Bregman Proximal Gradient Algorithms for Deep Matrix Factorization
Mukkamala MC, Westerkamp F, Laude E, Cremers D, Ochs P (2021)
Publication Type: Conference contribution
Publication year: 2021
Journal
Publisher: Springer Science and Business Media Deutschland GmbH
Book Volume: 12679 LNCS
Pages Range: 204-215
Conference Proceedings Title: Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Event location: Virtual, Online
ISBN: 9783030755485
DOI: 10.1007/978-3-030-75549-2_17
Abstract
A typical assumption for the convergence of first order optimization methods is the Lipschitz continuity of the gradient of the objective function. However, for many practical applications this assumption is violated. To overcome this issue extensions based on generalized proximity measures, known as Bregman distances, were introduced. This initiated the development of the Bregman Proximal Gradient (BPG) algorithms, which, however, rely on problem dependent Bregman distances. In this paper, we develop Bregman distances for deep matrix factorization problems, which yields a BPG algorithm with theoretical convergence guarantees, while allowing for a constant step size strategy. Moreover, we demonstrate that the algorithms based on the developed Bregman distance outperform their Euclidean counterparts as well as alternating minimization based approaches.
Involved external institutions
Germany (DE)How to cite
APA:
Mukkamala, M.C., Westerkamp, F., Laude, E., Cremers, D., & Ochs, P. (2021). Bregman Proximal Gradient Algorithms for Deep Matrix Factorization. In Abderrahim Elmoataz, Jalal Fadili, Yvain Quéau, Julien Rabin, Loïc Simon (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 204-215). Virtual, Online: Springer Science and Business Media Deutschland GmbH.
MLA:
Mukkamala, Mahesh Chandra, et al. "Bregman Proximal Gradient Algorithms for Deep Matrix Factorization." Proceedings of the 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021, Virtual, Online Ed. Abderrahim Elmoataz, Jalal Fadili, Yvain Quéau, Julien Rabin, Loïc Simon, Springer Science and Business Media Deutschland GmbH, 2021. 204-215.
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