Unsupervised Learning of Dirichlet Compound Negative Multinomial Mixture Model using Minorization-Maximization Approach

The Dirichlet Compound Negative Multinomial (DCNM) distribution is a probabilistic model used to model multivariate count data. The presence of the Gamma function in the density probability distribution increases significantly the time and computation complexity, especially for high-dimensional datasets. In this paper, we use an alternative parametrization of DCNM using rising polynomials. Then, we use the Minorization-Maximization approach, to learn the parameter estimates of the DCNM mixture model, which brings higher numerical stability, lower tendency of poor local maxima, initialization independence, and avoids cumbersome derivative calculations. Moreover, we propose a new learning method to simultaneously update the mixture’s parameters and find the optimal number of clusters, using the Minimum Description Length Criterion. The proposed approach is validated in two interesting applications, namely, topic detection and scene recognition, where the results demonstrate the robustness and efficiency of our new learning approach.