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

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.