Unified Bayesian Approach to Non-Negative Matrix Factorization
The goal of this work is to develop a unifying framework for Sparse NMF, which is the solution to the following problem:
$$\Vert X - WH \Vert_2^2 \; \; \text{subject to} \; \; W,H \geq 0 \; \; \text{and} \; \; \Vert H_{(:,i)} \Vert_0 \leq L \; \; \forall i $$
Our work presents a general sparsity promoting prior, the rectified power exponential scale mixture. As we show, this prior leads to many well known Sparse NMF algorithms, as well as several novel formulations.