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

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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