ExSEnt: Extrema-Segmented Entropy Analysis of Time Series

Abstract: We introduce Extrema-Segmented Entropy (ExSEnt), a feature-decomposed framework for quantifying time-series complexity that separates temporal from amplitude contributions. The method partitions a signal into monotonic segments by detecting sign changes in the first-order increments. For each segment, it extracts the interval duration and the net amplitude change, generating two sequences that reflect timing and magnitude variability, respectively. Complexity is then quantified by computing sample entropy on durations and amplitudes, together with their joint entropy. This decomposition reveals whether overall irregularity is driven by timing, amplitude, or their coupling, providing a richer and more interpretable characterization than unidimensional metrics. We validate ExSEnt on canonical nonlinear dynamical systems (Logistic map, Rossler system, Rulkov map), demonstrating its ability to track complexity changes across control parameter sweeps and detect transitions between periodic and chaotic regimes. Then, we illustrate the empirical utility of ExSEnt metrics to isolate feature-specific sources of complexity in real data (electromyography and ankle acceleration in Parkinsons disease). ExSEnt thus complements existing entropy measures by attributing complexity to distinct signal features, improving interpretability and supporting applications in a broad range of domains, including physiology, finance, and geoscience.