PRTools Contents PRTools User Guide
klm

KLM

### Karhunen-Loeve Mapping (PCA or MCA of mean covariance matrix)

[W,FRAC] = KLM(A,N)
[W,N] = KLM(A,FRAC)
W = A*KLM(N)
W = A*KLM(FRAC)

 Input A Dataset N or FRAC Number of dimensions (>= 1) or fraction of variance (< 1) to retain; if > 0, perform PCA; otherwise MCA.  Default: N = inf.

 Output W Affine Karhunen-Loeve mapping FRAC or N Fraction of variance or number of dimensions retained.

### Description

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.

ALTERNATIVE

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.