Efficient Computation of Recurrence Quantification Analysis Via Microstates

• This work uses the notion of microstates to statistically generalize RQA. • We reduce the time complexity to grow linearly with the series size. • We eliminate the excessive RAM usage in most recurrence analysis. Recurrence plot (RP) is a powerful tool in the study of nonlinear dynamics, being successfully applied in economics, medicine, geophysics, and astronomy. The Recurrence Quantification Analysis (RQA) consists of a methodology to compute RP quantifiers based on statistics over vertical/diagonal recurrent lines, densities, and other features of the RP. The traditional way to calculate the quantifiers computes each recurrent point individually and builds the histogram of the whole RP. Here we propose a new, statistical approach to calculate the quantifiers using the (recurrence) microstates, which are small representative chunks of the RP. The new way of statistically calculating the quantifiers converges fast and brings a computational gain. In particular, it reduces the time complexity from O ( K 2 ) to O ( K ), for K the size of the time-series. Moreover, we show that our results are independent of the system and series size.