The fuzzy c-means (FCM) algorithm is one of the most frequently used clustering algorithms. The weighting exponent m is a parameter that greatly influences the performance of the FCM. But there has been no theoretical basis for selecting the proper weighting exponent in the literature. In this paper, we develop a new theoretical approach to selecting the weighting exponent in the FCM. Based on this approach, we reveal the relation between the stability of the fixed points of the FCM and the data set itself. This relation provides the theoretical basis for selecting the weighting exponent in the FCM. The numerical experiments verify the effectiveness of our theoretical conclusion.
Different mutation operators have been proposed in evolutionary programming, but for each operator there are some types of optimization problems that cannot be solved efficiently. A mixed strategy, integrating several mutation operators into a single algorithm, can overcome this problem. Inspired by evolutionary game theory, this paper presents a mixed strategy evolutionary programming algorithm that employs the Gaussian, Cauchy, Lévy, and single-point mutation operators. The novel algorithm is tested on a set of 22 benchmark problems. The results show that the mixed strategy performs equally well or better than the best of the four pure strategies does, for all of the benchmark problems.
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