Rao-Burbea centroids applied to the statistical characterisation of time series and images through ordinal patterns

TL;DR

This paper introduces a method combining Burbea-Rao centroids with ordinal pattern mapping to analyze time series and images, demonstrating the effectiveness of Jensen-Shannon divergence in various applications.

Contribution

It proposes a novel approach integrating divergence measures and symbolic mapping for statistical characterization of complex data.

Findings

Jensen-Shannon divergence performs best among studied divergences.

The method effectively analyzes simulated and real time series.

The approach provides insights into textured image analysis.

Abstract

Divergences or similarity measures between probability distributions have become a very useful tool for studying different aspects of statistical objects such as time series, networks and images. Notably not every divergence provides identical results when applied to the same problem. Therefore it is convenient to have the widest possible set of divergences to be applied to the problems under study. Besides this choice an essential step in the analysis of every statistical object is the mapping of each one of their representing values into an alphabet of symbols conveniently chosen. In this work we attack both problems, that is, the choice of a family of divergences and the way to do the map into a symbolic sequence. For advancing in the first task we work with the family of divergences known as the Burbea-Rao centroids (BRC) and for the second one we proceed by mapping the original object into a symbolic sequence through the use of ordinal patterns. Finally we apply our proposals to analyse simulated and real time series and to real textured images. The main conclusion of our work is that the best BRC, at least in the studied cases, is the Jensen Shannon divergence, besides the fact that it verifies some interesting formal properties.