Abstract: We present a general Bayesian approach to probabilistic matrix factorization subject to linear constraints. The approach is based on a Gaussian observation model and Gaussian priors with bilinear equality and inequality constraints. We present an efficient Markov chain Monte Carlo inference procedure based on Gibbs sampling. Special cases of the proposed model are Bayesian formulations of non-negative matrix factorization and factor analysis. The method is evaluated on a blind source separation problem. We demonstrate that our algorithm can be used to extract meaningful and interpretable features that are remarkably different from features extracted using existing related matrix factorization techniques.
Demo code available: Matlab code implementing the algorithm described in the paper is available for download below.
- Mikkel N. Schmidt, Linearly constrained Bayesian matrix factorization for blind source separation, Neural Information Processing Systems, Advances in (NIPS), 2009
title = "Linearly constrained Bayesian matrix factorization for blind source separation",
author = "Mikkel N. Schmidt",
booktitle = "Neural Information Processing Systems, Advances in (NIPS)",
editor = "Y. Bengio and D. Schuurmans and J. Lafferty and C. K. I. Williams and A. Culotta",
month = "Dec",
pages = "1624--1632",
year = "2009"