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

Abstract : In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an αβ-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 αβ-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.
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Submitted on : Wednesday, March 6, 2019 - 2:20:53 PM
Last modification on : Tuesday, January 5, 2021 - 1:04:02 PM

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Gilles Delmaire, Mahmoud Omidvar, Matthieu Puigt, Frédéric Ledoux, Abdelhakim Limem, et al.. Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment. Entropy, MDPI, 2019, Information Theory Applications in Signal Processing, 21 (3), pp.253. ⟨10.3390/e21030253⟩. ⟨hal-02059209⟩

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