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Supervised Feature Selection via Quadratic Surface Regression with $$l_{2,1}$$ l 2 , 1 -Norm Regularization

Author

Listed:
  • Changlin Wang

    (Xinjiang University
    Xinjiang University)

  • Zhixia Yang

    (Xinjiang University
    Xinjiang University)

  • Junyou Ye

    (Xinjiang University
    Xinjiang University)

  • Xue Yang

    (Xinjiang University
    Xinjiang University)

  • Manchen Ding

    (Xinjiang University
    Xinjiang University)

Abstract

This paper proposes a supervised kernel-free quadratic surface regression method for feature selection (QSR-FS). The method is to find a quadratic function in each class and incorporates it into the least squares loss function. The $$l_{2,1}$$ l 2 , 1 -norm regularization term is introduced to obtain a sparse solution, and a feature weight vector is constructed by the coefficients of the quadratic functions in all classes to explain the importance of each feature. An alternating iteration algorithm is designed to solve the optimization problem of this model. The computational complexity of the algorithm is provided, and the iterative formula is reformulated to further accelerate computation. In the experimental part, feature selection and its downstream classification tasks are performed on eight datasets from different domains, and the experimental results are analyzed by relevant evaluation index. Furthermore, feature selection interpretability and parameter sensitivity analysis are provided. The experimental results demonstrate the feasibility and effectiveness of our method.

Suggested Citation

  • Changlin Wang & Zhixia Yang & Junyou Ye & Xue Yang & Manchen Ding, 2024. "Supervised Feature Selection via Quadratic Surface Regression with $$l_{2,1}$$ l 2 , 1 -Norm Regularization," Annals of Data Science, Springer, vol. 11(2), pages 647-675, April.
    • Handle: RePEc:spr:aodasc:v:11:y:2024:i:2:d:10.1007_s40745-024-00518-3
    DOI: 10.1007/s40745-024-00518-3
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    References listed on IDEAS

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    1. Yanqin Bai & Xiao Han & Tong Chen & Hua Yu, 2015. "Quadratic kernel-free least squares support vector machine for target diseases classification," Journal of Combinatorial Optimization, Springer, vol. 30(4), pages 850-870, November.
    2. Fu, Saiji & Tian, Yingjie & Tang, Long, 2023. "Robust regression under the general framework of bounded loss functions," European Journal of Operational Research, Elsevier, vol. 310(3), pages 1325-1339.
    3. Jian Luo & Shu-Cherng Fang & Zhibin Deng & Xiaoling Guo, 2016. "Soft Quadratic Surface Support Vector Machine for Binary Classification," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(06), pages 1-22, December.
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