Averaged Recurrence Quantification Analysis -- Method omitting the recurrence threshold choice

TL;DR

This paper introduces an almost parameter-free recurrence quantification analysis method that eliminates the threshold choice by averaging over a range of recurrence rates, tested on various chaotic and periodic signals.

Contribution

The authors propose a novel RQA approach that removes the need for threshold selection by averaging measures across multiple thresholds, utilizing GPU acceleration for efficiency.

Findings

Effective in sorting signals by signal-to-noise ratio

Works on diverse data including periodic, chaotic, and Lorenz systems

Handles very small SNRs with high accuracy

Abstract

Recurrence quantification analysis (RQA) is a well established method of nonlinear data analysis. In this work we present a new strategy for an almost parameter-free RQA. The approach finally omits the choice of the threshold parameter by calculating the RQA measures for a range of thresholds (in fact recurrence rates). Specifically, we test the ability of the RQA measure determinism, to sort data with respect to their signal to noise ratios. We consider a periodic signal, simple chaotic logistic equation, and Lorenz system in the tested data set with different and even very small signal to noise ratios of lengths $10^2, 10^3, 10^4,$ and $10^5$. To make the calculations possible a new effective algorithm was developed for streamlining of the numerical operations on Graphics Processing Unit (GPU).