Singular Value Decomposition versus Principal Component Analysis
From Wikimization
(Difference between revisions)
(8 intermediate revisions not shown.) | |||
Line 1: | Line 1: | ||
- | from <i>SVD meets PCA</i> | + | from [https://www.mathworks.com/videos/the-singular-value-decomposition-saves-the-universe-1481294462044.html <i>SVD meets PCA</i>] |
+ | 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.''” | “''The Wikipedia pages on SVD and PCA are quite good and contain a number of useful links, although not to each other.''” | ||
Line 27: | Line 28: | ||
</pre> | </pre> | ||
- | + | <i>coef, score, latent</i> definitions from | |
- | [https://stats.stackexchange.com/questions/134282/relationship-between-svd-and-pca-how-to-use-svd-to-perform-pca Relationship between SVD and PCA] | + | [https://www.mathworks.com/help/stats/pca.html Matlab pca()] |
+ | command. | ||
+ | |||
+ | Terminology like <i>variance</i> of principal components (PCs) can be found here: | ||
+ | [https://stats.stackexchange.com/questions/134282/relationship-between-svd-and-pca-how-to-use-svd-to-perform-pca Relationship between SVD and PCA]. | ||
+ | <br><b>(</b><i>Standard deviation</i> squared equals variance.<b>)</b> | ||
+ | <br>Sign of principal component vector is not unique. |
Current revision
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 squared equals variance.)
Sign of principal component vector is not unique.