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A derived least square extreme learning machine

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Abstract

Extreme learning machine (ELM) is a single hidden layer feedforward neural network and is proved to be a good machine learning tool. However, the singularity of the ELM activation function results in the poor generalization ability of the systems. This study proposes a least squares ELM with derivative characteristics (DLSELM). The activation function of the network consists of the original and derivative functions due to the introduction of derivative characteristics in the network. All weights and biases of the network are determined by a twice least squares method. Derivative characteristics increase the diversity of activation functions in the network. The regression accuracy of the network and the generalization ability of the system were greatly improved due to the weighs and biases of the DLSELM calculated by twice least methods. DLSELM is applied to different datasets for verifying their performance. Moreover, DLSELM possesses the best regression accuracy, stability, and generalization performance compared with the other networks.

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Data availability

The datasets analyzed during this study are available in the University of California machine learning database,Toronto machine learning database, UCI machine learning library. The pumping test data of agricultural irrigation well are not publicly available.

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Acknowledgements

The authors did not receive support from any organization for the submitted work. No funding was received to assist with the preparation of this manuscript. No funding was received for conducting this study. No funds, grants, or other support was received. The authors have no relevant financial or non-financial interests to disclose. The authors have no conflicts of interest to declare that are relevant to the content of this article. All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.The authors have no financial or proprietary interests in any material discussed in this article. Authors are responsible for correctness of the statements provided in the manuscript.

Funding

This project was supported by the National Natural Science Foundation of China (Grant No. 12102273), National Key R& Program of China (Grant No. 2021YFB3900602, No. 2021YFB3900604).

Author information

Authors and Affiliations

  1. School of Water Conservancy and Hydroelectric Power, Hebei University of Engineering, Handan, 056000, China

    Shuang Hou & Xiaosheng Wang

  2. School of Mechanical Engineering, Shijiazhuang Tiedao University, Shijiazhuang, 050043, China

    Yi Wang, Sixian Jia & Meiqi Wang

Authors
  1. Shuang Hou
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  2. Yi Wang
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  3. Sixian Jia
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  4. Meiqi Wang
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  5. Xiaosheng Wang
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Correspondence to Meiqi Wang.

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Hou, S., Wang, Y., Jia, S. et al. A derived least square extreme learning machine. Soft Comput 26, 11115–11127 (2022). https://doi.org/10.1007/s00500-022-07318-y

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