add ldsPca

Author: sth4nth

chapter13/LDS/ldsPca.m

@@ -3,10 +3,18 @@
 % Input:
 %   X: d x n data matrix
 %   k: dimension of hidden variable
-%   m: 
+%   m: stacking order for the Hankel matrix
 % Output:
-%   A: 
-%   C:
-%   Z:
+%   A: k x k transition matrix
+%   C: k x d emission matrix
+%   Z: k x n latent variable
+%   Y: d x n reconstructed data
 % reference: Bayesian Reasoning and Machine Learning (BRML) chapter 24.5.3 p.507
-% Written by Mo Chen (sth4nth@gmail.com).
+% Written by Mo Chen (sth4nth@gmail.com).
+[d,n] = size(X);
+H = reshape(X(:,hankel(1:m,m:n)),d*m,[]);
+[U,S,V] = svd(H,'econ');
+C = U(1:d,1:k);
+Z = S(1:k,1:k)*V(:,1:k)';
+A = Z(:,2:end)/Z(:,1:end-1); % estimated transition
+% Y = C*Z; % reconstructions