8700..ee37e1a02 100644 --- a/doc/pub/DimRed/html/._DimRed-bs021.html +++ b/doc/pub/DimRed/html/._DimRed-bs021.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -254,6 +256,7 @@ chapter 12.4 and discussion therein.
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs022.html b/doc/pub/DimRed/html/._DimRed-bs022.html index d613cfc50..b4a7a67e2 100644 --- a/doc/pub/DimRed/html/._DimRed-bs022.html +++ b/doc/pub/DimRed/html/._DimRed-bs022.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -258,6 +260,7 @@ X2D = X_centered28
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs023.html b/doc/pub/DimRed/html/._DimRed-bs023.html index 51348ffde..dbef737d6 100644 --- a/doc/pub/DimRed/html/._DimRed-bs023.html +++ b/doc/pub/DimRed/html/._DimRed-bs023.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -209,8 +211,7 @@ principal component is equal to

    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. +variance that lies along the axis of each principal component.

    @@ -234,6 +235,7 @@ More material to come here.

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  • »
    • diff --git a/doc/pub/DimRed/html/._DimRed-bs024.html b/doc/pub/DimRed/html/._DimRed-bs024.html index c9ffe037b..7d840e6fb 100644 --- a/doc/pub/DimRed/html/._DimRed-bs024.html +++ b/doc/pub/DimRed/html/._DimRed-bs024.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -182,32 +184,43 @@ MathJax.Hub.Config({ -

    More on the PCA

    - -

    -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: +

    Back to the Cancer Data

    +We can now repeat the above but applied to real data, in this case our breat cancer data.

    -

    pca = PCA()
-pca.fit(X)
-cumsum = np.cumsum(pca.explained_variance_ratio_)
-d = np.argmax(cumsum >= 0.95) + 1
-
    -

    -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: -

    +

    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()
 
-
-
    pca = PCA(n_components=0.95)
-X_reduced = pca.fit_transform(X)
+X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
+print(X_train.shape)
+print(X_test.shape)
+
+logreg = LogisticRegression()
+logreg.fit(X_train, y_train)
+print("Test set accuracy from Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
+
+from sklearn.preprocessing import MinMaxScaler, StandardScaler
+scaler = StandardScaler()
+scaler.fit(X_train)
+X_train_scaled = scaler.transform(X_train)
+X_test_scaled = scaler.transform(X_test)
+
+logreg.fit(X_train_scaled, y_train)
+print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
+
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2D_train = pca.fit_transform(X_train_scaled)
+X2D_test = pca.fit_transform(X_test_scaled)
+
+logreg.fit(X2D_train,y_train)
+print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X2D_test,y_test)))
 
    
 
    
 
    
@@ -230,6 +243,7 @@ X_reduced = pca
   
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+  
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  • »
    • 
 
 
diff --git a/doc/pub/DimRed/html/._DimRed-bs025.html b/doc/pub/DimRed/html/._DimRed-bs025.html
index dc43d79f6..213172eef 100644
--- a/doc/pub/DimRed/html/._DimRed-bs025.html
+++ b/doc/pub/DimRed/html/._DimRed-bs025.html
@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
               ('The final step', 2, None, '___sec20'),
               ('Principal Component Analysis', 2, None, '___sec21'),
               ('PCA and scikit-learn', 2, None, '___sec22'),
-              ('More on the PCA', 2, None, '___sec23'),
-              ('Incremental PCA', 2, None, '___sec24'),
-              ('Randomized PCA', 2, None, '___sec25'),
-              ('Kernel PCA', 2, None, '___sec26'),
-              ('LLE', 2, None, '___sec27'),
-              ('Other techniques', 2, None, '___sec28')]}
+              ('Back to the Cancer Data', 2, None, '___sec23'),
+              ('More on the PCA', 2, None, '___sec24'),
+              ('Incremental PCA', 2, None, '___sec25'),
+              ('Randomized PCA', 2, None, '___sec26'),
+              ('Kernel PCA', 2, None, '___sec27'),
+              ('LLE', 2, None, '___sec28'),
+              ('Other techniques', 2, None, '___sec29')]}
 end of tocinfo -->
 
