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Excerpt from Asymptotic Properties of K-Means Clustering Algorithm as a Density Estimation Procedure
Let X1, X2, qbe observations from some density f of a probability distribution F. To estimate the univariate density f using the random sample, the traditional method is the histogram. The asymptotic properties of the fixed cell histogram are given in the recent text by Tapia and Thompson Van Ryzin (1973) first proposed a variable cell histogram which is adaptive to the underlying density. His procedure is related to the nearest neighbour density estimates developed by Loftsgaarden and Quensenberry In this paper, it is proposed that the k - means clustering technique can be regarded as a practicable and convenient way of obtaining variable cell histograms in one or more dimensions.
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