Free Energy-based Competititve Learning for Self-Organizing Maps

R. Kamimura (Japan)

Keywords

Mutual information, free energy, entropy, competitive learning, selforganizing maps

Abstract

In this paper, we propose a new information-theoretic ap proach to self-organizing maps. We have so far proposed mutual information maximization to realize competitive learning. However, the computational complexity and fi delity to input patterns become serious when we try to ap ply it to self-organizing maps. To overcome these short comings, we introduce a free energy similar to that of sta tistical mechanics. By the free energy, we need not directly compute mutual information to simplify greatly computa tional procedures. In addition, in the free energy, errors be tween targets and outputs are naturally built in. This prop erty can solve the problem of fidelity to input patterns of mutual information maximization. In the free energy, we can increase mutual information, taking due attention to errors between targets and connection weights. To demon strate the performance of our free energy method, we ap plied the method to the famous Iris Problem. Experimental results showed that feature maps obtained by free energy minimization was significantly similar to those by the con ventional SOM.

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