# Cleve's Cubicle

(Difference between revisions)
 Revision as of 18:04, 17 October 2017 (edit)← Previous diff Revision as of 18:05, 17 October 2017 (edit) (undo)Next diff → Line 3: Line 3: SVD meets PCA, by Cleve Moler SVD meets PCA, by Cleve Moler - [https://www.mathworks.com/company/newsletters/articles/professor-svd.html MATLAB News & Notes, 2006, Cleve’s Corner] + [https://www.mathworks.com/company/newsletters/articles/professor-svd.html|target='_blank' MATLAB News & Notes, 2006, Cleve’s Corner]

## Revision as of 18:05, 17 October 2017

Singular Value Decomposition versus Principal Component Analysis

SVD meets PCA, 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.”```
```%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');

% U  vs. score
rho   = rank(X);
sense = sign(score).*sign(U*S(:,1:rho));  %account for negated left singular vector
sum(sum(abs(score - U*S(:,1:rho).*sense)))
% S  vs. latent
sum(abs(latent - diag(S(:,1:rho)).^2/(m-1)))
% V  vs. coef
sense2 = sign(coef).*sign(V(:,1:rho));    %account for corresponding negated right singular vector
sum(sum(abs(coef - V(:,1:rho).*sense2)))
```