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)
How to cite:
Riveaud, L.; Diego, M.; Lamberti, P. W. A Procustes's Procedure for Obtaining Divergences. Preprints2020, 2020110388. https://doi.org/10.20944/preprints202011.0388.v4
Riveaud, L.; Diego, M.; Lamberti, P. W. A Procustes's Procedure for Obtaining Divergences. Preprints 2020, 2020110388. https://doi.org/10.20944/preprints202011.0388.v4
Riveaud, L.; Diego, M.; Lamberti, P. W. A Procustes's Procedure for Obtaining Divergences. Preprints2020, 2020110388. https://doi.org/10.20944/preprints202011.0388.v4
APA Style
Riveaud, L., Diego, M., & Lamberti, P. W. (2021). A Procustes's Procedure for Obtaining Divergences. Preprints. https://doi.org/10.20944/preprints202011.0388.v4
Chicago/Turabian Style
Riveaud, L., Mateos Diego and Pedro Walter Lamberti. 2021 "A Procustes's Procedure for Obtaining Divergences" Preprints. https://doi.org/10.20944/preprints202011.0388.v4
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 we call gamma-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. We investigate their properties in the context of kernel theory. Finally, we apply our findings to the analysis of simulated and real time series.
Keywords
Divergences; Kernels; Time series analysis
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.
Commenter: Mateos Diego
Commenter's Conflict of Interests: Author