Karhunen-Loeve Mapping (PCA or MCA of mean covariance matrix)
[W,FRAC] = KLM(A,N)
The Karhunen-Loeve Mapping performs a principal component analysis (PCA) or minor component analysis (MCA) on the mean class 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*KLM(,N)*B. Default (N = inf): the features are decorrelated and ordered, but no feature reduction is performed.
V = KLM(A,0)
Returns the cummulative fraction of the explained variance. V(N) is the cumulative fraction of the explained variance by using N eigenvectors.
Use PCA for a principal component analysis on the total data covariance. Use FISHERM for optimizing the linear class separability (LDA).
This function is basically a wrapper around pcaklm.m.