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.
Original language | English |
---|---|
Title of host publication | IEEE International Conference on Data Mining, ICDM |
Number of pages | 6 |
Publisher | IEEE |
Publication date | 2012 |
Pages | 1068-1073 |
ISBN (Print) | 978-1-4673-4649-8 |
DOIs | |
Publication status | Published - 2012 |
Event | IEEE 12th International Conference on Data Mining - Brussels, Belgium Duration: 10 Dec 2012 → 13 Dec 2012 Conference number: 12 |
Conference
Conference | IEEE 12th International Conference on Data Mining |
---|---|
Number | 12 |
Country/Territory | Belgium |
City | Brussels |
Period | 10/12/2012 → 13/12/2012 |
Series | ICDM |
---|---|
ISSN | 1550-4786 |