JOURNAL ARTICLE

Real order total variation with applications to the loss functions in learning schemes.

  • Published In: Communications in Contemporary Mathematics, 2024, v. 26, n. 7. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Liu, Pan; Lu, Xin Yang; He, Kunlun 3 of 3

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. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Communications in Contemporary Mathematics. 2024/09, Vol. 26, Issue 7, p1
  • Document Type:Article
  • Subject Area:Mathematics
  • Publication Date:2024
  • ISSN:0219-1997
  • DOI:10.1142/S0219199723500165
  • Accession Number:177778538
  • Copyright Statement:Copyright of Communications in Contemporary Mathematics is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.