On Some Fuzzy Clustering Algorithms Based on Series Models

Abstract

Fuzzy c-means is a basic and general fuzzy clustering algorithm for vectorial data and several variants of this algorithm have been proposed. However, research and development of fuzzy clustering for series data is not as progressive as that for vectorial data. In particular, research on fuzzy clustering algorithms using series models is not advanced. In this work, we proposed several fuzzy clustering algorithms based on a combination of four types of series models, namely the autoregressive and moving average model, generalized autoregressive conditional heteroskedasticity model, hidden markov model, and linear Gaussian state space model, as well as three types of fuzzification techniques, namely Kullback-Leibler divergence regularization, Bezdek-type fuzzification, and q-divergence basis.