Robust mixture modeling using the Pearson type VII distribution

A mixture of Student t-distributions (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 using mixture of Pearson type VII distributions (MoP). An EM algorithm is developed for the maximum likelihood estimation of the model parameters. An outlier detection criterion is derived from the EM solution. Controlled experimental results on the synthetic datasets show that the MoP is more viable than the MoT. The MoP performs comparably if not better, on average, in terms of outlier detection accuracy and out-of-sample log-likelihood with the MoT. 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 favours the developed Pearson type VII mixtures.