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Regularized Discriminant Analysis

Jerome H. Friedman
Journal of the American Statistical Association
Vol. 84, No. 405 (Mar., 1989), pp. 165-175
DOI: 10.2307/2289860
Stable URL: http://www.jstor.org/stable/2289860
Page Count: 11
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Regularized Discriminant Analysis
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Abstract

Linear and quadratic discriminant analysis are considered in the small-sample, high-dimensional setting. Alternatives to the usual maximum likelihood (plug-in) estimates for the covariance matrices are proposed. These alternatives are characterized by two parameters, the values of which are customized to individual situations by jointly minimizing a sample-based estimate of future misclassification risk. Computationally fast implementations are presented, and the efficacy of the approach is examined through simulation studies and application to data. These studies indicate that in many circumstances dramatic gains in classification accuracy can be achieved.

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