Singular Value Decomposition versus Principal Component Analysis

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(Singular Value Decomposition <i>versus</i> Principal Component Analysis)
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coef = V(:,1:rho).*sense2
coef = V(:,1:rho).*sense2
</pre>
</pre>
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Good explanation of terminology like <i>variance of principal components</i> can be found here:
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[https://stats.stackexchange.com/questions/134282/relationship-between-svd-and-pca-how-to-use-svd-to-perform-pca Relationship between SVD and PCA]

Revision as of 21:11, 15 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

Good explanation of terminology like variance of principal components can be found here: Relationship between SVD and PCA

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