PENALIZED DISCRIMINANT-ANALYSIS

• 成果类型: Article
• 署名作者: HASTIE, T; BUJA, A; TIBSHIRANI, R
• 署名单位: AT&T; Nokia Corporation; Nokia Bell Labs; University of Toronto; University of Toronto; Telcordia Technologies
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324456
• 发表日期: 1995
• 页码: 73-102
• 关键词: tools

摘要

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.