@inproceedings{d3056a723d4b4c8484336fa45ef08938,
title = "Bregman divergences from comparative convexity",
abstract = "Comparative convexity is a generalization of ordinary convexity based on abstract means instead of arithmetic means. We define and study the Bregman divergences with respect to comparative convexity. As an example, we consider the convexity induced by quasi-arithmetic means, report explicit formulas, and show that those Bregman divergences are equivalent to conformal ordinary Bregman divergences on monotone embeddings.",
keywords = "Bregman divergence, Conformal divergence, Convexity, Quasi-arithmetic weighted mean, Regular mean, Skew Jensen divergence",
author = "Frank Nielsen and Richard Nock",
note = "Publisher Copyright: {\textcopyright} 2017, Springer International Publishing AG.; 3rd International Conference on Geometric Science of Information, GSI 2017 ; Conference date: 07-11-2017 Through 09-11-2017",
year = "2017",
doi = "10.1007/978-3-319-68445-1_74",
language = "English",
isbn = "9783319684444",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "639--647",
editor = "Frank Nielsen and Frederic Barbaresco and Frank Nielsen",
booktitle = "Geometric Science of Information - 3rd International Conference, GSI 2017, Proceedings",
address = "Germany",
}