Generalizing discriminant analysis using the generalized singular value decomposition

被引：245

作者：

Howland, P ^{[1
]}

Park, H ^{[1
]}

机构：

[1] Univ Minnesota, Dept Comp Sci & Engn, Minneapolis, MN 55455 USA

来源：

IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE | 2004年 / 26卷 / 08期

基金：

美国国家科学基金会;

关键词：

linear discriminant analysis; latent semantic indexing; principal component analysis; generalized singular value decomposition; QR decomposition; trace optimization;

D O I：

10.1109/TPAMI.2004.46

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Discriminant analysis has been used for decades to extract features that preserve class separability. It is commonly defined as an optimization problem involving covariance matrices that represent the scatter within and between clusters. The requirement that one of these matrices be nonsingular limits its application to data sets with certain relative dimensions. We examine a number of optimization criteria, and extend their applicability by using the generalized singular value decomposition to circumvent the nonsingularity requirement. The result is a generalization of discriminant analysis that can be applied even when the sample size is smaller than the dimension of the sample data. We use classification results from the reduced representation to compare the effectiveness of this approach with some alternatives, and conclude with a discussion of their relative merits.

引用

页码：995 / 1006

页数：12