(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.