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In this paper a new maximum a posteriori (MAP) approach based on mixtures of multinomials is proposed for discovering probabilistic patterns in sequences. The main advantage of the method is the ability to bypass the problem of overlapping patterns in neighboring positions of sequences by using a Markov random field (MRF) prior. This model consists of two components, the first models the pattern and the second the background. The Expectation-Maximization (EM) algorithm is used to estimate the model parameters and provides closed form updates. Special care is also taken to overcome the known dependence of the EM algorithm to initialization. This is done by applying an adaptive clustering scheme based on the k-means algorithm in order to produce good initial values for the pattern multinomial model. Experiments with artificial sets of sequences show that the proposed approach discovers qualitatively better patterns, in comparison with maximum likelihood (ML) and Gibbs sampling (GS) approaches.

A Mixture Model Based Markov Random Field for Discovering Patterns in Sequences