A Recurrence Plot-Based Distance Measure

Approximate Recurrence Quantification Analysis (aRQA) in Code of Best Practice

“…6.3, all stationary states SS (2) that are stable for 2 time points are illustrated by single circles. Moreover, double circles indicate stationary states SS (3) that are stable for 3 successive observations. The terms SS (2) and SS (3) can be computed by means of (6.14) and expressed in terms of the respective stationary state histograms ℏ( (1) ), ℏ( (2) ) and ℏ( (3) ):…”

“…By multiplying the length = 2 and number PP (2) of the identified structures we quantify all recurrence points that rest on diagonal lines, including those of overlapping structures. To subtract recurrence points of overlapping struc- (2) for embedding dimension = 2, and double circles show recurrences that are quantified by PP (3) for = 3 respectively tures we compute the pairwise proximities PP (3) of higher embedding dimension = 2 + 1, which are illustrated by double circles. Consequently, the determinism DET (2) for our sample time series is computed in the following way:…”

“…6.3 indicate all recurrence points that form vertical structures of minimum length = 2, which can be quantified in terms of SS (2) and SS (3) . For our sample trajectory in Fig.…”

“…Figure 6.3 illustrates how to compute the laminarity LAM (2) for our sample trajectory . As defined in (6.16), the laminarity LAM (2) for minimum vertical (or rather horizontal) line length = 2 can be computed in terms of SS (1) , SS (2) , and SS (3) . For example in Fig.…”

“…In recent years, recurrence quantification analysis (RQA) has gained popularity in the time series community [1][2][3], where recurrence plot-based tools have been developed (i) to measure the pairwise (dis)similarity between temporal measurements based on co-occurring patterns [3,4], (ii) for classification purposes in different scientific disciplines [5][6][7][8][9], (iii) to detect regime transitions [10][11][12], or even (iv) to study interrelationships and synchronization between different dynamical systems [13][14][15].…”