KLM

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

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

See also

mappings, datasets, pcaklm, pcldc, klldc, pca, fisherm,