Open Access
February, 1995 Penalized Discriminant Analysis
Trevor Hastie, Andreas Buja, Robert Tibshirani
Ann. Statist. 23(1): 73-102 (February, 1995). DOI: 10.1214/aos/1176324456


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.


Download Citation

Trevor Hastie. Andreas Buja. Robert Tibshirani. "Penalized Discriminant Analysis." Ann. Statist. 23 (1) 73 - 102, February, 1995.


Published: February, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0821.62031
MathSciNet: MR1331657
Digital Object Identifier: 10.1214/aos/1176324456

Primary: 62H30
Secondary: 62G07

Keywords: discrimination , regularization , Signal and image classification

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 1 • February, 1995
Back to Top