 
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
       
  • The final step
    • 
       
  • Principal Component Analysis
    • 
       
  • PCA and scikit-learn
    • 
-      
  • More on the PCA
    • 
-      
  • Incremental PCA
    • 
-      
  • Randomized PCA
    • 
-      
  • Kernel PCA
    • 
-      
  • LLE
    • 
-      
  • Other techniques
    • 
+      
  • Back to the Cancer Data
    • 
+      
  • More on the PCA
    • 
+      
  • Incremental PCA
    • 
+      
  • Randomized PCA
    • 
+      
  • Kernel PCA
    • 
+      
  • LLE
    • 
+      
  • Other techniques
    • 
 
         
       
@@ -182,15 +184,33 @@ MathJax.Hub.Config({
 
 
 
-
    Incremental PCA 
    
+
    More on the PCA 
    
 
 
    
-One problem with the preceding implementation of PCA is that it requires the whole training set to fit in
-memory in order for the SVD algorithm to run. Fortunately, Incremental PCA (IPCA) algorithms have
-been developed: you can split the training set into mini-batches and feed an IPCA algorithm one minibatch
-at a time. This is useful for large training sets, and also to apply PCA online (i.e., on the fly, as new
-instances arrive).
+Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to
+choose the number of dimensions that add up to a sufficiently large portion of the variance (e.g., 95%).
+Unless, of course, you are reducing dimensionality for data visualization — 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:
+
    
 
+
+
    pca = PCA()
+pca.fit(X)
+cumsum = np.cumsum(pca.explained_variance_ratio_)
+d = np.argmax(cumsum >= 0.95) + 1
+
    
+
    
+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:
+
    
+
+
+
    pca = PCA(n_components=0.95)
+X_reduced = pca.fit_transform(X)
+
    
 
    
 
    
 
@@ -211,6 +231,7 @@ instances arrive).
   
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+  
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    • 
 
 
diff --git a/doc/pub/DimRed/html/._DimRed-bs026.html b/doc/pub/DimRed/html/._DimRed-bs026.html
index a4e1b973d..e3a14c74a 100644
--- a/doc/pub/DimRed/html/._DimRed-bs026.html
+++ b/doc/pub/DimRed/html/._DimRed-bs026.html
@@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source
               ('The final step', 2, None, '___sec20'),
               ('Principal Component Analysis', 2, None, '___sec21'),
               ('PCA and scikit-learn', 2, None, '___sec22'),
-              ('More on the PCA', 2, None, '___sec23'),
-              ('Incremental PCA', 2, None, '___sec24'),
-              ('Randomized PCA', 2, None, '___sec25'),
-              ('Kernel PCA', 2, None, '___sec26'),
-              ('LLE', 2, None, '___sec27'),
-              ('Other techniques', 2, None, '___sec28')]}
+              ('Back to the Cancer Data', 2, None, '___sec23'),
+              ('More on the PCA', 2, None, '___sec24'),
+              ('Incremental PCA', 2, None, '___sec25'),
+              ('Randomized PCA', 2, None, '___sec26'),
+              ('Kernel PCA', 2, None, '___sec27'),
+              ('LLE', 2, None, '___sec28'),
+              ('Other techniques', 2, None, '___sec29')]}
 end of tocinfo -->
 
 
@@ -161,12 +162,13 @@ MathJax.Hub.Config({
       
  • The final step
    • 
       
  • Principal Component Analysis
    • 
       
  • PCA and scikit-learn
    • 
-      
  • More on the PCA
    • 
-      
  • Incremental PCA
    • 
-      
  • Randomized PCA
    • 
-      
  • Kernel PCA
    • 
-      
  • LLE
    • 
-      
  • Other techniques
    • 
+      
  • Back to the Cancer Data
    • 
+      
  • More on the PCA
    • 
+      
  • Incremental PCA
    • 
+      
  • Randomized PCA
    • 
+      
  • Kernel PCA
    • 
+      
  • LLE
    • 
+      
  • Other techniques
    • 
 
         
       
@@ -182,18 +184,14 @@ MathJax.Hub.Config({
 
 
 
-
    Randomized PCA 
    
+
    Incremental PCA 
    
 
 
    
-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 \( n \).
-
-
    
-
    - - +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).

