Evolutionary Neural Gas (ENG): A Model of Self Organizing Network from Input Categorization

Despite their claimed biological plausibility, most self organizing networks have strict topological constraints and consequently they cannot take into account a wide range of external stimuli. Furthermore their evolution is conditioned by deterministic laws which often are not correlated with the structural parameters and the global status of the network, as it should happen in a real biological system. In nature the environmental inputs are noise affected and fuzzy. Which thing sets the problem to investigate the possibility of emergent behaviour in a not strictly constrained net and subjected to different inputs. It is here presented a new model of Evolutionary Neural Gas (ENG) with any topological constraints, trained by probabilistic laws depending on the local distortion errors and the network dimension. The network is considered as a population of nodes that coexist in an ecosystem sharing local and global resources. Those particular features allow the network to quickly adapt to the environment, according to its dimensions. The ENG model analysis shows that the net evolves as a scale-free graph, and justifies in a deeply physical sense- the term gas here used.Comment: 16 pages, 8 figure

Magnification Control in Self-Organizing Maps and Neural Gas

We consider different ways to control the magnification in self-organizing maps (SOM) and neural gas (NG). Starting from early approaches of magnification control in vector quantization, we then concentrate on different approaches for SOM and NG. We show that three structurally similar approaches can be applied to both algorithms: localized learning, concave-convex learning, and winner relaxing learning. Thereby, the approach of concave-convex learning in SOM is extended to a more general description, whereas the concave-convex learning for NG is new. In general, the control mechanisms generate only slightly different behavior comparing both neural algorithms. However, we emphasize that the NG results are valid for any data dimension, whereas in the SOM case the results hold only for the one-dimensional case.Comment: 24 pages, 4 figure

Batch and median neural gas

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.Comment: In Special Issue after WSOM 05 Conference, 5-8 september, 2005, Pari

Building Adaptive Basis Functions with a Continuous Self-Organizing Map

This paper introduces CSOM, a continuous version of the Self-Organizing Map (SOM). The CSOM network generates maps similar to those created with the original SOM algorithm but, due to the continuous nature of the mapping, CSOM outperforms the SOM on function approximation tasks. CSOM integrates self-organization and smooth prediction into a single process. This is a departure from previous work that required two training phases, one to self-organize a map using the SOM algorithm, and another to learn a smooth approximation of a function. System performance is illustrated with three examples.Office of Naval Research (N00014-95-10409, N00014-95-0657

Effects of Irregular Topology in Spherical Self-Organizing Maps

We explore the effect of different topologies on properties of self-organizing maps (SOM). We suggest several diagnostics for measuring topology-induced errors in SOM and use these in a comparison of four different topologies. The results show that SOM is less sensitive to localized irregularities in the network structure than the literature may otherwise suggest. Further, the results support the use of spherical topologies as a solution to the boundary problem in traditional SOM.