# (Sequential) Principal Component Analysis

1. Aug 6, 2009

### javicm

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