Preprint Article Version 4 Preserved in Portico This version is not peer-reviewed

A Procustes's Procedure for Obtaining Divergences

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. Preprints 2020, 2020110388 (doi: 10.20944/preprints202011.0388.v4). Riveaud, L.; Diego, M.; Lamberti, P.W. A Procustes's Procedure for Obtaining Divergences. Preprints 2020, 2020110388 (doi: 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

Comments (1)

Comment 1
Received: 3 September 2021
Commenter: Mateos Diego
Commenter's Conflict of Interests: Author
Comment: We changed  the title.
+ Respond to this comment

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 1
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.