    @@ -214,6 +212,7 @@ previous algorithms when \( d \) is much smaller than \( n \).

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  • »
    • diff --git a/doc/pub/DimRed/html/._DimRed-bs027.html b/doc/pub/DimRed/html/._DimRed-bs027.html index 20413ce9d..e5767b817 100644 --- a/doc/pub/DimRed/html/._DimRed-bs027.html +++ b/doc/pub/DimRed/html/._DimRed-bs027.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -182,28 +184,14 @@ MathJax.Hub.Config({ -

    Kernel PCA

    -
    -
    -

    +

    Randomized PCA

    -The kernel trick is a mathematical technique that implicitly maps instances into a -very high-dimensional space (called the feature space), enabling nonlinear classification and regression -with Support Vector Machines. Recall that a linear decision boundary in the high-dimensional feature -space corresponds to a complex nonlinear decision boundary in the original space. -It turns out that the same trick can be applied to PCA, making it possible to perform complex nonlinear -projections for dimensionality reduction. This is called Kernel PCA (kPCA). It is often good at -preserving clusters of instances after projection, or sometimes even unrolling datasets that lie close to a -twisted manifold. -For example, the following code uses Scikit-Learn’s KernelPCA class to perform kPCA with an -

    +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 \( n \). - -

    from sklearn.decomposition import KernelPCA
-rbf_pca = KernelPCA(n_components = 2, kernel="rbf", gamma=0.04)
-X_reduced = rbf_pca.fit_transform(X)
-

    @@ -227,6 +215,7 @@ X_reduced = rbf_pca28
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  • »
    • diff --git a/doc/pub/DimRed/html/._DimRed-bs028.html b/doc/pub/DimRed/html/._DimRed-bs028.html index a221d679b..9cbb7aa9f 100644 --- a/doc/pub/DimRed/html/._DimRed-bs028.html +++ b/doc/pub/DimRed/html/._DimRed-bs028.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -182,14 +184,32 @@ MathJax.Hub.Config({ -

    LLE

    +

    Kernel PCA

    +
    +
    +

    -Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction -(NLDR) technique. It is a Manifold Learning technique that does not rely on projections like the previous -algorithms. In a nutshell, LLE works by first measuring how each training instance linearly relates to its -closest neighbors (c.n.), and then looking for a low-dimensional representation of the training set where -these local relationships are best preserved (more details shortly). +The kernel trick is a mathematical technique that implicitly maps instances into a +very high-dimensional space (called the feature space), enabling nonlinear classification and regression +with Support Vector Machines. Recall that a linear decision boundary in the high-dimensional feature +space corresponds to a complex nonlinear decision boundary in the original space. +It turns out that the same trick can be applied to PCA, making it possible to perform complex nonlinear +projections for dimensionality reduction. This is called Kernel PCA (kPCA). It is often good at +preserving clusters of instances after projection, or sometimes even unrolling datasets that lie close to a +twisted manifold. +For example, the following code uses Scikit-Learn’s KernelPCA class to perform kPCA with an +

    + + +

    from sklearn.decomposition import KernelPCA
+rbf_pca = KernelPCA(n_components = 2, kernel="rbf", gamma=0.04)
+X_reduced = rbf_pca.fit_transform(X)
+
    +

    +

    +
    +

    @@ -208,6 +228,7 @@ these local relationships are best preserved (more details shortly).

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    • +
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    • diff --git a/doc/pub/DimRed/html/._DimRed-bs029.html b/doc/pub/DimRed/html/._DimRed-bs029.html index b53f979ac..bf5d8c9b0 100644 --- a/doc/pub/DimRed/html/._DimRed-bs029.html +++ b/doc/pub/DimRed/html/._DimRed-bs029.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -182,22 +184,16 @@ MathJax.Hub.Config({ -

    Other techniques

    +

    LLE

    -There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn. +Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction +(NLDR) technique. It is a Manifold Learning technique that does not rely on projections like the previous +algorithms. In a nutshell, LLE works by first measuring how each training instance linearly relates to its +closest neighbors (c.n.), and then looking for a low-dimensional representation of the training set where +these local relationships are best preserved (more details shortly).

