Analysis of ocular dominance pattern formation in a high-dimensional self-organizing-map model

Using a distortion measure for the states emerging in self-organizing maps (SOMs) we mathematically analyse a recently proposed high-dimensional map formation model for ocular dominance patterns. We calculate critical values of parameters for ocular dominance states to occur, and we determine how the pattern layout depends on these parameters. The analysis reveals an increase of ocular dominance bandwidth with decreasing correlation, consistent with a recently observed increase of bandwidth in strabismic cats. In subsequent simulations these analytical results are corroborated, irrespective of the specific normalization procedure (multiplicative or subtractive) employed in the simulations.