Figure 1.

(a) A schematic description of the NMF model with data augmentation. (b) Graphical model with hyperparameters. Each source element s _ν,i,τ is Poisson distributed with intensity t _ν,i v _i,τ. The observations are given by x _ν,τ = ∑_i s _ν,i,τ. In matrix notation, we write X = ∑ S _i. We can analytically integrate out over S. Due to superposition property of Poisson distribution, intensities add up, and we obtain 〈X〉 = TV. Given X, the NMF algorithm is shown to seek the maximum likelihood estimates of the templates T and excitations V. In our Bayesian treatment, we further assume that elements of T and V are Gamma distributed with hyperparameters Θ.