Abstract
Multiplicative updates are widely used for nonnegative matrix factorization (NMF) as an efficient computational method. In this paper, we consider a class of constrained optimization problems in which a polynomial function of the product of two matrices is minimized subject to the nonnegativity constraints. These problems are closely related to NMF because the polynomial function covers many error function used for NMF. We first derive a multiplicative update rule for those problems by using the unified method developed by Yang and Oja. We next prove that a modified version of the update rule has the global convergence property in the sense of Zangwill under certain conditions. This result can be applied to many existing multiplicative update rules for NMF to guarantee their global convergence.
| Original language | English |
|---|---|
| Title of host publication | 2016 24th European Signal Processing Conference, EUSIPCO 2016 |
| Publisher | European Signal Processing Conference, EUSIPCO |
| Pages | 438-442 |
| Number of pages | 5 |
| Volume | 2016-November |
| ISBN (Electronic) | 9780992862657 |
| DOIs | |
| Publication status | Published - Nov 28 2016 |
| Event | 24th European Signal Processing Conference, EUSIPCO 2016 - Budapest, Hungary Duration: Aug 28 2016 → Sep 2 2016 |
Other
| Other | 24th European Signal Processing Conference, EUSIPCO 2016 |
|---|---|
| Country | Hungary |
| City | Budapest |
| Period | 8/28/16 → 9/2/16 |
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ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering
Cite this
Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence. / Takahashi, Norikazu; Seki, Masato.
2016 24th European Signal Processing Conference, EUSIPCO 2016. Vol. 2016-November European Signal Processing Conference, EUSIPCO, 2016. p. 438-442 7760286.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence
AU - Takahashi, Norikazu
AU - Seki, Masato
PY - 2016/11/28
Y1 - 2016/11/28
N2 - Multiplicative updates are widely used for nonnegative matrix factorization (NMF) as an efficient computational method. In this paper, we consider a class of constrained optimization problems in which a polynomial function of the product of two matrices is minimized subject to the nonnegativity constraints. These problems are closely related to NMF because the polynomial function covers many error function used for NMF. We first derive a multiplicative update rule for those problems by using the unified method developed by Yang and Oja. We next prove that a modified version of the update rule has the global convergence property in the sense of Zangwill under certain conditions. This result can be applied to many existing multiplicative update rules for NMF to guarantee their global convergence.
AB - Multiplicative updates are widely used for nonnegative matrix factorization (NMF) as an efficient computational method. In this paper, we consider a class of constrained optimization problems in which a polynomial function of the product of two matrices is minimized subject to the nonnegativity constraints. These problems are closely related to NMF because the polynomial function covers many error function used for NMF. We first derive a multiplicative update rule for those problems by using the unified method developed by Yang and Oja. We next prove that a modified version of the update rule has the global convergence property in the sense of Zangwill under certain conditions. This result can be applied to many existing multiplicative update rules for NMF to guarantee their global convergence.
UR - http://www.scopus.com/inward/record.url?scp=85005939708&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85005939708&partnerID=8YFLogxK
U2 - 10.1109/EUSIPCO.2016.7760286
DO - 10.1109/EUSIPCO.2016.7760286
M3 - Conference contribution
AN - SCOPUS:85005939708
VL - 2016-November
SP - 438
EP - 442
BT - 2016 24th European Signal Processing Conference, EUSIPCO 2016
PB - European Signal Processing Conference, EUSIPCO
ER -