Batch and median neural gas

Marie Cottrell (1, 2) , Barbara Hammer (3) , Alexander Hasenfuss (3) , Thomas Villmann (4)

1 CES - Centre d'économie de la Sorbonne
2 SAMOS - Statistique Appliquée et MOdélisation Stochastique
3 Institute of Computer Science
4 Clinic for Psychotherapy

Neural Gas (NG) constitutes a very robust clustering algorithm given euclidian 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.

Mots clés: Neural gas; batch algorithm; proximity data; median clustering; convergence

Domaines: Statistiques [math.ST]; Informatique; Automates cellulaires et gaz sur réseau [nlin.CG]

Marie Cottrell, Barbara Hammer, Alexander Hasenfuss, Thomas Villmann. Batch and median neural gas. Neural Networks, 2006, 19, pp.762-771. ⟨10.1016/j.neunet.2006.05.018⟩. ⟨hal-00107462⟩