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 \(l_{2,1}\) -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.
