Some Theoretical Aspects of the Neural Gas Vector Quantizer

Authors:
Thomas Villmann;Barbara Hammer;Michael Biehl
Affiliations:
Medical Department, University Leipzig, Leipzig, Germany 04103;Institute of Computer Science, Clausthal University of Technology, Clausthal, Germany 38678;Institute of Mathematics and Computing Science, University of Groningen, Groningen, The Netherlands 9700 AK
Venue:
Similarity-Based Clustering
Year:
2009

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ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part I

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Abstract

We investigate the neural gas quantizer in the light of statistical physics concepts. We show that this algorithm can be extended to a vector quantizer with general differentiable similarity measure offering a greater flexibility. Further, we show that the neighborhood cooperativeness control parameter is not equivalent to an inverse temperature like in the deterministic annealing vector quantizer introduced by K. Rose et al. Instead, an annealed variant of neural gas can be obtained using the formalism proposed by T. Heskes for self-organizing maps.