Averaged recurrence quantification analysis
Radim Pánis, Karel Adámek, Norbert Marwan
Abstract
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 $$10^2, 10^3, 10^4,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>3</mml:mn> </mml:msup> <mml:mo>,</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>4</mml:mn> </mml:msup> <mml:mo>,</mml:mo> </mml:mrow> </mml:math> and $$10^5$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>5</mml:mn> </mml:msup> </mml:math> . To make the calculations possible, a new effective algorithm was developed for streamlining of the numerical operations on graphics processing unit (GPU).