Nonparametric Discriminant Analysis

Authors:
K. Fukunaga;J. M. Mantock
Affiliations:
Department of Electrical Engineering, Purdue University, West Lafayette, IN 47907.;Department of Electrical Engineering, Purdue University, West Lafayette, IN 47907/ Aerospace Corporation, Los Angeles, CA 90009/ Texas Instruments, Inc., Lewisville, TX 75067.
Venue:
IEEE Transactions on Pattern Analysis and Machine Intelligence
Year:
1983

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Abstract

A nonparametric method of discriminant analysis is proposed. It is based on nonparametric extensions of commonly used scatter matrices. Two advantages result from the use of the proposed nonparametric scatter matrices. First, they are generally of full rank. This provides the ability to specify the number of extracted features desired. This is in contrast to parametric discriminant analysis, which for an L class problem typically can determine at most L 1 features. Second, the nonparametric nature of the scatter matrices allows the procedure to work well even for non-Gaussian data sets. Using the same basic framework, a procedure is proposed to test the structural similarity of two distributions. The procedure works in high-dimensional space. It specifies a linear decomposition of the original data space in which a relative indication of dissimilarity along each new basis vector is provided. The nonparametric scatter matrices are also used to derive a clustering procedure, which is recognized as a k-nearest neighbor version of the nonparametric valley seeking algorithm. The form which results provides a unified view of the parametric nearest mean reclassification algorithm and the nonparametric valley seeking algorithm.