The Annals of Statistics

Penalized Discriminant Analysis

Trevor Hastie, Andreas Buja, and Robert Tibshirani

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Fisher's linear discriminant analysis (LDA) is a popular data-analytic tool for studying the relationship between a set of predictors and a categorical response. In this paper we describe a penalized version of LDA. It is designed for situations in which there are many highly correlated predictors, such as those obtained by discretizing a function, or the grey-scale values of the pixels in a series of images. In cases such as these it is natural, efficient and sometimes essential to impose a spatial smoothness constraint on the coefficients, both for improved prediction performance and interpretability. We cast the classification problem into a regression framework via optimal scoring. Using this, our proposal facilitates the use of any penalized regression technique in the classification setting. The technique is illustrated with examples in speech recognition and handwritten character recognition.

Article information

Ann. Statist. Volume 23, Number 1 (1995), 73-102.

First available in Project Euclid: 11 April 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
Secondary: 62G07: Density estimation

Signal and image classification discrimination regularization


Hastie, Trevor; Buja, Andreas; Tibshirani, Robert. Penalized Discriminant Analysis. Ann. Statist. 23 (1995), no. 1, 73--102. doi:10.1214/aos/1176324456.

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