Calculating Conditions for the Emergence of Structure in Self-Organizing Maps
The self-organization of sensotopic maps in the brain has been modeled with various approaches, using models with linear [1, 2, 3, 4] and nonlinear [5, 6, 7] lateral interaction functions. In the realm of visual maps, all models are able to generate ocular dominance or orientation structure . Models differ, however, with regard to more subtle effects, like the impact of input correlation on ocular dominance stripe width, the self-organization of oriented receptive fields from non-oriented stimuli or correlation functions, or the preferred angle of intersection between ocular dominance and orientation column systems. For a correct assessment of the behavior of particular models with regard to these or other phenomena, it is dangerous to rely on simulations only. Rather, analytic results on conditions for the pattern formation in map models are desirable. We present here a method for calculating such conditions for a map model with strong lateral nonlinearity, the high-dimensional version of Kohonen’s Self-Organizing Map (SOM). Using this method we then analyze two relevant models, a SOM-model for the development of orientation maps and a SOM-model for the development of ocular dominance maps.
Unable to display preview. Download preview PDF.
- 1.C. von der Malsburg, Kybernetik 14, 85 (1973); Biol. Cyb. 32, 49 (1979).Google Scholar
- 3.K. D. Miller, J. Neurose. 14, 409 (1994).Google Scholar
- 4.M. Miyashita, S. Tanaka, NeuroRep. 3, 69 (1992).Google Scholar
- 10.M. Riesenhuber, H.-U. Bauer, T. Geisel, Biol. Cyb., in print (1996).Google Scholar
- 11.K. D. Miller, submitted to Neur. Comp. (1995).Google Scholar
- 13.K. Obermayer, Adaptive Neuronale Netze und ihre Anwendung als Modelle der Entwicklung kortikaler Karten, infix Verlag, Sankt Augustin (1993).Google Scholar
- 17.C. von der Malsburg, Neural and Electronic Networks,Eds. Zornetzer et al., Academic Press. 421 (1994).Google Scholar