Alternative membership function for sequential fuzzy clustering

Abstract

This paper presents an alternative membership function for fuzzy c-mean. According to this membership function and Bezdek's definition, we derive two sequential algorithms for fuzzy c-mean. Both of them are stochastic gradient descent algorithms which minimize Bezdek's objective functional. Analytical result indicates that both algorithms are actually compatible with each other. The convergence properties of both algorithms are studied. As the update equations are so simple, these sequential algorithms are embedded into neural network to form a class of fuzzy neural network analogue to unsupervised type neural network such that competitive learning is a special case.<>