Magnification Control in Self-Organizing Maps and Neural Gas

Details Magnification Control in Self-Organizing Maps and Neural Gas Magnification Control in Self-Organizing Maps and Neural Gas

2006-09-20

arxiv.org/abs/cond-mat/0609517v1

Neural Computation 8, 446-469 (2006)

Physics

Condensed Matter

Disordered Systems and Neural Networks

24 pages, 4 figures

Scientific paper

10.1162/089976606775093918

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.

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