On fuzzy clustering for categorical multivariate data induced by polya mixture models

In this paper, three fuzzy clustering models for categorical multivariate data are proposed based on the Polya mixture model and q-divergence. A conventional fuzzy clustering model for categorical multivariate data is constructed by fuzzifying a multinomial mixture model (MMM) via regularizing Kullback-Leibler (KL) divergence appearing in a pseudo likelihood of an MMM, whereas MMM is extended to a Polya mixture model (PMM) and no fuzzy counterpart to PMM is proposed. The first proposed model is constructed by fuzzifying PMM, by means of regularizing KL-divergence appearing in a pseudo likelihood of the model. The other two models are derived by modifying the first proposed algorithm, which is based on the fact that one of the three fuzzy clustering models for vectorial data is similar to the first proposed model, and that another fuzzy clustering model for vectorial data can connect the other two fuzzy clustering models for vectorial data based on q-divergence. In numerical experiments, the properties of the membership of the proposed methods were observed using an artificial dataset.