Singular Value Decomposition versus Principal Component Analysis
From Wikimization
Singular Value Decomposition versus Principal Component Analysis
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.”
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