Principal component analysis (PCA or MCA on overall covariance matrix)
[W,FRAC] = PCAM(A,N)
This routine performs a principal component analysis (PCA) or minor component analysis (MCA) on the overall covariance matrix (weighted by the class prior probabilities). It finds a rotation of the dataset A to an N-dimensional linear subspace such that at least (for PCA) or at most (for MCA) a fraction FRAC of the total variance is preserved.
PCA is applied when N (or FRAC) >= 0; MCA when N (or FRAC) < 0. If N is given (abs(N) >= 1), FRAC is optimised. If FRAC is given (abs(FRAC) < 1), N is optimised.
Objects in a new dataset B can be mapped by B*W, W*B or by A*PCA(,N)*B. Default (N = inf): the features are decorrelated and ordered, but no feature reduction is performed.
V = PCAM(A,0)
Returns the cumulative fraction of the explained variance. V(N) is the cumulative fraction of the explained variance by using N eigenvectors.
Use KLM for a principal component analysis on the mean class covariance. Use FISHERM for optimizing the linear class separability (LDA).
Note that this routine is identical to the PCAM rouitne located in the PRTools main directory. It thereby avoids confusion with the PCA routine in the Stats toolbox if called by a dataset as a first parameter. Users should preferably call PCAM for the PRTools routine and use PCA for for the Stats version.