Kullback-leibler NMF under linear equality constraints. Application to pollution source apportionment

Non negative matrix factorisation (NMF) coupled to divergence measure has been investigated in the frame of an application to polluant source identification. It relies on receptor modelling which considers the data matrix as the result of cumulative effects of p sources. NMF aims at finding a contribution matrix G and a profile matrix F by minimizing a specific cost function. The focus is made here on the Kullback-Leibler divergence (KL) cost function. Linear equality constraints are incorporated into parts of the decomposition and general mutiplicative like expressions, which take into account these constraints, are derived. This method is applied in the frame of source apportionment of particulate matter.