On Some Fuzzy Clustering Algorithms with Cluster-Wise Covariance

In many fuzzy clustering algorithms, the KL-divergence-regularized method based on the Gaussian mixture model, fuzzy classification maximum likelihood, and a fuzzy mixture of Student’s-t distributions have been proposed for cluster-wise anisotropic data, whereas more other types of fuzzification technique have been applied to fuzzy clustering for cluster-wise isotropic data. In this study, some fuzzy clustering algorithms are proposed based on the combinations between four types of fuzzification—namely, the Bezdek-type fuzzification, KL-divergence regularization, fuzzy classification maximum likelihood, and q-divergence-basis—and two types of mixture model—namely, the Gaussian mixture model and t-mixture model. Numerical experiments are conducted to demonstrate the features of the proposed methods.