    -Here are some of the most popular: - -

      -
    • Multidimensional Scaling (MDS) reduces dimensionality while trying to preserve the distances between the instances.
      • -
    • Isomap creates a graph by connecting each instance to its nearest neighbors, then reduces dimensionality while trying to preserve the geodesic distances between the instances.
      • -
    • t-Distributed Stochastic Neighbor Embedding (t-SNE) reduces dimensionality while trying to keep similar instances close and dissimilar instances apart. It is mostly used for visualization, in particular to visualize clusters of instances in high-dimensional space (e.g., to visualize the MNIST images in 2D).
      • -
    • Linear Discriminant Analysis (LDA) is actually a classification algorithm, but during training it learns the most discriminative axes between the classes, and these axes can then be used to define a hyperplane onto which to project the data. The benefit is that the projection will keep classes as far apart as possible, so LDA is a good technique to reduce dimensionality before running another classification algorithm such as a Support Vector Machine (SVM) classifier discussed in the SVM lectures.
      • -
    - -

      @@ -213,6 +209,8 @@ Here are some of the most popular:
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      • +
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    • »
    diff --git a/doc/pub/DimRed/html/._DimRed-bs030.html b/doc/pub/DimRed/html/._DimRed-bs030.html index 0e96ca026..aa8394e93 100644 --- a/doc/pub/DimRed/html/._DimRed-bs030.html +++ b/doc/pub/DimRed/html/._DimRed-bs030.html @@ -93,9 +93,9 @@ Automatically generated HTML file from DocOnce source ('Proof of the PCA Theorem', 2, None, '___sec18'), ('PCA Proof continued', 2, None, '___sec19'), ('The final step', 2, None, '___sec20'), - ('PCA and Scikit-Learn Functionality', 2, None, '___sec21'), - ('Principal Component Analysis', 2, None, '___sec22'), - ('PCA and scikit-learn', 2, None, '___sec23'), + ('Principal Component Analysis', 2, None, '___sec21'), + ('PCA and scikit-learn', 2, None, '___sec22'), + ('Back to the Cancer Data', 2, None, '___sec23'), ('More on the PCA', 2, None, '___sec24'), ('Incremental PCA', 2, None, '___sec25'), ('Randomized PCA', 2, None, '___sec26'), @@ -160,9 +160,9 @@ MathJax.Hub.Config({
  • Proof of the PCA Theorem
  • PCA Proof continued
  • The final step
    • -
  • PCA and Scikit-Learn Functionality
    • -
  • Principal Component Analysis
    • -
  • PCA and scikit-learn
    • +
  • Principal Component Analysis
    • +
  • PCA and scikit-learn
    • +
  • Back to the Cancer Data
  • More on the PCA
  • Incremental PCA
  • Randomized PCA
    • diff --git a/doc/pub/DimRed/html/DimRed-bs.html b/doc/pub/DimRed/html/DimRed-bs.html index 396bd951a..bc9ba42c9 100644 --- a/doc/pub/DimRed/html/DimRed-bs.html +++ b/doc/pub/DimRed/html/DimRed-bs.html @@ -95,12 +95,13 @@ Automatically generated HTML file from DocOnce source ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -161,12 +162,13 @@ MathJax.Hub.Config({
  • The final step
  • Principal Component Analysis
  • PCA and scikit-learn
    • -
  • More on the PCA
    • -
  • Incremental PCA
    • -
  • Randomized PCA
    • -
  • Kernel PCA
    • -
  • LLE
    • -
  • Other techniques
    • +
  • Back to the Cancer Data
    • +
  • More on the PCA
    • +
  • Incremental PCA
    • +
  • Randomized PCA
    • +
  • Kernel PCA
    • +
  • LLE
    • +
  • Other techniques
    • @@ -225,7 +227,7 @@ MathJax.Hub.Config({
  • 9
  • 10
  • ...
    • -
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    • +
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    • diff --git a/doc/pub/DimRed/html/DimRed-reveal.html b/doc/pub/DimRed/html/DimRed-reveal.html index be7cae712..b92b94473 100644 --- a/doc/pub/DimRed/html/DimRed-reveal.html +++ b/doc/pub/DimRed/html/DimRed-reveal.html @@ -1232,13 +1232,54 @@ principal component is equal to

    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. +variance that lies along the axis of each principal component.

