Issue No. 08 - August (1975 vol. 24)

ISSN: 0018-9340

pp: 835-838

J.C. Bezdek , Department of Mathematics and Statistics, Marquette University

ABSTRACT

An algorithm is described for generating fuzzy partitions which extremize a fuzzy extension of the k-means squared-error criterion function on finite data sets X. It is shown how this algorithm may be applied to the problem of estimating the parameters (a priori probabilities, means, and covariances) of mixture of multivariate normal densities, given a finite sample X drawn from the mixture. The behavior of the algorithm is compared with that of the ordinary ISODATA clustering process and the maximum likelihood method, for a specific bivariate mixture.

INDEX TERMS

Fuzzy sets, maximum likelihood, mixed normal distributions, parametric estimation, pattern classification, unsupervised learning.

CITATION

J.C. Dunn, J.C. Bezdek, "Optimal Fuzzy Partitions: A Heuristic for Estimating the Parameters in a Mixture of Normal Distributions",

*IEEE Transactions on Computers*, vol. 24, no. , pp. 835-838, August 1975, doi:10.1109/T-C.1975.224317