Cleve's Cubicle

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-Singular Value Decomposition <i>versus</i> Principal Component Analysis
+#REDIRECT [[Singular Value Decomposition versus Principal Component Analysis]]
-<i>SVD meets PCA</i>, by Cleve Moler
-[https://www.mathworks.com/company/newsletters/articles/professor-svd.html MATLAB News & Notes, 2006, Cleve’s Corner]
-<pre>“The Wikipedia pages on SVD and PCA are
- quite good and contain a number of useful links,
- although not to each other.”</pre>
-<pre>
-%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)))
-</pre>