In this paper, we examine the problem of modeling overdispersed frequency vectors that are naturally generated by several machine learning and computer vision applications.
We consider a statistical framework based on a mixture of Multinomial Scaled Dirichlet (MSD) distributions that we have previously proposed in [1]. Given that the likelihood function plays a key role in statistical inference, e.g. in maximum likelihood estimation and Fisher information matrix investigation, we propose to improve the efficiency of computing the MSD log-likelihood by approximating its function based on Bernoulli polynomials. As compared to [1], the log-likelihood function is computed using the proposed mesh algorithm and a model selection approach is seamlessly integrated with the parameters estimation. The improved clustering framework offers a good compromise between other techniques and improves the approach used before for the same model. The merits of the proposed approach are validated via a challenging application that involves human action recognition.