On the distribution and convergence of feature space in self-organizing maps

Yin, H. and Allinson, N. M. (1995) On the distribution and convergence of feature space in self-organizing maps. Neural computation, 7 (6). pp. 1178-1187. ISSN 0899-7667

Full content URL: http://dx.doi.org/10.1162/neco.1995.7.6.1178

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Item Type:Article
Item Status:Live Archive

Abstract

In this paper an analysis of the statistical and the convergence properties of Kohonen's self-organizing map of any dimension is presented. Every feature in the map is considered as a sum of a number of random variables. We extend the Central Limit Theorem to a particular case, which is then applied to prove that the feature space during learning tends to multiple gaussian distributed stochastic processes, which will eventually converge in the mean-square sense to the probabilistic centers of input subsets to form a quantization mapping with a minimum mean squared distortion either globally or locally. The diminishing effect, as training progresses, of the initial states on the value of the feature map is also shown.

Keywords:algorithm, article, artificial intelligence, artificial neural network, normal distribution, statistical model, statistics, Algorithms, Models, Statistical, Neural Networks (Computer), Stochastic Processes
Subjects:G Mathematical and Computer Sciences > G400 Computer Science
Divisions:College of Science > School of Computer Science
ID Code:8603
Deposited On:12 Jul 2013 10:19

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