PCA

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

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

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

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

Description

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.

ALTERNATIVE

    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).

Note that this routine is identical to the PCAM rouitne located in the  PRTools main directory. It thereby avoids confusion with the PCA routine  in the Stats toolbox if called by a dataset as a first parameter.  Users should preferably call PCAM for the PRTools routine and use PCA for  for the Stats version.

See also

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