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On competitive learning

We derive learning rates such that all training patterns are equally important statistically and the learning outcome is independent of the order in which training patterns are presented, if the competitive neurons win the same sets of training patterns regardless the order of presentation. We show that under these schemes, the learning rules in the two different weight normalization approaches, the length-constraint and the sum-constraint, yield practically the same results, if the competitive neurons win the same sets of training patterns with both constraints. These theoretical results are illustrated with computer simulations.