# Singular Value Decomposition versus Principal Component Analysis

### From Wikimization

(Difference between revisions)

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coef = V(:,1:rho).*sense2 | coef = V(:,1:rho).*sense2 | ||

</pre> | </pre> | ||

+ | |||

+ | <i>coef, score, latent</i> definitions from Matlab | ||

+ | [https://www.mathworks.com/help/stats/pca.html pca()] | ||

+ | command. | ||

Good explanation of terminology like <i>variance of principal components</i> can be found here: | Good explanation of terminology like <i>variance of principal components</i> 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] | [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 21:15, 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.*”

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.

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