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In this correspondence, an approach to unsupervised pattern classifiers is discussed. The classifiers discussed here have the ability of obtaining the consistent estimates of unknown statistics of input patterns without knowing the a priori probability of each category's occurrence where the input patterns are of a mixture distribution. An analysis is made about their asymptotic behavior in order to show that the classifiers converge to the Bayes' minmum error classifier. Also, some results of a computer simulation on learning processes are shown.