Fuzzy Clustering/Co-clustering and Probabilistic Mixture Models-Induced Algorithms

While fuzzy c-means (FCM) and its variants have become popular tools in many application fields, their fuzzy partition natures were often discussed only from the empirical viewpoints without theoretical insight. This chapter reviews some fuzzy clustering models induced by probabilistic mixture concepts and discusses the effects of introduction of adjustable fuzziness penalties into statistical models. First, the entropy regularization-based FCM proposed by Miyamoto et al. is revisited from the Gaussian mixtures viewpoint and the fuzzification mechanism is compared with the standard FCM. Second, the regularization concept is discussed in fuzzy co-clustering context and a multinomial mixtures-induced clustering model is reviewed. Some illustrative examples demonstrate the characteristics of fuzzy clustering algorithms with adjustable fuzziness penalties, and the interpretability of object partition is shown to be improved. Finally, a possible future direction of fuzzy clustering research is discussed.