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Entropy 2019, 21(3), 253; https://doi.org/10.3390/e21030253

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

1
Laboratoire LISIC–EA 4491, Université du Littoral Côte d’Opale, F-62228 Calais, France
2
Laboratoire UCEIV–EA 4492, Université du Littoral Côte d’Opale, SFR CONDORCET FR CNRS 3417, F-59140 Dunkerque, France
*
Author to whom correspondence should be addressed.
Current address: Savencia Group, F-78220 Viroflay, France.
Received: 19 January 2019 / Revised: 21 February 2019 / Accepted: 26 February 2019 / Published: 6 March 2019
(This article belongs to the Special Issue Information Theory Applications in Signal Processing)
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Abstract

In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an α β -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 α β -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. View Full-Text
Keywords: non-negative matrix factorization; informed NMF; robust cost function; source apportionment; air pollution non-negative matrix factorization; informed NMF; robust cost function; source apportionment; air pollution
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Delmaire, G.; Omidvar, M.; Puigt, M.; Ledoux, F.; Limem, A.; Roussel, G.; Courcot, D. Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment. Entropy 2019, 21, 253.

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