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Principal Component Analysis/Karhunen-Loeve Mapping

(PCA or MCA of overall/mean covariance matrix)


 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.

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


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.


    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).

See also

mappings, datasets, pcldc, klldc, pcam, klm, fisherm,

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PRTools User Guide

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