Asymptotic Properties of Univariate Sample K-Means Clusters (Classic Reprint)
Book Details
Author(s)M. Anthony Wong
PublisherForgotten Books
ISBN / ASIN1330286987
ISBN-139781330286982
AvailabilityUsually ships in 1 to 4 weeks
Sales Rank99,999,999
MarketplaceUnited States 🇺🇸
Description
Excerpt from Asymptotic Properties of Univariate Sample K-Means Clusters
A random sample of size N is divided into k clusters that minimize the within clusters sum of squares locally. Some large sample properties of this k-means clustering method (as k approaches ∞ with N) are obtained. In one dimension, it is established that the sample k-means clusters are such that the within-cluster sums of squares are asymptotically equal, and that the sizes of the cluster intervals are inversely proportional to the one-third power of the underlying density at the midpoints of the intervals. The difficulty involved in generalizing the results to the multivariate case is mentioned.
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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
A random sample of size N is divided into k clusters that minimize the within clusters sum of squares locally. Some large sample properties of this k-means clustering method (as k approaches ∞ with N) are obtained. In one dimension, it is established that the sample k-means clusters are such that the within-cluster sums of squares are asymptotically equal, and that the sizes of the cluster intervals are inversely proportional to the one-third power of the underlying density at the midpoints of the intervals. The difficulty involved in generalizing the results to the multivariate case is mentioned.
About the Publisher
Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com
This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
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