SEQUENTIAL COMPETITIVE LEARNING AND THE FUZZY C-MEANS CLUSTERING ALGORITHMS

Several recent papers have described sequential competitive learning a lgorithms that are curious hybrids of algorithms used to optimize the fuzzy c-means (FCM) and learning vector quantization (LVQ) models. Fir st, we show that these hybrids do not optimize the FCM functional. The n we show that the gradient descent conditions they use are not necess ary conditions for optimization of a sequential version of the FCM fun ctional. We give a numerical example that demonstrates some weaknesses of the sequential scheme proposed by Chung and Lee. And finally, we e xplain why these algorithms may work at times, by exhibiting the stoch astic approximation problem that they unknowingly attempt to solve. Co pyright (C) 1996 Published by Elsevier Science Ltd