In our recent work, we introduced a constrained weighted Non-negative Matrix Factorization (NMF) method using a β-divergence cost function. We assumed that some components of the factorization were known and were used to inform our NMF algorithm. In this paper, we are provided some intervals of possible values for some factorization components. We thus introduce an extended version of our previous work combining an improved divergence expression and some matrix normalizationswhile using the known / bounded information. Some experiments on simulated mixtures of particulate matter sources show the relevance of these approaches.