Expected classification error of the Fisher linear classifier with pseudo-inverse covariance matrix

Authors:
Sarunas Raudys;Robert P. W. Duin
Affiliations:
Institute of Mathematics and Informatics, Akademijos 4, Vilnius 2600, Lithuania;Faculty of Applied Physics, Delft University of Technology, P.O. Box 5046, 2600 GA Delft, Netherlands
Venue:
Pattern Recognition Letters
Year:
1998

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Abstract

The pseudo-Fisher linear classifier is considered as the ''diagonal'' Fisher linear classifier applied to the principal components corresponding to non-zero eigenvalues of the sample covariance matrix. An asymptotic formula for the expected (generalization) error of the Fisher classifier with the pseudo-inversion is derived which explains the peaking behaviour: with an increasing number of learning observations from one up to the number of features, the generalization error first decreases, and then starts to increase.