Recurrence Quantification Analysis (RQA)

Contents

The structures in recurrence plots can be computed by measures of complexity. Several measures base on the distributions of the lengths of diagonal or vertical lines. These measures can be used to find, for instance, hidden transitions of a process.

The measures can be computed by the CRP toolbox. Now we consider an EEG measurement of an optical stimulus.

x = load('eeg.dat');

The file consists of measurements on 59 electrodes. The sampling time was 4 ms and the measurement started at 400 ms before and ended 900 ms after the stimulus.

t = -400:4:900;

We are interested in the RQA measures within overlapping sliding windows of 240 ms.

Y = crqa(x(:,1), 3, 4, 1, 60, 5);
plot(t(1:5:length(Y)), Y(1:5:end, 1)), ylabel('RR')
(plugin used)

The recurrence rate reveals a change in the brain dynamics 200 ms after the stimulus by a rapid drop. The other measures exhibit a transition at this time as well.

Recommended reading:

http://www.recurrence-plot.tk

N. Marwan, M. C. Romano, M. Thiel, J. Kurths: Recurrence Plots for the Analysis of Complex Systems, Physics Reports, in press.

Exercise

1. Recurrence quantification analysis

Compare and comment the RQA measures of Gaussian white noise, a sine and the Lorenz system.

2. Detect transitions by means of recurrence quantification

2.1. Calculate series from the logistic map x(i+1) = a x(i) ( 1 - x(i) ) for a from interval [3.5 4]. 2.2. Compute the RQA measures RR, DET, 1/Lmean and LAM for these series as function of the control parameter a and interpret the result.