Modeling Dyadic Data with Binary Latent Factors

We introduce binary matrix factorization, a novel model for unsupervised ma- trix decomposition. The decomposition is learned by fitting a non-parametric Bayesian probabilistic model with binary latent variables to a matrix of dyadic data. Unlike bi-clustering models, which assign each row or column to a single cluster based on a categorical hidden feature, our binary feature model reflects the prior belief that items and attributes can be associated with more than one latent cluster at a time. We provide simple learning and inference rules for this new model and show how to extend it to an infinite model in which the number of features is not a priori fixed but is allowed to grow with the size of the data. One of the major goals of probabilistic unsupervised learning is to discover underlying or hidden structure in a dataset by using latent variables to describe a complex data generation process.