Robust Fuzzy Classification Maximum Likelihood Clustering with Multivariate t-Distributions

Mixtures of distributions have been used as probability models for clustering data. Classification maximum likelihood (CML) procedure is a popular mixture of maximum likelihood approach to clustering. Yang (1993) extended CML to fuzzy CML (FCML) for a normal mixture model, called FCML-N. However, normal distributions are not robust for outliers. In general, t-distributions should be more robust to outliers than normal distributions. In this paper we consider FCML with multivariate t-distributions and then create a robust clustering algorithm, called FCML-T. To compare with the expectation & maximization for multivariate t-distributions (EM-T), the proposed FCML-T uses a much simpler equation for solving the degrees of freedom. Some numerical and real experimental examples are used to compare the FCML-T with FCML-N, EM for normal mixtures (EM-N) and EM-T. The results demonstrate the superiority and usefulness of the proposed FCML-T algorithm.