Regensburg 2007 – wissenschaftliches Programm
Bereiche | Tage | Auswahl | Suche | Downloads | Hilfe
DY: Fachverband Dynamik und Statistische Physik
DY 30: Poster II
DY 30.17: Poster
Donnerstag, 29. März 2007, 16:00–18:00, Poster D
Topographical Stability of Self-Organizing Neural Maps: The case of nonlinear Concave/Convex learning — Fabien Molle1,2 and •Jens Christian Claussen2 — 1Theoretical Physics, Göteborg Universitetet, Sweden — 2Theoretical Physics, Univ. Kiel, Germany
The apparant self-organizing dynamics of biological topographic feature maps has, apart from the biological modeling, provided various methods of Neural Vector Quantizers as Kohonen's Self-Organizing Map and Martinetz' Neural Gas. The invariant density of the attractor states has been studied extensively the last two decades. In most cases the neural output density adapts the input data density by a power law, which in many cases can be calculated analytically, and even be influenced systematically by modifications in the learning rule [1,2]. Here, we consider a nonlinear learning rule investigated in [2], which is capable to generate information-theoretically optimal maps at least in the 1D case [2]. However, much less is known for the learning dynamics. We introduce a simple crossproduct based stability measure to detect topological defects of the representation when the learning rate is increased [3]. The stability border shows a similar shape for all considered cases, but with different maximal learning rate. The exploration of these stability properties is relevant for applications of neural vector quantizers.
[1] J.C.Claussen, Complexity 8(4),15(2003); Neural Computation 17,996(2005), Claussen & T.Villmann, Neurocomputing 63,124(2005) [2] T. Villmann & J.C.Claussen, Neural Computation 18, 446 (2006) [3] F. Molle & J.C. Claussen, Lect. Notes Comp. Sci. 4131, 208 (2006)