Fuzzy Clustering with Generalized Entropy Based on Neural Network

Abstract

In order to solve the optimization problem with generalized entropy’s objective function, where weight index and the generalized entropy coefficient may be equal or not equal to each other, the multi-synapses neural network is used in this chapter. For the constraints of the objective function, we use augmented Lagrange multipliers instead of Lagrange multipliers to construct augmented Lagrange function. On the basis of multi-synapses neural network, we obtain a generalized entropy fuzzy c-means (FCM) algorithm, namely GEFCM. Moreover, to solve Lagrange multipliers’ assignment problem, we use randomly selected method and iterated method to determine them. Experimental results show that for the different weight index and generalized entropy coefficient in data clustering, algorithm’s performance has a very large difference. Especially, when weight index is greater than 2, good clustering results are also obtained with presented algorithm GEFCM.