javicm
Aug6-09, 09:38 AM
Hello everybody!
Any of you have read the paper "EM algorithms for PCA and SPCA" of Sam Roweis? If so, maybe you could help me! :-) I have some problems with equation 2b, well, in fact my problem is that I don't manage to deduce it. If you didn't read the paper but are curious, how could you prove that
\frac{N(Cx,R)|_yN(0,I)|_x}{N(0,CC^T+R)|_y} follows this distribution: N(\beta y, I-\beta C)|_x, where N(A,B)|_c means a normal (Gaussian) distribution with mean A, covariance matrix B and evaluated at c, and \beta = C^T(CC^T+R)^{-1}.
Thanks a lot!
Javier
Any of you have read the paper "EM algorithms for PCA and SPCA" of Sam Roweis? If so, maybe you could help me! :-) I have some problems with equation 2b, well, in fact my problem is that I don't manage to deduce it. If you didn't read the paper but are curious, how could you prove that
\frac{N(Cx,R)|_yN(0,I)|_x}{N(0,CC^T+R)|_y} follows this distribution: N(\beta y, I-\beta C)|_x, where N(A,B)|_c means a normal (Gaussian) distribution with mean A, covariance matrix B and evaluated at c, and \beta = C^T(CC^T+R)^{-1}.
Thanks a lot!
Javier