Some smooth divergences for $\ell_{1}-$approximations

TL;DR

This paper introduces smooth special cases of generalized and new scaled shift divergences, providing approximations for the weighted -distance and -norm, which are fundamental in many applications.

Contribution

It develops novel smooth divergences, called scaled shift divergences, and derives their approximations for the weighted -distance and norm.

Findings

Derived approximations for weighted -distance and norm.

Introduced new scaled shift divergences.

Extended the class of -based divergence measures.

Abstract

For some smooth special case of generalized $\varphi-$divergences as well as of new divergences (called scaled shift divergences), we derive approximations of the omnipresent (weighted) $\ell_{1}-$distance and (weighted) $\ell_{1}-$norm.