Exercise:PCA and Whitening
From Ufldl
(→Step 4b: Check covariance) |
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== PCA, PCA whitening and ZCA implementation == | == PCA, PCA whitening and ZCA implementation == | ||
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+ | === Step 0: Load data === | ||
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+ | [[File:raw_images.png|240px|alt=Raw images|Raw images]] | ||
=== Step 1: Implement PCA === | === Step 1: Implement PCA === | ||
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Visualise the covariance matrix. You should see a line across the diagonal against a blue background. | Visualise the covariance matrix. You should see a line across the diagonal against a blue background. | ||
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+ | [[File:pca_covar.png|240px]] | ||
=== Step 2: Find number of components to retain === | === Step 2: Find number of components to retain === | ||
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Visualise the data, and compare it to the raw data. You should observe that the raw and processed data are of comparable quality. For comparison, you may wish to generate a PCA reduced image which retains only 50% of the variance. | Visualise the data, and compare it to the raw data. You should observe that the raw and processed data are of comparable quality. For comparison, you may wish to generate a PCA reduced image which retains only 50% of the variance. | ||
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+ | [[File:pca_images.png|240px|alt=PCA dimension-reduced images (99% variance)|PCA dimension-reduced images (99% variance)]] [[File:raw_images.png|240px|alt=Raw images|Raw images]] [[File:pca_images_50.png|240px|alt=PCA dimension-reduced images (50% variance)|PCA dimension-reduced images (50% variance)]] | ||
=== Step 4: PCA with whitening and regularisation === | === Step 4: PCA with whitening and regularisation === | ||
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Visualise the covariance matrix. You should see a red line across the diagonal against a blue background. | Visualise the covariance matrix. You should see a red line across the diagonal against a blue background. | ||
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+ | [[File:pca_whitened_covar.png|240px]] | ||
=== Step 5: ZCA whitening === | === Step 5: ZCA whitening === | ||
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Visualise the data, and compare it to the raw data. You should observe that the whitened images have enhanced edges. | Visualise the data, and compare it to the raw data. You should observe that the whitened images have enhanced edges. | ||
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+ | [[File:zca_whitened_images.png|240px|alt=ZCA whitened images|ZCA whitened images]] [[File:raw_images.png|240px|alt=Raw images|Raw images]] |