Robust Mixture Modeling with Pearson Type VII Distribution

Mixture of Student t-distribution (MoT) has been widely used to model multivariate data sets with atypical observations, or outliers for robust clustering. In this paper, we developed a novel robust clustering approach by modeling the data sets with mixture of Pearson type VII distribution (MoP). An EM algorithm is developed for the maximum likelihood estimation of the model parameters. Outlier detection criterion is derived from the EM solution. Controlled experimental results on synthetic datasets show that the MoP performs comparably, on average, with the MoT in terms of outlier detection accuracy and out-of-sample log-likelihood, but the MoP is more stable. Furthermore, we compared the performances of the Pearson type VII and the student t mixtures on the classification of several benchmark pattern recognition data sets. The comparison favors the developed Pearson type VII mixtures.