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- Title
Real order total variation with applications to the loss functions in learning schemes.
- Authors
Liu, Pan; Lu, Xin Yang; He, Kunlun
- Abstract
Loss functions are an essential part in modern data-driven approaches, such as bi-level training scheme and machine learnings. In this paper, we propose a loss function consisting of a r -order (an)-isotropic total variation semi-norms TV r , r ∈ ℝ + , defined via the Riemann–Liouville (RL) fractional derivative. We focus on studying key theoretical properties, such as the lower semi-continuity and compactness with respect to both the function and the order of derivative r , of such loss functions.
- Subjects
DERIVATIVES (Mathematics); CALCULUS of variations
- Publication
Communications in Contemporary Mathematics, 2024, Vol 26, Issue 7, p1
- ISSN
0219-1997
- Publication type
Article
- DOI
10.1142/S0219199723500165