On an alternative formulation of the Fisher criterion that overcomes the small sample problem

Authors:
Marco Loog
Affiliations:
IT University of Copenhagen, Rued Langgaards Vej 7, 2300 Copenhagen S, Denmark
Venue:
Pattern Recognition
Year:
2007

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Abstract

In two very recently published rapid and brief communications, both from the same authors, an alternative formulation of the well-known Fisher criterion is presented in order to overcome the 'small sample problem'. A theorem in the first of the two communications provides the basis for the equivalence of both formulations. By providing a simple counterexample, we disprove the theorem. Subsequently, based on an illustrative example, we demonstrate that their criterion differs from the classical one and argue that the proposed criterion is not a suitable measure of discriminability.