Abstract
We propose a novel iterative algorithm for nonnegative matrix factorization with the alpha-divergence. The proposed algorithm is based on the coordinate descent and the Newton method. We show that the proposed algorithm has the global convergence property in the sense that the sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. We also show through numerical experiments that the proposed algorithm is much faster than the multiplicative update rule.
| Original language | English |
|---|---|
| Title of host publication | Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings |
| Publisher | Springer Verlag |
| Pages | 335-344 |
| Number of pages | 10 |
| Volume | 10634 LNCS |
| ISBN (Print) | 9783319700861 |
| DOIs | |
| Publication status | Published - Jan 1 2017 |
| Event | 24th International Conference on Neural Information Processing, ICONIP 2017 - Guangzhou, China Duration: Nov 14 2017 → Nov 18 2017 |
Publication series
| Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
|---|---|
| Volume | 10634 LNCS |
| ISSN (Print) | 0302-9743 |
| ISSN (Electronic) | 1611-3349 |
Other
| Other | 24th International Conference on Neural Information Processing, ICONIP 2017 |
|---|---|
| Country | China |
| City | Guangzhou |
| Period | 11/14/17 → 11/18/17 |
Fingerprint
Keywords
- Alpha-divergence
- Global convergence
- Newton method
- Nonnegative matrix factorization
ASJC Scopus subject areas
- Theoretical Computer Science
- Computer Science(all)
Cite this
A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence. / Nakatsu, Satoshi; Takahashi, Norikazu.
Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings. Vol. 10634 LNCS Springer Verlag, 2017. p. 335-344 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10634 LNCS).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - A novel newton-type algorithm for nonnegative matrix factorization with alpha-divergence
AU - Nakatsu, Satoshi
AU - Takahashi, Norikazu
PY - 2017/1/1
Y1 - 2017/1/1
N2 - We propose a novel iterative algorithm for nonnegative matrix factorization with the alpha-divergence. The proposed algorithm is based on the coordinate descent and the Newton method. We show that the proposed algorithm has the global convergence property in the sense that the sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. We also show through numerical experiments that the proposed algorithm is much faster than the multiplicative update rule.
AB - We propose a novel iterative algorithm for nonnegative matrix factorization with the alpha-divergence. The proposed algorithm is based on the coordinate descent and the Newton method. We show that the proposed algorithm has the global convergence property in the sense that the sequence of solutions has at least one convergent subsequence and the limit of any convergent subsequence is a stationary point of the corresponding optimization problem. We also show through numerical experiments that the proposed algorithm is much faster than the multiplicative update rule.
KW - Alpha-divergence
KW - Global convergence
KW - Newton method
KW - Nonnegative matrix factorization
UR - http://www.scopus.com/inward/record.url?scp=85035081672&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85035081672&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-70087-8_36
DO - 10.1007/978-3-319-70087-8_36
M3 - Conference contribution
SN - 9783319700861
VL - 10634 LNCS
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 335
EP - 344
BT - Neural Information Processing - 24th International Conference, ICONIP 2017, Proceedings
PB - Springer Verlag
ER -