Name
Abstract | ||
|---|---|---|
Non-negative matrix factorization (NMF) provides a lower rank approximation of a matrix. Due to nonnegativity imposed on the factors, it gives a latent structure that is often more physically meaningful than other lower rank approximations such as singular value decomposition (SVD). Most of the algorithms proposed in literature for NMF have been based on minimizing the Frobenius norm. This is partly due to the fact that the minimization problem based on the Frobenius norm provides much more flexibility in algebraic manipulation than other divergences. In this paper we propose a fast NMF algorithm that is applicable to general Bregman divergences. Through Taylor series expansion of the Bregman divergences, we reveal a relationship between Bregman divergences and Euclidean distance. This key relationship provides a new direction for NMF algorithms with general Bregman divergences when combined with the scalar block coordinate descent method. The proposed algorithm generalizes several recently proposed methods for computation of NMF with Bregman divergences and is computationally faster than existing alternatives. We demonstrate the effectiveness of our approach with experiments conducted on artificial as well as real world data. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1145/2339530.2339582 | KDD |
Keywords | Field | DocType |
bregman divergence,lower rank,key relationship,nmf algorithm,fast nmf algorithm,frobenius norm,bregman divergence nmf,lower rank approximation,general bregman divergence,proposed algorithm,taylor expansion,non-negative matrix factorization,non negative matrix factorization,euclidean distance,taylor series expansion,singular value decomposition | Singular value decomposition,Data mining,Applied mathematics,Mathematical optimization,Euclidean distance,Matrix decomposition,Matrix norm,Non-negative matrix factorization,Bregman divergence,Coordinate descent,Mathematics,Taylor series | Conference |
Citations | PageRank | References |
13 | 0.65 | 17 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Liangda Li | 1 | 148 | 7.22 |
| Guy Lebanon | 2 | 936 | 80.79 |
| Haesun Park | 3 | 3546 | 232.42 |