Cleve's Cubicle

From Wikimization

(Difference between revisions)
Jump to: navigation, search
(Singular Value Decomposition <i>versus</i> Principal Component Analysis)
Line 1: Line 1:
-
== Singular Value Decomposition <i>versus</i> Principal Component Analysis ==
+
#REDIRECT [[Singular Value Decomposition <i>versus</i> Principal Component Analysis]]
-
 
+
-
from <i>SVD meets PCA</i>, 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.''”
+
-
<br>[https://www.mathworks.com/company/newsletters/articles/professor-svd.html <math>-</math>MATLAB News & Notes, Cleve’s Corner, 2006]
+
-
 
+
-
<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');
+
-
 
+
-
% 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
+
-
</pre>
+

Revision as of 16:24, 12 September 2018

  1. REDIRECT [[Singular Value Decomposition versus Principal Component Analysis]]
Personal tools