PRTools Contents PRTools User Guide
pcaklm

PCAKLM

### Principal Component Analysis/Karhunen-Loeve Mapping

(PCA or MCA of overall/mean covariance matrix)

[W,FRAC] = PCAKLM(TYPE,A,N)
[W,N] = PCAKLM(TYPE,A,FRAC)

 Input A Dataset TYPE Type of mapping: 'pca' or 'klm'. Default: 'pca'. 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

Performs a principal component analysis (PCA) or minor component analysis  (MCA) on the overall or 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 = PCAKLM(A,TYPE,0)

Returns the cumulative fraction of the explained variance. V(N) is the  cumulative fraction of the explained variance by using N eigenvectors.

This function should not be called directly, only trough PCA or KLM.  Use FISHERM for optimizing the linear class separability (LDA).