Article
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Preserved in Portico This version is not peer-reviewed
Gamma-Divergence. An Introduction to New Divergence Family
Version 1
: Received: 11 November 2020 / Approved: 13 November 2020 / Online: 13 November 2020 (15:45:32 CET)
Version 2 : Received: 27 May 2021 / Approved: 28 May 2021 / Online: 28 May 2021 (11:53:11 CEST)
Version 3 : Received: 28 June 2021 / Approved: 29 June 2021 / Online: 29 June 2021 (11:37:12 CEST)
Version 4 : Received: 2 September 2021 / Approved: 3 September 2021 / Online: 3 September 2021 (10:26:53 CEST)
Version 2 : Received: 27 May 2021 / Approved: 28 May 2021 / Online: 28 May 2021 (11:53:11 CEST)
Version 3 : Received: 28 June 2021 / Approved: 29 June 2021 / Online: 29 June 2021 (11:37:12 CEST)
Version 4 : Received: 2 September 2021 / Approved: 3 September 2021 / Online: 3 September 2021 (10:26:53 CEST)
How to cite: Riveaud, L.; Diego, M.; Lamberti, P. W. Gamma-Divergence. An Introduction to New Divergence Family. Preprints 2020, 2020110388. https://doi.org/10.20944/preprints202011.0388.v1 Riveaud, L.; Diego, M.; Lamberti, P. W. Gamma-Divergence. An Introduction to New Divergence Family. Preprints 2020, 2020110388. https://doi.org/10.20944/preprints202011.0388.v1
Abstract
Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application, a more appropriate measure may be necessary. In this paper we introduce a family of divergences called γ-Divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. In addition, we define a generalised entropy closely related to the γ-Divergences. Finally, we apply our findings to the analysis of simulated and real time series.
Keywords
Information Theory; Entropy; Divergence; Divergence families
Subject
Physical Sciences, Acoustics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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