Computational Intelligence and Neuroscience 
Volume 2008 (2008), Article ID 361705, 10 pages
doi:10.1155/2008/361705
Research Article

Nonnegative Matrix Factorization with Gaussian Process Priors

Mikkel N. Schmidt1 and Hans Laurberg2

 1Department of Informatics and Mathematical Modelling, Technical University of Denmark, Richard Petersens Plads, DTU-Building 321, 2800 Lyngby, Denmark
2Department of Electronic Systems, Aalborg University, Niels Jernes Vej 12, 9220 Aalborg Ø., Denmark
Received 31 October 2007; Revised 16 January 2008; Accepted 10 February 2008

Recommended by Wenwu Wang

Abstract

We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance function. This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries. The method is demonstrated with an example from chemical shift brain imaging.