Robust and Sparse Kernel-Free Quadratic Surface LSR via L2,p-Norm With Feature Selection for Multi-Class Image Classification

Least Squares Regression (LSR) is a powerful machine learning method for image classification and feature selection. In this study, a framework approach is introduced for the multi-classification problem based on the $L_{2,p}$ -norm, utilizing more general loss functions and regularization terms, which is a robust sparse kernel-free quadratic surface least squares regression (RSQSLSR). The nonlinear relationship between features is addressed using a quadratic kernel-free technique combined with $\epsilon $ -dragging technology and manifold regularization to learn soft labels, which can achieve the goal of feature selection and classification, simultaneously. This model utilizes K quadratic surfaces mapping samples from the input space to the label space, preserving the local structure of the samples. To enhance practical applications, such as image classification, a simplified version of the method is proposed. An iterative algorithm for RSQSLSR is designed and its convergence is proved theoretically. The salient features and theoretical analysis of our proposed method are comprehensively discussed in this paper. Extensive experiments on synthetic and real datasets validate the effectiveness of our method, surpassing other state-of-the-art methods in terms of classification accuracy and feature selection performance.