title: Generalizing discriminant analysis using the generalized singular value decomposition.
abstract: 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.
authors.affiliation: Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN 55455, USA. howland@cs.umn.edu
authors.forename: Peg
authors.initials: P
authors.lastname: Howland
authors.forename: Haesun
authors.initials: H
authors.lastname: Park
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D016000:Cluster Analysis; D016002:Discriminant Analysis; D004282:Documentation / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods*; D016239:MEDLINE; D009323:Natural Language Processing; D009716:Numerical Analysis, Computer-Assisted; D010363:Pattern Recognition, Automated / Q000379:methods*; D015203:Reproducibility of Results; D018401:Sample Size; D012680:Sensitivity and Specificity