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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from <i>SVD meets PCA</i> slide by Cleve Moler.
“''The Wikipedia pages on SVD and PCA are quite good and contain a number of useful links, although not to each other.''”
“''The Wikipedia pages on SVD and PCA are quite good and contain a number of useful links, although not to each other.''”

Revision as of 12:21, 16 September 2018

from SVD meets PCA slide by Cleve Moler.

The Wikipedia pages on SVD and PCA are quite good and contain a number of useful links, although not to each other.
LaTeX: -MATLAB News & Notes, Cleve’s Corner, 2006

%relationship of pca to svd
m=3;  n=7;
A = randn(m,n);

[coef,score,latent] = pca(A)

X       = A - mean(A);
[U,S,V] = svd(X,'econ');

% S  vs. latent
rho   = rank(X);
latent = diag(S(:,1:rho)).^2/(m-1)

% U  vs. score
sense = sign(score).*sign(U*S(:,1:rho));  %account for negated left singular vector
score = U*S(:,1:rho).*sense

% V  vs. coef
sense2 = sign(coef).*sign(V(:,1:rho));    %account for corresponding negated right singular vector
coef = V(:,1:rho).*sense2

coef, score, latent definitions from Matlab pca() command.

Terminology like variance of principal components (PCs) can be found here: Relationship between SVD and PCA.
Standard deviation is square root of variance.

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