    -

    More on the PCA

    +

    Back to the Cancer Data

    +We can now repeat the above but applied to real data, in this case our breat cancer data. +

    + + +

    import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.model_selection import  train_test_split 
+from sklearn.datasets import load_breast_cancer
+from sklearn.linear_model import LogisticRegression
+cancer = load_breast_cancer()
+
+X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
+print(X_train.shape)
+print(X_test.shape)
+
+logreg = LogisticRegression()
+logreg.fit(X_train, y_train)
+print("Test set accuracy from Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
+
+from sklearn.preprocessing import MinMaxScaler, StandardScaler
+scaler = StandardScaler()
+scaler.fit(X_train)
+X_train_scaled = scaler.transform(X_train)
+X_test_scaled = scaler.transform(X_test)
+
+logreg.fit(X_train_scaled, y_train)
+print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
+
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2D_train = pca.fit_transform(X_train_scaled)
+X2D_test = pca.fit_transform(X_test_scaled)
+
+logreg.fit(X2D_train,y_train)
+print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X2D_test,y_test)))
+
    +
    + + +
    +

    More on the PCA

    Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to @@ -1269,7 +1310,7 @@ X_reduced = pca.fit_transform(X)

    -

    Incremental PCA

    +

    Incremental PCA

    One problem with the preceding implementation of PCA is that it requires the whole training set to fit in @@ -1281,7 +1322,7 @@ instances arrive).

    -

    Randomized PCA

    +

    Randomized PCA

    Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic @@ -1295,7 +1336,7 @@ previous algorithms when \( d \) is much smaller than \( n \).

    -

    Kernel PCA

    +

    Kernel PCA

    @@ -1321,7 +1362,7 @@ X_reduced = rbf_pca.fit_transform(X)

    -

    LLE

    +

    LLE

    Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction @@ -1333,7 +1374,7 @@ these local relationships are best preserved (more details shortly).

    -

    Other techniques

    +

    Other techniques

    There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn. diff --git a/doc/pub/DimRed/html/DimRed-solarized.html b/doc/pub/DimRed/html/DimRed-solarized.html index 0925346bb..2933d3b74 100644 --- a/doc/pub/DimRed/html/DimRed-solarized.html +++ b/doc/pub/DimRed/html/DimRed-solarized.html @@ -115,12 +115,13 @@ div { text-align: justify; text-justify: inter-word; } ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -1170,13 +1171,53 @@ principal component is equal to

    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. +variance that lies along the axis of each principal component.











    -

    More on the PCA

    +

    Back to the Cancer Data

    +We can now repeat the above but applied to real data, in this case our breat cancer data. +

    + + +

    import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.model_selection import  train_test_split 
+from sklearn.datasets import load_breast_cancer
+from sklearn.linear_model import LogisticRegression
+cancer = load_breast_cancer()
+
+X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
+print(X_train.shape)
+print(X_test.shape)
+
+logreg = LogisticRegression()
+logreg.fit(X_train, y_train)
+print("Test set accuracy from Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
+
+from sklearn.preprocessing import MinMaxScaler, StandardScaler
+scaler = StandardScaler()
+scaler.fit(X_train)
+X_train_scaled = scaler.transform(X_train)
+X_test_scaled = scaler.transform(X_test)
+
+logreg.fit(X_train_scaled, y_train)
+print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
+
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2D_train = pca.fit_transform(X_train_scaled)
+X2D_test = pca.fit_transform(X_test_scaled)
+
+logreg.fit(X2D_train,y_train)
+print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X2D_test,y_test)))
+
    +

    +









    + +

    More on the PCA

    Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to @@ -1206,7 +1247,7 @@ X_reduced = pca.fit_transform(X)











    -

    Incremental PCA

    +

    Incremental PCA

    One problem with the preceding implementation of PCA is that it requires the whole training set to fit in @@ -1218,7 +1259,7 @@ instances arrive).











