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6 x 9, illustrated
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0899-7667
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1530-888X
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Neural Computation

January 1995, Vol. 7, No. 1, Pages 25-35
(doi: 10.1162/neco.1995.7.1.25)
© 1995 Massachusetts Institute of Technology
A Type of Duality between Self-Organizing Maps and Minimal Wiring
Article PDF (560.33 KB)
Abstract

I show here that two interpretations of neural maps are closely related. The first, due to Kohonen, sees these maps as forming by an adaptive process in response to stimuli. The second—the minimal wiring or dimension-reduction perspective—interprets the maps as the solution of a minimization problem, where the goal is to keep the “wiring” between neurons with similar receptive fields as short as possible. Recent work by Luttrell provides a bridging concept, by showing that Kohonen's algorithm can be regarded as an approximation to gradient descent on a certain functional. I show how this functional can be generalized in a way that allows it to be interpreted as a measure of wirelength.