Generalizing discriminant analysis using the generalized singular value decomposition.

Peg Howland; Haesun Park

doi:10.1109/tpami.2004.46

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Generalizing discriminant analysis using the generalized singular value decomposition.

Peg Howland·Haesun Park

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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.

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Algorithms Artificial Intelligence Cluster Analysis Discriminant Analysis Documentation Information Storage and Retrieval MEDLINE Natural Language Processing Numerical Analysis, Computer-Assisted Pattern Recognition, Automated Reproducibility of Results Sample Size Sensitivity and Specificity Evaluation Study Journal Article Research Support, U.S. Gov't, Non-P.H.S.Validation Study

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Peg Howland, Haesun Park. 2004. Generalizing discriminant analysis using the generalized singular value decomposition.. https://doi.org/10.1109/tpami.2004.46

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