Exercise:PCA and Whitening
From Ufldl
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==== Step 1a: Implement PCA ==== | ==== Step 1a: Implement PCA ==== | ||
| - | In this step, you will implement PCA to obtain <math>x_{\rm rot}</math>, the matrix in which the data is "rotated" to the basis comprising the principal components (i.e. the | + | In this step, you will implement PCA to obtain <math>x_{\rm rot}</math>, the matrix in which the data is "rotated" to the basis comprising the principal components (i.e. the eigenvectors of <math>\Sigma</math>). Note that in this part of the exercise, you should ''not'' whiten the data. |
==== Step 1b: Check covariance ==== | ==== Step 1b: Check covariance ==== | ||
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=== Step 5: ZCA whitening === | === Step 5: ZCA whitening === | ||
| - | Now implement ZCA whitening to produce the matrix <math>x_{ZCAWhite}</math>. Visualize <math>x_{ZCAWhite}</math> and compare it to the raw data, <math>x</math>. You should observe that whitening results in, among other things, enhanced edges. Try repeating this with <tt>epsilon</tt> set to 1, 0.1, and 0.01, and see what you obtain. | + | Now implement ZCA whitening to produce the matrix <math>x_{ZCAWhite}</math>. Visualize <math>x_{ZCAWhite}</math> and compare it to the raw data, <math>x</math>. You should observe that whitening results in, among other things, enhanced edges. Try repeating this with <tt>epsilon</tt> set to 1, 0.1, and 0.01, and see what you obtain. The example shown below (left image) was obtained with <tt>epsilon</tt> = 0.1. |
<table> | <table> | ||
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[[Category:Exercises]] | [[Category:Exercises]] | ||
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| + | {{PCA}} | ||
