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

AutorStephan Spiegel, David Schultz, Norbert Marwan
QuelleRecurrence Plots and Their Quantifications: Expanding Horizons: Proceedings of the 6th International Symposium on Recurrence Plots, Grenoble, France, 17-19 June 2015 
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Recurrence quantification analysis (RQA) is a well-known tool for studying nonlinear behavior of dynamical systems, e.g. for finding transitions in climate data or classifying reading abilities. But the construction of a recurrence plot and the subsequent quantification of its small and large scale structures is computational demanding, especially for long time series or data streams with high sample rate. One way to reduce the time and space complexity of RQA are approximations, which are sufficient for many data analysis tasks, although they do not guarantee exact solutions. In earlier work, we proposed how to approximate diagonal line based RQA measures and showed how these approximations perform in finding transitions for difference equations. The present work aims at extending these approximations to vertical line based RQA measures and investigating the runtime/accuracy of our approximate RQA measures on real-life climate data. Our empirical evaluation shows that the proposed approximate RQA measures achieve tremendous speedups without losing much of the accuracy.