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Permutation entropy with vector embedding delays
Douglas J Little1, Deb M Kane1
1MQ Photonics Research Centre, Department of Physics and Astronomy, Macquarie University, North Ryde, NSW 2109, Australia.
Physical Review. E
|January 20, 2018
Summary
This study introduces vector embedding delays for permutation entropy (PE) analysis, enhancing time series structure detection. This novel method reveals hidden correlations in complex data, outperforming traditional scalar approaches.
Area of Science:
- Nonlinear dynamics
- Time series analysis
- Information theory
Background:
- Permutation entropy (PE) is a key statistic for time series structure detection.
- Reduced PE values indicate characteristic timescales of underlying structures.
- Traditional PE uses scalar embedding delays, potentially limiting structure identification.
Purpose of the Study:
- To investigate a generalized PE scheme using vector embedding delays.
- To explore the capability of vector delays in identifying complex time series structures.
- To compare the effectiveness of vector versus scalar delays in PE analysis.
Main Methods:
- Developed a generalized permutation entropy calculation using vector embedding delays.
- Applied the method to diverse data: numerical (noise, sine wave, logistic map) and experimental (laser data).
- Visualized results using PE maps to identify low PE regions indicating structure.
Main Results:
- Vector embedding delays enable the calculation of PE in a (D-1)-dimensional space.
- Successfully identified temporal structures in laser cavity data, previously ambiguous with scalar delays.
- PE maps effectively highlight combinations of delays revealing correlation structures.
Conclusions:
- Vector embedding delays offer a more sensitive approach to time series analysis.
- This generalized PE method can uncover masked or ambiguous structures.
- The technique has broad applicability in nonlinear science and experimental data analysis.
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