    -

    Randomized PCA

    +

    Randomized PCA

    Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic @@ -1233,7 +1274,7 @@ previous algorithms when \( d \) is much smaller than \( n \).











    -

    Kernel PCA

    +

    Kernel PCA

    @@ -1262,7 +1303,7 @@ X_reduced = rbf_pca.fit_transform(X)











    -

    LLE

    +

    LLE

    Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction @@ -1274,7 +1315,7 @@ these local relationships are best preserved (more details shortly).











    -

    Other techniques

    +

    Other techniques

    There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn. diff --git a/doc/pub/DimRed/html/DimRed.html b/doc/pub/DimRed/html/DimRed.html index 60f22749e..d6f859567 100644 --- a/doc/pub/DimRed/html/DimRed.html +++ b/doc/pub/DimRed/html/DimRed.html @@ -120,12 +120,13 @@ div { text-align: justify; text-justify: inter-word; } ('The final step', 2, None, '___sec20'), ('Principal Component Analysis', 2, None, '___sec21'), ('PCA and scikit-learn', 2, None, '___sec22'), - ('More on the PCA', 2, None, '___sec23'), - ('Incremental PCA', 2, None, '___sec24'), - ('Randomized PCA', 2, None, '___sec25'), - ('Kernel PCA', 2, None, '___sec26'), - ('LLE', 2, None, '___sec27'), - ('Other techniques', 2, None, '___sec28')]} + ('Back to the Cancer Data', 2, None, '___sec23'), + ('More on the PCA', 2, None, '___sec24'), + ('Incremental PCA', 2, None, '___sec25'), + ('Randomized PCA', 2, None, '___sec26'), + ('Kernel PCA', 2, None, '___sec27'), + ('LLE', 2, None, '___sec28'), + ('Other techniques', 2, None, '___sec29')]} end of tocinfo --> @@ -1175,13 +1176,53 @@ principal component is equal to

    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. +variance that lies along the axis of each principal component.











    -

    More on the PCA

    +

    Back to the Cancer Data

    +We can now repeat the above but applied to real data, in this case our breat cancer data. +

    + + +

    import matplotlib.pyplot as plt
+import numpy as np
+from sklearn.model_selection import  train_test_split 
+from sklearn.datasets import load_breast_cancer
+from sklearn.linear_model import LogisticRegression
+cancer = load_breast_cancer()
+
+X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)
+print(X_train.shape)
+print(X_test.shape)
+
+logreg = LogisticRegression()
+logreg.fit(X_train, y_train)
+print("Test set accuracy from Logistic Regression: {:.2f}".format(logreg.score(X_test,y_test)))
+
+from sklearn.preprocessing import MinMaxScaler, StandardScaler
+scaler = StandardScaler()
+scaler.fit(X_train)
+X_train_scaled = scaler.transform(X_train)
+X_test_scaled = scaler.transform(X_test)
+
+logreg.fit(X_train_scaled, y_train)
+print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X_test_scaled,y_test)))
+
+#thereafter we do a PCA with Scikit-learn
+from sklearn.decomposition import PCA
+pca = PCA(n_components = 2)
+X2D_train = pca.fit_transform(X_train_scaled)
+X2D_test = pca.fit_transform(X_test_scaled)
+
+logreg.fit(X2D_train,y_train)
+print("Test set accuracy scaled data: {:.2f}".format(logreg.score(X2D_test,y_test)))
+
    +

    +









    + +

    More on the PCA

    Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to @@ -1211,7 +1252,7 @@ X_reduced = pca











    -

    Incremental PCA

    +

    Incremental PCA

    One problem with the preceding implementation of PCA is that it requires the whole training set to fit in @@ -1223,7 +1264,7 @@ instances arrive).











    -

    Randomized PCA

    +

    Randomized PCA

    Scikit-Learn offers yet another option to perform PCA, called Randomized PCA. This is a stochastic @@ -1238,7 +1279,7 @@ previous algorithms when \( d \) is much smaller than \( n \).











