Name
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 approximately 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 Movie lens 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. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1109/ICDM.2012.106 | ICDM |
Keywords | Field | DocType |
linear constraints,inequality constraint,equality constraint,constraint function,nmf,approximation theory,multiplicative algorithm,data structures,multiplicative algorithms,movie lens data,linear constraint,nmf algorithm,constrained nonnegative matrix factorization,unweighted nmf algorithm,speech denoising,item recommendation,non-negative matrix factorization,different metrics,parts-based data representation,constrained nmf,data clustering,recall rate,constrained non-negative matrix factorization,singular value decomposition,text mining,non negative matrix factorization | Singular value decomposition,Data structure,Multiplicative function,Computer science,Matrix decomposition,Algorithm,Factorization,Constrained clustering,Non-negative matrix factorization,Cluster analysis | Conference |
ISSN | ISBN | Citations |
1550-4786 | 978-1-4673-4649-8 | 4 |
PageRank | References | Authors |
0.44 | 10 | 6 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Chengbin Peng | 1 | 63 | 4.01 |
| Ka-Chun Wong | 2 | 291 | 40.18 |
| Alyn Rockwood | 3 | 950 | 179.19 |
| Xiangliang Zhang | 4 | 728 | 87.74 |
| Jinling Jiang | 5 | 24 | 2.06 |
| David E. Keyes | 6 | 407 | 81.69 |