Composite multi-span amplitude-aware ordinal transition network: Fine-grained representation and quantification of complex system time series

Ordinal transition networks (OTNs) provide a network-based representation for analyzing the temporal dynamics of complex systems. However, traditional OTNs primarily focus on the frequency of ordinal pattern transitions, often neglecting critical amplitude variations within these patterns. Furthermore, single-span transition modeling constrains the ability to capture multi-scale dynamic characteristics in time series analysis. To address these limitations, we propose a composite multi-span amplitude-aware ordinal transition network (CMAOTN), which enhances the traditional OTN by integrating multi-span transitions and employing the Earth Mover’s Distance (EMD) to quantify amplitude differences. This approach improves sensitivity to amplitude variations and provides a more comprehensive representation of complex system dynamics. Based on CMAOTN, we further propose a new complexity metric, composite multi-span amplitude-aware ordinal transition entropy (CMAOTE), to quantify the complexity of nonlinear time series. Experiments on synthetic data demonstrate that CMAOTE effectively differentiates complexity levels and remains robust even in noisy, low-sample environments. The effectiveness of CMAOTE was further validated on real-world datasets, including highly non-stationary ECG signals and structured mechanical vibration data, showcasing its adaptability across diverse practical applications.