Multiplicative algorithms for constrained non-negative matrix factorization

Handle URI:
http://hdl.handle.net/10754/564631
Title:
Multiplicative algorithms for constrained non-negative matrix factorization
Authors:
Peng, Chengbin ( 0000-0002-7445-2638 ) ; Wong, Kachun; Rockwood, Alyn P.; Zhang, Xiangliang ( 0000-0002-3574-5665 ) ; Jiang, Jinling; Keyes, David E. ( 0000-0002-4052-7224 )
Abstract:
Non-negative matrix factorization (NMF) provides the advantage of parts-based data representation through additive only combinations. It has been widely adopted in areas like item recommending, text mining, data clustering, speech denoising, etc. In this paper, we provide an algorithm that allows the factorization to have linear or approximatly linear constraints with respect to each factor. We prove that if the constraint function is linear, algorithms within our multiplicative framework will converge. This theory supports a large variety of equality and inequality constraints, and can facilitate application of NMF to a much larger domain. Taking the recommender system as an example, we demonstrate how a specialized weighted and constrained NMF algorithm can be developed to fit exactly for the problem, and the tests justify that our constraints improve the performance for both weighted and unweighted NMF algorithms under several different metrics. In particular, on the Movielens data with 94% of items, the Constrained NMF improves recall rate 3% compared to SVD50 and 45% compared to SVD150, which were reported as the best two in the top-N metric. © 2012 IEEE.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Computer Science Program; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Machine Intelligence & kNowledge Engineering Lab
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2012 IEEE 12th International Conference on Data Mining
Conference/Event name:
12th IEEE International Conference on Data Mining, ICDM 2012
Issue Date:
Dec-2012
DOI:
10.1109/ICDM.2012.106
Type:
Conference Paper
ISSN:
15504786
ISBN:
9780769549057
Appears in Collections:
Conference Papers; Applied Mathematics and Computational Science Program; Extreme Computing Research Center; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorPeng, Chengbinen
dc.contributor.authorWong, Kachunen
dc.contributor.authorRockwood, Alyn P.en
dc.contributor.authorZhang, Xiangliangen
dc.contributor.authorJiang, Jinlingen
dc.contributor.authorKeyes, David E.en
dc.date.accessioned2015-08-04T07:05:33Zen
dc.date.available2015-08-04T07:05:33Zen
dc.date.issued2012-12en
dc.identifier.isbn9780769549057en
dc.identifier.issn15504786en
dc.identifier.doi10.1109/ICDM.2012.106en
dc.identifier.urihttp://hdl.handle.net/10754/564631en
dc.description.abstractNon-negative matrix factorization (NMF) provides the advantage of parts-based data representation through additive only combinations. It has been widely adopted in areas like item recommending, text mining, data clustering, speech denoising, etc. In this paper, we provide an algorithm that allows the factorization to have linear or approximatly linear constraints with respect to each factor. We prove that if the constraint function is linear, algorithms within our multiplicative framework will converge. This theory supports a large variety of equality and inequality constraints, and can facilitate application of NMF to a much larger domain. Taking the recommender system as an example, we demonstrate how a specialized weighted and constrained NMF algorithm can be developed to fit exactly for the problem, and the tests justify that our constraints improve the performance for both weighted and unweighted NMF algorithms under several different metrics. In particular, on the Movielens data with 94% of items, the Constrained NMF improves recall rate 3% compared to SVD50 and 45% compared to SVD150, which were reported as the best two in the top-N metric. © 2012 IEEE.en
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.subjectLinear constraintsen
dc.subjectMultiplicative algorithmen
dc.subjectNon-negative matrix factorizationen
dc.titleMultiplicative algorithms for constrained non-negative matrix factorizationen
dc.typeConference Paperen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentComputer Science Programen
dc.contributor.departmentApplied Mathematics and Computational Science Programen
dc.contributor.departmentExtreme Computing Research Centeren
dc.contributor.departmentMachine Intelligence & kNowledge Engineering Laben
dc.identifier.journal2012 IEEE 12th International Conference on Data Miningen
dc.conference.date10 December 2012 through 13 December 2012en
dc.conference.name12th IEEE International Conference on Data Mining, ICDM 2012en
dc.conference.locationBrusselsen
dc.contributor.institutionDepartment of Computer Science, University of Toronto, Toronto, Canadaen
dc.contributor.institutionDepartment of Computer Science, Aalborg University, Aalborg, Denmarken
kaust.authorPeng, Chengbinen
kaust.authorZhang, Xiangliangen
kaust.authorKeyes, David E.en
kaust.authorRockwood, Alyn P.en
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