A Type of Duality between Self-Organizing Maps and Minimal Wiring
- 1 January 1995
- journal article
- Published by MIT Press in Neural Computation
- Vol. 7 (1) , 25-35
- https://doi.org/10.1162/neco.1995.7.1.25
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.Keywords
This publication has 10 references indexed in Scilit:
- Self-organizing maps: ordering, convergence properties and energy functionsBiological Cybernetics, 1992
- A principle for the formation of the spatial structure of cortical feature maps.Proceedings of the National Academy of Sciences, 1990
- Derivation of a class of training algorithmsIEEE Transactions on Neural Networks, 1990
- A dimension reduction framework for understanding cortical mapsNature, 1990
- Ocular Dominance Column Development: Analysis and SimulationScience, 1989
- An analogue approach to the travelling salesman problem using an elastic net methodNature, 1987
- Optimal Numberings of an $N \times N$ ArraySIAM Journal on Algebraic Discrete Methods, 1986
- A model for the formation of ocular dominance stripesProceedings of the Royal Society of London. B. Biological Sciences, 1980
- How patterned neural connections can be set up by self-organizationProceedings of the Royal Society of London. B. Biological Sciences, 1976
- Self-organization of orientation sensitive cells in the striate cortexBiological Cybernetics, 1973