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Generalizing Skew Jensen Divergences and Bregman Divergences With Comparative Convexity

Nock, Richard; Nielsen, Frank

Description

Comparative convexity is a generalization of ordinary convexity based on abstract means instead of arithmetic means. We introduce the generalized skew Jensen divergences and their corresponding Bregman divergences with respect to comparative convexity. To illustrate those novel families of divergences, we consider the convexity induced by quasi-arithmetic means, and report explicit formula for the corresponding Bregman divergences. In particular, we show that those new Bregman divergences are...[Show more]

CollectionsANU Research Publications
Date published: 2017
Type: Journal article
URI: http://hdl.handle.net/1885/218066
Source: IEEE Signal Processing Letters
DOI: 10.1109/LSP.2017.2712195

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