Publisher's Synopsis
Excerpt from Asymptotic Properties of Bivariate K-Means Clusters
In outline, the proof of Theorem 2 requires first showing that the polygon with n edges and area A which has the minimum within polygon sum of squares is regular (see Lemma For any polygon divided into R clusters, 3 lower bound for the limiting value (lim inf) of the within cluster sum of squares may then be found by assuming the clusters are regular hexagons (theorem An upper bound may also be found by covering the polygon with regular hexagons. Since the ratio of the two bounds approaches 1 as k w, Theorem 2 follows. 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.
