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Simplicial complex entropy for time series analysis
Lev Guzmán-Vargas1, Alvaro Zabaleta-Ortega2, Aldo Guzmán-Sáenz3
1Unidad Profesional Interdisciplinaria en Ingeniería y Tecnologías Avanzadas, Instituto Politécnico Nacional, 07340, Mexico City, Mexico. lguzmanv@ipn.mx.
Scientific Reports
|December 20, 2023
Summary
This study introduces a new entropy measure, simplicial complex approximate entropy, to better characterize complex system dynamics. The method effectively quantifies irregularity in random and chaotic time series and differentiates physiological signals.
Area of Science:
- Complexity Science
- Time Series Analysis
- Nonlinear Dynamics
Background:
- Complex systems in nature exhibit dynamic behaviors requiring robust analysis methods.
- Existing time series irregularity measures struggle with stochastic and chaotic dynamics.
- Novel approaches are needed for detailed characterization of complex system dynamics.
Purpose of the Study:
- To introduce a new entropy measure, simplicial complex approximate entropy (SCAE).
- To evaluate SCAE's capability in characterizing irregularity in various complex dynamics.
- To demonstrate SCAE's potential in differentiating physiological states and chaotic systems.
Main Methods:
- Developed simplicial complex approximate entropy based on conditional probability of simplicial complex elements.
- Applied SCAE to simulated random sequences and low-dimensional chaotic dynamics.
- Utilized SCAE to analyze cardiac interbeat sequences and coupled chaotic maps.
Main Results:
- SCAE provides a wide range of values, revealing details missed by standard methods.
- The method successfully quantifies irregularity in random and chaotic time series.
- SCAE consistently differentiates cardiac signals from healthy and heart failure patients and identifies changes in coupled chaotic maps.
Conclusions:
- Simplicial complex approximate entropy offers enhanced characterization of complex system dynamics.
- The revealed structures by simplicial complexes are crucial for detailed analysis.
- This approach shows promise for diverse applications in analyzing complex systems.
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