Mixtures of Dirichlet-Multinomial distributions for supervised and unsupervised classification of short text data

Topic detection in short textual data is a challenging task due to its representation as high-dimensional and extremely sparse document-term matrix. In this paper we focus on the problem of classifying textual data on the base of their (unique) topic. For unsupervised classification, a popular approach called Mixture of Unigrams consists in considering a mixture of multinomial distributions over the word counts, each component corresponding to a different topic. The multinomial distribution can be easily extended by a Dirichlet prior to the compound mixtures of Dirichlet-Multinomial distributions, which is preferable for sparse data. We propose a gradient descent estimation method for fitting the model, and investigate supervised and unsupervised classification performance on real empirical problems.