TY - GEN
T1 - Bregman Proximal Gradient Algorithms for Deep Matrix Factorization
AU - Mukkamala, Mahesh Chandra
AU - Westerkamp, Felix
AU - Laude, Emanuel
AU - Cremers, Daniel
AU - Ochs, Peter
N1 - Publisher Copyright:
© 2021, Springer Nature Switzerland AG.
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85106427710&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-75549-2_17
DO - 10.1007/978-3-030-75549-2_17
M3 - Conference contribution
AN - SCOPUS:85106427710
SN - 9783030755485
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 204
EP - 215
BT - Scale Space and Variational Methods in Computer Vision - 8th International Conference, SSVM 2021, Proceedings
A2 - Elmoataz, Abderrahim
A2 - Fadili, Jalal
A2 - Quéau, Yvain
A2 - Rabin, Julien
A2 - Simon, Loïc
PB - Springer Science and Business Media Deutschland GmbH
T2 - 8th International Conference on Scale Space and Variational Methods in Computer Vision, SSVM 2021
Y2 - 16 May 2021 through 20 May 2021
ER -