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Principal Component Analysis

Principal Component Analysis. Principal Component Analysis. Objective: Project the data onto a lower dimensional space while minimizing the information loss. Principal Component Analysis. load mnist m = mean(data); for i= 1:size ( data_m,2 ) data_m (:,i) = data(:, i) - m(i); end

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Principal Component Analysis

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  1. Principal Component Analysis

  2. Principal Component Analysis Objective: Project the data onto a lower dimensional space while minimizing the information loss

  3. Principal Component Analysis load mnist m = mean(data); for i=1:size(data_m,2) data_m(:,i) = data(:,i) - m(i); end [pc,evals] = pca_OF(data_m); pc_data = data_m*pc(1:200,:)';

  4. Principal Component Analysis function [pc,evals] = pca_OF(x) [pc,evals] = eig(cov(x)); evals = diag(evals); [evals, si] = sort(-evals); %Sort eigenvalues evals = -evals; pc = pc(:,si)'; %Sort eigenvectors by magnitude of eigenvalues

  5. Sorted Eigenvalues

  6. Normalized Cumulative Variance (information preserved)

  7. Projecting the digits onto the first two PCs

  8. Projecting the digits onto PCs 1 and 3

  9. Projecting the digits onto PCs 2 and 3

  10. Recognition Accuracies and Running Times with MNIST dataset

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