Discrete Component Analysis

This article presents a unified theory for analysis of components in discrete data, and compares the methods with techniques such as independent component analysis, non-negative matrix factorisation and latent Dirichlet allocation. The main families of algorithms discussed are a variational approximation, Gibbs sampling, and Rao-Blackwellised Gibbs sampling. Applications are presented for voting records from the United States Senate for 2003, and for the Reuters-21578 newswire collection.