{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,18]],"date-time":"2024-06-18T23:14:27Z","timestamp":1718752467814},"reference-count":55,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2019,3,6]],"date-time":"2019-03-06T00:00:00Z","timestamp":1551830400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"In this paper, we propose informed weighted non-negative matrix factorization (NMF) methods using an \u03b1 \u03b2 -divergence cost function. The available information comes from the exact knowledge\/boundedness of some components of the factorization\u2014which are used to structure the NMF parameterization\u2014together 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 \u03b1 \u03b2 -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.<\/jats:p>","DOI":"10.3390\/e21030253","type":"journal-article","created":{"date-parts":[[2019,3,7]],"date-time":"2019-03-07T15:52:22Z","timestamp":1551973942000},"page":"253","source":"Crossref","is-referenced-by-count":6,"title":["Informed Weighted Non-Negative Matrix Factorization Using \u03b1\u03b2-Divergence Applied to Source Apportionment"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-4425-4507","authenticated-orcid":false,"given":"Gilles","family":"Delmaire","sequence":"first","affiliation":[{"name":"Laboratoire LISIC\u2013EA 4491, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, F-62228 Calais, France"}]},{"given":"Mahmoud","family":"Omidvar","sequence":"additional","affiliation":[{"name":"Laboratoire LISIC\u2013EA 4491, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, F-62228 Calais, France"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-3264-4981","authenticated-orcid":false,"given":"Matthieu","family":"Puigt","sequence":"additional","affiliation":[{"name":"Laboratoire LISIC\u2013EA 4491, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, F-62228 Calais, France"}]},{"ORCID":"http:\/\/orcid.org\/0000-0001-6475-1450","authenticated-orcid":false,"given":"Fr\u00e9d\u00e9ric","family":"Ledoux","sequence":"additional","affiliation":[{"name":"Laboratoire UCEIV\u2013EA 4492, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, SFR CONDORCET FR CNRS 3417, F-59140 Dunkerque, France"}]},{"given":"Abdelhakim","family":"Limem","sequence":"additional","affiliation":[{"name":"Laboratoire LISIC\u2013EA 4491, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, F-62228 Calais, France"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-8531-1566","authenticated-orcid":false,"given":"Gilles","family":"Roussel","sequence":"additional","affiliation":[{"name":"Laboratoire LISIC\u2013EA 4491, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, F-62228 Calais, France"}]},{"given":"Dominique","family":"Courcot","sequence":"additional","affiliation":[{"name":"Laboratoire UCEIV\u2013EA 4492, Universit\u00e9 du Littoral C\u00f4te d\u2019Opale, SFR CONDORCET FR CNRS 3417, F-59140 Dunkerque, France"}]}],"member":"1968","published-online":{"date-parts":[[2019,3,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1080\/10962247.2016.1140693","article-title":"Review of receptor modeling methods for source apportionment","volume":"66","author":"Hopke","year":"2016","journal-title":"J. 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