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Subspace Classifier

    W = SUBSC(A,F)
    W = A*SUBSC([],F)
    W = A*SUBSC(F)

 A Dataset
 F Desired model dimensionality or fraction of retained  variance per class

 W Subspace classifier


Each class in the trainingset A is described by linear subspace of  dimensionality F (F>=1), or such that at least a fraction F (F<1) of its  varianceis retained. This is realised by calling PCAM(AI,F) or for  each subset AI of A (objects of class I). For each class a model is  built that assumes that the distances of the objects to the class  subspaces follow a one-dimensional distribution.

New objects are assigned to the class of the nearest subspace.  Classification by D = B*W, in which W is a trained subspace classifier  and B is a testset, returns a dataset D with one-dimensional densities  for each of the classes in its columns. The result may be improved in  case of multi-class problems by a trained combiner, e.g.  W = A*(SUBSC*QDC([],[],1e-6))

If F is NaN it is optimised by REGOPTC.

This routine will only use the classes with more than two training  objects.


E. Oja, The Subspace Methods of Pattern Recognition, Wiley, New York, 1984.

See also

datasets, mappings, pcam, fisherc, fisherm, gaussm, regoptc,

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PRTools User Guide

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