Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time series analysis

TL;DR

The paper introduces the permutation Jensen-Shannon distance, a symbolic, computationally efficient measure for quantifying similarity between complex time series, demonstrating its robustness and versatility across various applications.

Contribution

It presents a novel ordinal symbolic distance based on Jensen-Shannon divergence, combining simplicity, speed, and robustness for complex time series analysis.

Findings

Effective in characterizing different dynamics

Robust against outliers and artifacts

Suitable for large-scale data analysis

Abstract

The main motivation of this paper is to introduce the permutation Jensen-Shannon distance, a symbolic tool able to quantify the degree of similarity between two arbitrary time series. This quantifier results from the fusion of two concepts, the Jensen-Shannon divergence and the encoding scheme based on the sequential ordering of the elements in the data series. The versatility and robustness of this ordinal symbolic distance for characterizing and discriminating different dynamics are illustrated through several numerical and experimental applications. Results obtained allow us to be optimistic about its usefulness in the field of complex time series analysis. Moreover, thanks to its simplicity, low computational cost, wide applicability and less susceptibility to outliers and artifacts, this ordinal measure can efficiently handle large amounts of data and help to tackle the current big data challenges.