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

• URL: http://arxiv.org/abs/2204.04582v1
• Date: Sun, 10 Apr 2022 02:44:04 GMT
• Title: Real order total variation with applications to the loss functions in learning schemes
• Authors: Pan Liu, Xin Yang Lu, Kunlun He
• Abstract summary: We propose a loss function consisting of a $r$-order (an)-isotropic total variation semi-norms $TVr$, $rin mathbbR+$. 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.
• Score: 5.8868325478050165
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Loss function are an essential part in modern data-driven approach, 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 $TV^r$, $r\in \mathbb{R}^+$, defined via the Riemann-Liouville (R-L) 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.

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