Convergence and Ordering of Kohonen's Batch Map

Authors:
Yizong Cheng
Affiliations:
Department of Electrical and Computer Engineering and Computer Science, University of Cincinnati, Cincinnati, OH 45221, U.S.A.
Venue:
Neural Computation
Year:
1997

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Abstract

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.