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

Changlin Wang, Zhixia Yang (), Junyou Ye, Xue Yang and Manchen Ding
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Changlin Wang: Xinjiang University
Zhixia Yang: Xinjiang University
Junyou Ye: Xinjiang University
Xue Yang: Xinjiang University
Manchen Ding: Xinjiang University

Annals of Data Science, 2024, vol. 11, issue 2, No 10, 647-675

Abstract: 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.

Keywords: Feature selection; Least squares regression; Quadratic surface; Kernel-free trick; Sparse regularization term (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s40745-024-00518-3

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