    -

    Kernel PCA

    +

    Kernel PCA

    @@ -1267,7 +1308,7 @@ X_reduced = rbf_pcaLLE +

    LLE

    Locally Linear Embedding (LLE) is another very powerful nonlinear dimensionality reduction @@ -1279,7 +1320,7 @@ these local relationships are best preserved (more details shortly).











    -

    Other techniques

    +

    Other techniques

    There are many other dimensionality reduction techniques, several of which are available in Scikit-Learn. diff --git a/doc/pub/DimRed/ipynb/DimRed.ipynb b/doc/pub/DimRed/ipynb/DimRed.ipynb index c76867fcf..d42b6364e 100644 --- a/doc/pub/DimRed/ipynb/DimRed.ipynb +++ b/doc/pub/DimRed/ipynb/DimRed.ipynb @@ -1431,8 +1431,57 @@ "Another very useful piece of information is the explained variance ratio of each principal component,\n", "available via the $explained\\_variance\\_ratio$ variable. It indicates the proportion of the dataset’s\n", "variance that lies along the axis of each principal component. \n", - "More material to come here.\n", "\n", + "## Back to the Cancer Data\n", + "We can now repeat the above but applied to real data, in this case our breat cancer data." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from sklearn.model_selection import train_test_split \n", + "from sklearn.datasets import load_breast_cancer\n", + "from sklearn.linear_model import LogisticRegression\n", + "cancer = load_breast_cancer()\n", + "\n", + "X_train, X_test, y_train, y_test = train_test_split(cancer.data,cancer.target,random_state=0)\n", + "print(X_train.shape)\n", + "print(X_test.shape)\n", + "\n", + "logreg = LogisticRegression()\n", + "logreg.fit(X_train, y_train)\n", + "print(\"Test set accuracy from Logistic Regression: {:.2f}\".format(logreg.score(X_test,y_test)))\n", + "\n", + "from sklearn.preprocessing import MinMaxScaler, StandardScaler\n", + "scaler = StandardScaler()\n", + "scaler.fit(X_train)\n", + "X_train_scaled = scaler.transform(X_train)\n", + "X_test_scaled = scaler.transform(X_test)\n", + "\n", + "logreg.fit(X_train_scaled, y_train)\n", + "print(\"Test set accuracy scaled data: {:.2f}\".format(logreg.score(X_test_scaled,y_test)))\n", + "\n", + "#thereafter we do a PCA with Scikit-learn\n", + "from sklearn.decomposition import PCA\n", + "pca = PCA(n_components = 2)\n", + "X2D_train = pca.fit_transform(X_train_scaled)\n", + "X2D_test = pca.fit_transform(X_test_scaled)\n", + "\n", + "logreg.fit(X2D_train,y_train)\n", + "print(\"Test set accuracy scaled data: {:.2f}\".format(logreg.score(X2D_test,y_test)))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ "## More on the PCA\n", "\n", "Instead of arbitrarily choosing the number of dimensions to reduce down to, it is generally preferable to\n", @@ -1445,7 +1494,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 16, "metadata": { "collapsed": false }, @@ -1468,7 +1517,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 17, "metadata": { "collapsed": false }, @@ -1515,7 +1564,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 18, "metadata": { "collapsed": false }, diff --git a/doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz b/doc/pub/DimRed/ipynb/ipynb-DimRed-src.tar.gz index 3b0146384d3d443cbd22ca6ed4e6e5c15c42ddca..2b7fcb7fc2372bf54a61b9182d6690c94f3cec9c 100644 GIT binary patch literal 191 zcmV;w06_mAiwFSuk+EF>1MSaC3c@fD2H>uHia9|^Owz7}cHu&h;ssKY+Ne!xl7hXx zeSoeMH${Yeo1bBZVWup$`MyZ}-AAiI2&I(5lv&E=M4P3aVaxy%#wfuk%P=5J2%{08 z^-g-}o#%Eur8!IOq<%X$j@9*tJ$-1MSaE3c@fD1>mlGia9|^nkKG=cHu&h;ssKY+Ne!xl7hXx z{Q+GmZi)!`HjglmFjE%Wd|xE~?xWQpgjklrlp99pMCtOLVN3xNN;5L{7z2a}VQBwTLwN6j_X!+cm( 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