Reliable line-based quantification for probabilistic recurrence plots

Develop reliable definitions and computational procedures for diagonal-line-based recurrence quantification measures (such as determinism and average diagonal line length) for probabilistic recurrence plots in which each entry Qi,j(ε) represents the recurrence probability p(|xi − xj| < ε) arising from time series with uncertainties, and demonstrate that these measures provide robust and interpretable results comparable to the binary case.

Background

For time series with measurement or age uncertainties, the authors introduce a Bayesian approach yielding probabilistic recurrence matrices Qi,j(ε) = p(|xi − xj| < ε) instead of the conventional binary recurrence matrices. This representation is designed to explicitly encode uncertainty in the recurrence structure.

While such probabilistic recurrence plots support complex-network-based analysis, the standard line-based quantifiers used in recurrence quantification analysis (e.g., diagonal line statistics) are not straightforward to define in this non-binary setting. Although initial suggestions exist, the authors emphasize that a reliable, well-founded methodology for line-based measures remains unresolved.