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November 1996 A self-organizing cluster process
Robert M. Burton, William G. Faris
Ann. Appl. Probab. 6(4): 1232-1247 (November 1996). DOI: 10.1214/aoap/1035463330

Abstract

The state of the self-organizing cluster process is a finite subset of points in a bounded region. This subset represents an evolving discrete approximation to a continuous probability distribution in the region. The dynamics of the process is determined by an independent sequence of random points in the region chosen according to the distribution. At each time step the random point attracts the nearest point in the finite set. In this way the subset learns to approximate its environment. It is shown that initial states approach each other exponentially fast for all time with probability one. Thus all memory of the initial state is lost; the environment alone determines future history.

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Robert M. Burton. William G. Faris. "A self-organizing cluster process." Ann. Appl. Probab. 6 (4) 1232 - 1247, November 1996. https://doi.org/10.1214/aoap/1035463330

Information

Published: November 1996
First available in Project Euclid: 24 October 2002

zbMATH: 0870.60063
MathSciNet: MR1422984
Digital Object Identifier: 10.1214/aoap/1035463330

Subjects:
Primary: 60J10 , 68T10 , 92B20
Secondary: 62H30 , 62J20

Keywords: cluster , Kohonen , Markov chain , neural network , pattern recognition , random transformation , self-organization

Rights: Copyright © 1996 Institute of Mathematical Statistics

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Vol.6 • No. 4 • November 1996
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