Asymptotic Properties of K-Means Clustering Algorithm as a Density Estimation Procedure (Classic Reprint) - Softcover
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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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Asymptotic Properties of K-Means Clustering Algorithm as a Density Estimation
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Paperback. Condition: New. Print on Demand. This book explores the k-means clustering algorithm, a significant technique in data analysis for grouping similar observations into clusters. Historically used for cluster analysis, the author shows how k-means can also be used to generate variable cell histograms, a powerful tool for estimating probability density functions. The author presents the mathematical foundations of k-means, establishing its asymptotic properties as a density estimation method under specific conditions. Two histogram estimates based on k-means clustering are proposed, and their uniform consistency in probability is proven. Empirical examples illustrate the performance of the proposed estimates. Providing a solid theoretical framework and practical insights, this book deepens our understanding of k-means as a valuable technique for density estimation, expanding its applications in statistical modeling and data analysis. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781334434174_0
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Asymptotic Properties of KMeans Clustering Algorithm as a Density Estimation Procedure Classic Reprint
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