A Nonparametric Valley-Seeking Technique for Cluster Analysis

Authors:
Warren L. G. Koontz;Keinosuke Fukunaga
Affiliations:
School of Electrical Engineering, Purdue University, Lafayette, Ind./ Bell Telephone Laboratories, Inc., Holmdel, N. J. 07733.;School of Electrical Engineering, Purdue University, Lafayette, Ind.
Venue:
IEEE Transactions on Computers
Year:
1972

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Abstract

The problem of clustering multivariate observations is viewed as the replacement of a set of vectors with a set of labels and representative vectors. A general criterion for clustering is derived as a measure of representation error. Some special cases are derived by simplifying the general criterion. A general algorithm for finding the optimum classification with respect to a given criterion is derived. For a particular case, the algorithm reduces to a repeated application of a straightforward decision rule which behaves as a valley-seeking technique. Asymptotic properties of the procedure are developed. Numerical examples are presented for the finite sample case.