Monthly
288 pp. per issue
6 x 9, illustrated
ISSN
0899-7667
E-ISSN
1530-888X
2014 Impact factor:
2.21

Neural Computation

Spring 1991, Vol. 3, No. 1, Pages 54-66
(doi: 10.1162/neco.1991.3.1.54)
© 1991 Massachusetts Institute of Technology
Dynamics and Formation of Self-Organizing Maps
Article PDF (563.39 KB)
Abstract

Amari (1983, 1989) proposed a mathematical formulation on the self-organization of synaptic efficacies and neural response fields under the influence of external stimuli. The dynamics as well as the equilibrium properties of the cortical map were obtained analytically for neurons with binary input-output transfer functions. Here we extend this approach to neurons with arbitrary sigmoidal transfer function. Under the assumption that both the intracortical connection and the stimulus-driven thalamic activity are well localized, we are able to derive expressions for the cortical magnification factor, the point-spread resolution, and the bandwidth resolution of the map. As a highlight, we show analytically that the receptive field size of a cortical neuron in the map is inversely proportional to the cortical magnification factor at that map location, the experimentally well-established rule of inverse magnification in retinotopic and somatotopic maps.