Efficient Computation of Log-likelihood Function in Clustering Overdispersed Count Data Using Multinomial Beta-Liouville Distribution

In this paper, we present an overdispersed count data clustering algorithm, which uses the mesh method for computing the log-likelihood function, of the multinomial Beta-Liouville distribution (MBLD). In one of the recent research papers, the use of the mesh algorithm, which involves the approximation of the multinomial Dirichlet distribution's (MDD) log-likelihood function, based on the Bernoulli polynomials, has been proposed instead of using the traditional numerical computation of the log-likelihood function which either results in instability, or leads to long run times that make its use infeasible when modeling large-scale data. Therefore, we extend the mesh algorithm approach for computing the log likelihood function of the MBLD, which is a more flexible distribution. A finite mixture model based on MBLD, is optimized by expectation-maximization, and attempts to achieve a high accuracy for count data clustering. We evaluate the performance of the proposed approach, through a set of empirical experiments, that concern natural scenes categorization.