Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment

In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an [Formula: see text]-divergence cost function. The available information comes from the exact knowledge/boundedness of some components of the factorization—which are used to structure the NMF parameterization—together with the row sum-to-one property of one matrix factor. In this contribution, we extend our previous work which partly involved some of these aspects to [Formula: see text]-divergence cost functions. We derive new update rules which are extendthe previous ones and take into account the available information. Experiments conducted for several operating conditions on realistic simulated mixtures of particulate matter sources show the relevance of these approaches. Results from a real dataset campaign are also presented and validated with expert knowledge.