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Neural Computation, Vol 9, 1667-1676, Copyright © 1997 by The MIT Press

NOTES

Convergence and Ordering of Kohonen's Batch Map

Yizong Cheng

The convergence and ordering of Kohonen's batch-mode self-organizing map with Heskes and Kappen's (1993) winner selection are proved. Selim and Ismail's (1984) objective function for k-means clustering is generalized in the convergence proof of the self-organizing map. It is shown that when the neighborhood relation is doubly decreasing, order in the map is preserved. An unordered map becomes ordered when a degenerate state of ordering is entered, where the number of distinct winners is one or two. One strategy to enter this state is to run the algorithm with a broad neighborhood relation.




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J COGNITIVE NEUROSCIENCE NEURAL COMPUTATION MIT PRESS JOURNALS
Copyright © 1997 by The MIT Press.