Nonnegative Matrix Factorization with Gaussian Process Priors

Figure 1

Toy example data matrix (upper left), underlying noise-free nonnegative data (upper right), and estimates using the four methods described in the text. The data has a fairly large amount of noise, and the underlying nonnegative factors are smooth in both directions. The LS-NMF and CNMF decompositions are nonsmooth since these methods are not model of correlations in the factors. The GPP-NMF, which uses a smooth prior, finds a smooth solution. When using the correct prior, the soulution is very close to the true underlying data.