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A Central Limit Theorem for k-Means Clustering
The Annals of Probability
Vol. 10, No. 4 (Nov., 1982), pp. 919-926
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/2243547
Page Count: 8
You can always find the topics here!Topics: Central limit theorem, Mathematical vectors, Mathematical integrals, Approximation, Lebesgue measures, Polyhedrons, Boundary points, Matrices, Surface integrals, Statism
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A set of n points in Euclidean space is partitioned into the k groups that minimize the within groups sum of squares. Under the assumption that the n points come from independent sampling on a fixed distribution, conditions are found to assure asymptotic normality of the vector of means of the k groups. The method of proof makes novel application of a functional central limit theorem for empirical processes--a generalization of Donsker's theorem due to Dudley.
The Annals of Probability © 1982 Institute of Mathematical Statistics