Singular Value Decomposition versus Principal Component Analysis
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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]. | [https://stats.stackexchange.com/questions/134282/relationship-between-svd-and-pca-how-to-use-svd-to-perform-pca Relationship between SVD and PCA]. | ||
<br><i>Standard deviation</i> is square root of variance. | <br><i>Standard deviation</i> is square root of variance. | ||
| + | <br>Sign of principal component vectors are not unique. | ||
Revision as of 20:39, 17 September 2018
from SVD meets PCA slide [17:46] 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
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.
Sign of principal component vectors are not unique.