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.
Chemical shift imaging data: The result of the GPP-NMF decomposition of the chemial shift brain imaging data is shown here. The recovered spectra physically meaningful and correspond to muscle and brain tissue. The spatial distribution in the brain is highly separated between brain and muscle tissue, as compared to the result of previous methods. This is due to the exponential, smooth, and symmetric prior distribution. The inclusion of prior information results in a solution which much more clearly separates the data in two factors which are spatially located on the edge of the scull and inside the head respectively. The details are given in the paper.
- Mikkel N. Schmidt and Hans Laurberg, Non-negative matrix factorization with Gaussian process priors, Computational Intelligence and Neuroscience, 2008
title = "Non-negative matrix factorization with Gaussian process priors",
author = "Mikkel N. Schmidt and Hans Laurberg",
journal = "Computational Intelligence and Neuroscience",
year = "2008"