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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.25 No.3
- 발행연도
- 2021.9
- 수록면
- 107 - 116 (10page)
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초록· 키워드
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We introduce optimization algorithms using Bregman Divergence for solving non-negative matrix factorization (NMF) problems. Bregman divergence is known a generalization of some divergences such as Frobenius norm and KL divergence and etc. Some algorithms can be applicable to not only NMF with Frobenius norm but also NMF with more general Bregman divergence. Matrix Factorization is a popular non-convex optimization problem, for which alternating minimization schemes are mostly used. We develop the Bregman proximal gradient method applicable for all NMF formulated in any Bregman divergences. In the derivation of NMF algorithm for Bregman divergence, we need to use majorization/minimization(MM) for a proper auxiliary function. We present algorithmic aspects of NMF for Bregman divergence by using MM of auxiliary function.
목차
ABSTRACT
1. INTRODUCTION
2. RELATED WORKS AND PROBLEM DEFINITION
3. OPTIMIZATION ALGORITHM IN THE FRAMEWORK OF BREGMAN DIVERGENCE
4. NMF METHODS USING BREGMAN DIVERGENCE
5. CONCLUSION
REFERENCES
참고문헌 (22)
참고문헌 신청
Masoud Ahookhosh / Multi-block Bregman proximal alternating linearized minimization and its application to orthogonal nonnegative matrix factorization
Heinz H. Bauschke / 2007 / A descent Lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications / INFORMS 79:21
Jerome Bolte / 2018 / First order methods beyond convexity and lipschitz gradient continuity with applications to quadratic inverse problems / SIAM Journal on Optimization 28(3):2131~2151
Andrzej Cichocki / 2010 / Families of alpha- beta- and gamma- divergences: Flexible and robust measures of Similarities / Entropy 12(6):1532~1568
Andrzej Cichocki / 2008 / Non-negative matrix factorization with α-divergence / Pattern Recognition Letters 29:1433~1440
Heinz H. Bauschke / 2007 / A descent Lemma beyond Lipschitz gradient continuity: first-order methods revisited and applications / INFORMS 79:21
Jerome Bolte / 2018 / First order methods beyond convexity and lipschitz gradient continuity with applications to quadratic inverse problems / SIAM Journal on Optimization 28(3):2131~2151
Andrzej Cichocki / 2010 / Families of alpha- beta- and gamma- divergences: Flexible and robust measures of Similarities / Entropy 12(6):1532~1568
Andrzej Cichocki / 2008 / Non-negative matrix factorization with α-divergence / Pattern Recognition Letters 29:1433~1440
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