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M-estimator-based online sequential extreme learning machine for predicting chaotic time series with outliers

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Abstract

An M-estimator-based online sequential extreme learning machine (M-OSELM) is proposed to predict chaotic time series with outliers. The M-OSELM develops from the online sequential extreme learning machine (OSELM) algorithm and retains the same excellent sequential learning ability as OSELM, but replaces the conventional least-squares cost function with a robust M-estimator-based cost function to enhance the robustness of the model to outliers. By minimizing the M-estimator-based cost function, the possible outliers are prevented from entering the model’s output weights updating scheme. Meanwhile, in the sequential learning process of M-OSELM, a sequential parameter estimation approach based on error sliding window is introduced to estimate the threshold value of the M-estimator function for online outlier detection. Thanks to the built-in median operation and sliding window strategy, this approach is efficient to provide a stable estimator continuously without high computational costs, and then the potential outliers can be effectively detected. Simulation results show that the proposed M-OSELM has an excellent immunity to outliers and can always achieve better performance than its counterparts for prediction of chaotic time series when the training dataset contains outliers, ensuring at the same time all benefits of an online sequential approach.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant Nos. 61139002, 61379064), the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (Grant No. 2014BAJ04B02), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2012672), the Fundamental Research Funds for the Central Universities of Ministry of Education of China (Grant Nos. 3122014D032, 3122013P013), the Open Project Foundation of Information Technology Research Base of Civil Aviation Administration of China (Grant No. CAAC-ITRB-201401). All of these supports are appreciated.

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Authors and Affiliations

  1. School of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Wei Guo & Tao Xu

  2. School of Computer Science and Technology, Civil Aviation University of China, Tianjin, 300300, China

    Tao Xu

  3. Information Technology Research Base of Civil Aviation Administration of China, Tianjin, 300300, China

    Tao Xu

  4. School of Information Engineering, Yancheng Teachers University, Yancheng, 224002, China

    Wei Guo & Keming Tang

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  1. Wei Guo
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  2. Tao Xu
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Correspondence to Tao Xu.

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Guo, W., Xu, T. & Tang, K. M-estimator-based online sequential extreme learning machine for predicting chaotic time series with outliers. Neural Comput & Applic 28, 4093–4110 (2017). https://doi.org/10.1007/s00521-016-2301-0

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  • DOI: https://doi.org/10.1007/s00521-016-2301-0

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