The Use of a Distance Measure in Regularised Discriminant Analysis

J. P. Koolaard (), S. Ganesalingam and C. R. O. Lawoko
Additional contact information
J. P. Koolaard: Crop and Food Research Limited
S. Ganesalingam: Massey University
C. R. O. Lawoko: National Australia Bank

Computational Statistics, 2002, vol. 17, issue 2, No 3, 185-202

Abstract: Summary Friedman (1989) proposed a regularised discriminant function (RDF) as a compromise between the normal-based linear and quadratic discriminant functions, by considering alternatives to the usual maximum likelihood estimates for the covariance matrices. These alternatives are characterised by two (regularisation) parameters, the values of which are customised to individual situations by jointly minimising a sample-based (cross-validated) estimate of future misclassification risk. This technique appears to provide considerable gains in classification accuracy in many circumstances, although it is computationally intensive. Because of the computational burden inherent in the RDF, and with regards to criticisms of the technique by Rayens et al. (1991), we investigated whether information about appropriate values of the two regularisation parameters could be obtained from examining the behaviour of the Bhattacharyya distance between the various populations. This distance measure is found to give information which leads to unique and generally appropriate values for the regularisation parameters being selected.

Keywords: Regularised discriminant function; regularisation parameter; Bhattacharyya distance (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/s001800200101

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