Asymptotic Properties of Univariate Population K-Means Clusters (Classic Reprint)
Liczba stron: 22
Wydanie: 2018 r.
Excerpt from Asymptotic Properties of Univariate Population K-Means Clusters<br><br>The k - means method has been widely used in clustering applications (see Blashfield and Aldenderfer, and the efficient computational algorithm given in Hartigan and Wong (1979) has been included in the multivariate programs bmdpkm of the bmdp statistical package. The properties of sample k-means clusters have also been studied by several investigators. In Fisher and Fisher and Van Ness it is shown that k-means clusters are convex, i.e., if an observation is a weighted average of observations in a cluster, the observation is also in the cluster. And the asymptotic convergence (as N Go) of the sample k-means clusters to the population k - means cluster for fixed number of clusters k has been studied by macqueen Hartigan and Pollard in which conditions that ensure the almost sure convergence of the set of means of the k-means clusters can be found. However, little work have been done in examining the properties of population k-means clusters, especially when k becomes large. In Dalenius it is shown that the cut - point between neighbor ing population clusters is the average of the means in the clusters, and in Cox the cut - points for the k-means clusters in the standard normal distribution are given for k 1, 2, 6.<br><br>About the Publisher<br><br>Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com<br><br>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.