Robust mixture clustering using 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 real pattern recognition data sets. The comparison favours the developed Pearson type VII mixtures.

Research highlights
► Introduced a new probability distribution, called Pearson Type VII.
► Provided a scalar mixture representation for the Pearson Type VII distribution.
► Developed an EM algorithm to fit the finite mixture model for robust clustering.
► Compared the developed algorithm with the mixture of Student t-distribution.