Batch and median neural gas

  • Authors:
  • Marie Cottrell;Barbara Hammer;Alexander Hasenfuß;Thomas Villmann

  • Affiliations:
  • SAMOS-MATISSE, Université Paris I, Paris CEDEX, France;Institute of Computer Science, Clausthal University of Technology, Clausthal-Zellerfeld, Germany;Institute of Computer Science, Clausthal University of Technology, Clausthal-Zellerfeld, Germany;Clinic for Psychotherapy, Universität Leipzig, Leipzig, Germany

  • Venue:
  • Neural Networks - 2006 Special issue: Advances in self-organizing maps--WSOM'05
  • Year:
  • 2006

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Abstract

Neural Gas (NG) constitutes a very robust clustering algorithm given Euclidean data which does not suffer from the problem of local minima like simple vector quantization, or topological restrictions like the self-organizing map. Based on the cost function of NG, we introduce a batch variant of NG which shows much faster convergence and which can be interpreted as an optimization of the cost function by the Newton method. This formulation has the additional benefit that, based on the notion of the generalized median in analogy to Median SOM, a variant for non-vectorial proximity data can be introduced. We prove convergence of batch and median versions of NG, SOM, and k-means in a unified formulation, and we investigate the behavior of the algorithms in several experiments.