Exercise:PCA and Whitening

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(PCA, PCA whitening and ZCA implementation)
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==== Step 1a: Implement PCA ====
==== Step 1a: Implement PCA ====
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In this step, you will implement PCA to obtain <math>x_{rot}</math>, the matrix in which the data is "rotated" to the basis comprising the principal components (i.e. the eigenbasis of <math>\Sigma</math>).
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In this step, you will implement PCA to obtain <math>x_{rot}</math>, the matrix in which the data is "rotated" to the basis comprising the principal components (i.e. the eigenbasis 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 4a: Implement PCA with whitening and regularisation ====
==== Step 4a: Implement PCA with whitening and regularisation ====
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Now implement PCA with whitening and regularisation to produce the matrix <math>x_{PCAWhite}</math>.
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Now implement PCA with whitening and regularisation to produce the matrix <math>x_{PCAWhite}</math> with the following parameters:
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epsilon = 1e-4
==== Step 4b: Check covariance ====
==== Step 4b: Check covariance ====

Revision as of 05:18, 29 April 2011

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