Increment Entropy as a Measure of Complexity for Time Series
Abstract
:1. Introduction
2. Increment Entropy
Vectors | ||||||
---|---|---|---|---|---|---|
3 | 3 | 2 | 0 | 0 | 4 | |
3 | 2 | 0 | 4 | |||
2 | 4 | 1 | 1 | |||
4 | 1 | 2 | 1 | 4 | ||
4 | 20 | 1 | 4 | 1 | 4 | |
4 | 20 | 10 | 1 | 3 | 2 | |
20 | 10 | 11 | 4 | 1 | 0 | |
10 | 11 | 8 | 1 | 1 | 4 |
3. Simulation and Results
3.1. Results on Logistic Time Series
3.2. Relationship to Other Approaches
3.2.1. Distinguishing Analogous Patterns
3.2.2. Detecting Energetic Change and Structural Change
Entropy | Regular | Energetic Mutation | Structural Mutation | |
---|---|---|---|---|
IncrEn | 1.3235 ± 0.1380 | 1.3264 ± 0.1372 | 1.3529 ± 0.1378 | |
0.6849 ± 0.0379 | 0.6937 ± 0.0387 | 0.7044 ± 0.0388 | ||
0.4600 ± 0.0000 | 0.4698 ± 0.0014 | 0.4788 ± 0.0033 | ||
PE | 0.6367 ± 0.0643 | 0.6367 ± 0.0643 | 0.6386 ± 0.0621 | |
0.6271 ± 0.0825 | 0.6275 ± 0.0828 | 0.6397 ± 0.0791 | ||
0.4600 ± 0.0000 | 0.4611 ± 0.0031 | 0.4788 ± 0.0033 | ||
SampEn | 0.0082 ± 0.0577 | 0.0083 ± 0.0577 | 0.0082 ± 0.0577 | |
0.0000 ± 0.0000 | 0.0000 ± 0.0000 | 0.0000 ± 0.0000 | ||
0.0000 ± 0.0000 | 0.0000 ± 0.0000 | 0.0000 ± 0.0000 |
3.2.3. Invariance of IncrEn
3.3. Application to Seizure Detection from EEG Signals
3.4. Application to Bearing Fault Detection by Vibration
4. Discussion
5. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Liu, X.; Jiang, A.; Xu, N.; Xue, J. Increment Entropy as a Measure of Complexity for Time Series. Entropy 2016, 18, 22. https://doi.org/10.3390/e18010022
Liu X, Jiang A, Xu N, Xue J. Increment Entropy as a Measure of Complexity for Time Series. Entropy. 2016; 18(1):22. https://doi.org/10.3390/e18010022
Chicago/Turabian StyleLiu, Xiaofeng, Aimin Jiang, Ning Xu, and Jianru Xue. 2016. "Increment Entropy as a Measure of Complexity for Time Series" Entropy 18, no. 1: 22. https://doi.org/10.3390/e18010022