Abstract
Fuzzy c-means (FCM) approach is the method for partitioning data into clusters by minimizing an objective function. Therefore, it is important to devise the objective function from which a simple clustering algorithm can be derived. An entropy term was introduced by Miyamoto in the FCM objective function. We proposed an objective function of the fuzzy counterpart of Gaussian mixture models (GMMs) clustering. The objective function is based on Kullback-Leibler divergence instead of the entropy. Miyamoto derived a hard clustering algorithm by linearizing the Kullback-Leibler divergence term of the objective function. In the hard c-means (HCM) clustering approach, covariance matrices are introduced as decision variables. Taking into account this method, for quick and stable convergence of FCM-like clustering, we propose the semi-hard clustering approach by constraining the membership in an interval. The semi-hard clustering result is used for a classifier design. The novel membership function suggested by GMMs and our generalized FCM approach is used for the classifier. The free parameters of the membership function are selected by particle swarm optimization (PSO). In terms of classification performance on UCI benchmark data, the classifier is comparable to the support vector machine (SVM) and surpasses the k-nearest neighbor (k-NN) classifier.
