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On the computational complexity of the empirical mode decomposition algorithm

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  • Wang, Yung-Hung
  • Yeh, Chien-Hung
  • Young, Hsu-Wen Vincent
  • Hu, Kun
  • Lo, Men-Tzung

Abstract

It has been claimed that the empirical mode decomposition (EMD) and its improved version the ensemble EMD (EEMD) are computation intensive. In this study we will prove that the time complexity of the EMD/EEMD, which has never been analyzed before, is actually equivalent to that of the Fourier Transform. Numerical examples are presented to verify that EMD/EEMD is, in fact, a computationally efficient method.

Suggested Citation

  • Wang, Yung-Hung & Yeh, Chien-Hung & Young, Hsu-Wen Vincent & Hu, Kun & Lo, Men-Tzung, 2014. "On the computational complexity of the empirical mode decomposition algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 159-167.
    • Handle: RePEc:eee:phsmap:v:400:y:2014:i:c:p:159-167
    DOI: 10.1016/j.physa.2014.01.020
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    References listed on IDEAS

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    Cited by:

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    10. Wang, Yung-Hung & Young, Hsu-Wen Vincent & Lo, Men-Tzung, 2016. "The inner structure of empirical mode decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1003-1017.
    11. Wei Sun & Ming Duan, 2019. "Analysis and Forecasting of the Carbon Price in China’s Regional Carbon Markets Based on Fast Ensemble Empirical Mode Decomposition, Phase Space Reconstruction, and an Improved Extreme Learning Machin," Energies, MDPI, vol. 12(2), pages 1-27, January.
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    13. Wei Jiang & Yanhe Xu & Yahui Shan & Han Liu, 2018. "Degradation Tendency Measurement of Aircraft Engines Based on FEEMD Permutation Entropy and Regularized Extreme Learning Machine Using Multi-Sensor Data," Energies, MDPI, vol. 11(12), pages 1-18, November.
    14. Xuejiao Ma & Dandan Liu, 2016. "Comparative Study of Hybrid Models Based on a Series of Optimization Algorithms and Their Application in Energy System Forecasting," Energies, MDPI, vol. 9(8), pages 1-34, August.
    15. Xiao, Liye & Shao, Wei & Yu, Mengxia & Ma, Jing & Jin, Congjun, 2017. "Research and application of a combined model based on multi-objective optimization for electrical load forecasting," Energy, Elsevier, vol. 119(C), pages 1057-1074.
    16. Hufang Yang & Zaiping Jiang & Haiyan Lu, 2017. "A Hybrid Wind Speed Forecasting System Based on a ‘Decomposition and Ensemble’ Strategy and Fuzzy Time Series," Energies, MDPI, vol. 10(9), pages 1-30, September.
    17. Xing Zhang & Chongchong Zhang & Zhuoqun Wei, 2019. "Carbon Price Forecasting Based on Multi-Resolution Singular Value Decomposition and Extreme Learning Machine Optimized by the Moth–Flame Optimization Algorithm Considering Energy and Economic Factors," Energies, MDPI, vol. 12(22), pages 1-23, November.
    18. Liu, Cong & Tan, Bin & Fu, Mingyu & Li, Jinlian & Wang, Jun & Hou, Fengzhen & Yang, Albert, 2021. "Automatic sleep staging with a single-channel EEG based on ensemble empirical mode decomposition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    19. Vincent Douchamps & Matteo Volo & Alessandro Torcini & Demian Battaglia & Romain Goutagny, 2024. "Gamma oscillatory complexity conveys behavioral information in hippocampal networks," Nature Communications, Nature, vol. 15(1), pages 1-19, December.
    20. Yeh, Chien-Hung & Lo, Men-Tzung & Hu, Kun, 2016. "Spurious cross-frequency amplitude–amplitude coupling in nonstationary, nonlinear signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 454(C), pages 143-150.
    21. Qiang Gao & He-Sheng Tang & Jia-Wei Xiang & Yongteng Zhong, 2018. "A multi-sensor fault detection strategy for axial piston pump using the Walsh transform method," International Journal of Distributed Sensor Networks, , vol. 14(4), pages 15501477187, April.
    22. Wang, Deyun & Luo, Hongyuan & Grunder, Olivier & Lin, Yanbing & Guo, Haixiang, 2017. "Multi-step ahead electricity price forecasting using a hybrid model based on two-layer decomposition technique and BP neural network optimized by firefly algorithm," Applied Energy, Elsevier, vol. 190(C), pages 390-407.
    23. Neeraj Bokde & Andrés Feijóo & Daniel Villanueva & Kishore Kulat, 2019. "A Review on Hybrid Empirical Mode Decomposition Models for Wind Speed and Wind Power Prediction," Energies, MDPI, vol. 12(2), pages 1-42, January.
    24. Young, Hsu-Wen Vincent & Hsu, Ke-Hsin & Pham, Van-Truong & Tran, Thi-Thao & Lo, Men-Tzung, 2017. "A new approach to sparse decomposition of nonstationary signals with multiple scale structures using self-consistent nonlinear waves," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 1-10.
    25. Sun, Wei & Zhang, Chongchong, 2018. "Analysis and forecasting of the carbon price using multi—resolution singular value decomposition and extreme learning machine optimized by adaptive whale optimization algorithm," Applied Energy, Elsevier, vol. 231(C), pages 1354-1371.

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    Keywords

    EMD; EEMD; Time; Space; Complexity;
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