Multiplicative algorithms for constrained non-negative matrix factorization

Chengbin Peng, Kachun Wong, Alyn Rockwood, Xiangliang Zhang, Jinling Jiang, David E. Keyes

Research output: Chapter in Book/Report/Conference proceedingConference contribution

6 Scopus citations

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.
Original languageEnglish (US)
Title of host publication2012 IEEE 12th International Conference on Data Mining
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages1068-1073
Number of pages6
ISBN (Print)9780769549057
DOIs
StatePublished - Dec 2012

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