Robust informed split gradient NMF using Alpha ß-divergence for source apportionment

Abstract

Source apportionment is a very challenging topic for which non-negative source separation is well-suited. Recently, we proposed several informed Non-negative Matrix Factorization (NMF) for which some expert knowledge was introduced. These methods were all dealing with some set values of one factor together with the row sum-to-one property by either processing each constraint alternatingly or using a new parameterization which involves all of them. However, this last method was sensitive to the presence of outliers. In this paper, we thus propose a new robust informed Split Gradient NMF method which is based on a weighted αβ-divergence cost function. Experiments conducted for several input SNR with and without outliers on simulated mixtures of particulate matter sources show the relevance of the new approach.