title: Batch and median neural gas.
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.
authors.affiliation: SAMOS-MATISSE, Université Paris I, 90, rue de Tolbiac, 75634 Paris CEDEX 13, France.
authors.forename: Marie
authors.initials: M
authors.lastname: Cottrell
authors.forename: Barbara
authors.initials: B
authors.lastname: Hammer
authors.forename: Alexander
authors.initials: A
authors.lastname: Hasenfuss
authors.forename: Thomas
authors.initials: T
authors.lastname: Villmann
mesh_terms: D000465:Algorithms; D002619:Chemical Warfare Agents; D002875:Chromosomes; D003198:Computer Simulation; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*
chemical_list: D002619:Chemical Warfare Agents