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Principal component analysis (PCA or MCA on overall covariance matrix)

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

 A Dataset
 N Desired output dimensionality (>= 1), default N = inf.
 FRAC Fraction of cumulative variance (< 1) to retain,  if > 0, perform PCA; otherwise MCA.

 W Affine PCA mapping
 FRAC Fraction of cumulative variance retained.
 N Number of dimensions retained.


This routine performs a principal component analysis (PCA) or minor  component analysis (MCA) on the overall 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*PCA([],N)*B.  Default (N = inf): the features are decorrelated and ordered, but no  feature reduction is performed.


    V = PCAM(A,0)

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

Use KLM for a principal component analysis on the mean class covariance.  Use FISHERM for optimizing the linear class separability (LDA).

See also

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

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PRTools User Guide

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