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

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 pseu...

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Bibliographic Details
Published in:Pattern recognition letters 1998-04, Vol.19 (5), p.385-392
Main Authors: Raudys, Sarunas, Duin, Robert P.W.
Format: Article
Language:English
Subjects:
Dimensionality
Fisher linear discriminant
Generalization error
Pseudo-inversion
Sample size
Scissors effect
Statistical classification
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Summary: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.
ISSN:0167-8655
1872-7344
DOI:10.1016/S0167-8655(98)00016-6