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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.
Keywords Divergence Kullback-Leibler, Divergence analysis, $\ell1-$distance/norm, Generalized $\varphi-$divergences