Non-negative matrix factorization with Gaussian process priors
Abstract: We present a general method for including prior knowledge in a non-negative matrix factorization based on Gaussian process priors. We assume that the non-negative parameters of 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 which 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.