Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment
Laboratoire LISIC–EA 4491, Université du Littoral Côte d’Opale, F-62228 Calais, France
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
In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an
-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
-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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
Share & Cite This Article
MDPI and ACS Style
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.
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(3):253.
Delmaire, Gilles; Omidvar, Mahmoud; Puigt, Matthieu; Ledoux, Frédéric; Limem, Abdelhakim; Roussel, Gilles; Courcot, Dominique. 2019. "Informed Weighted Non-Negative Matrix Factorization Using αβ-Divergence Applied to Source Apportionment." Entropy 21, no. 3: 253.
Show more citation formats
Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
[Return to top]
For more information on the journal statistics, click here
Multiple requests from the same IP address are counted as one view.