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- | Singular Value Decomposition <i>versus</i> Principal Component Analysis | + | #REDIRECT [[Singular Value Decomposition versus Principal Component Analysis]] |
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- | from <i>SVD meets PCA</i>, slide by Cleve Moler
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- | “''The Wikipedia pages on SVD and PCA are quite good and contain a number of useful links, although not to each other.''”
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- | <br>[https://www.mathworks.com/company/newsletters/articles/professor-svd.html <math>-</math>MATLAB News & Notes, Cleve’s Corner, 2006]
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- | <pre>
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- | %relationship of pca to svd
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- | m=3; n=7;
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- | A = randn(m,n);
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- | [coef,score,latent] = pca(A)
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- | X = A - mean(A);
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- | [U,S,V] = svd(X,'econ');
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- | % S vs. latent
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- | rho = rank(X);
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- | latent = diag(S(:,1:rho)).^2/(m-1)
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- | % U vs. score
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- | sense = sign(score).*sign(U*S(:,1:rho)); %account for negated left singular vector
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- | score = U*S(:,1:rho).*sense
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- | % V vs. coef
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- | sense2 = sign(coef).*sign(V(:,1:rho)); %account for corresponding negated right singular vector
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- | coef = V(:,1:rho).*sense2
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- | </pre>
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Current revision
- REDIRECT Singular Value Decomposition versus Principal Component Analysis