Robust and Sparse Kernel-Free Quadratic Surface LSR via L<sub>2,p</sub>-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 <inline-formula> <tex-math notation="LaTeX">$L_{2,p}$ </te...
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2025-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10848070/ |
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| author | Yongqi Zhu Zhixia Yang Junyou Ye Yongxing Hu |
| author_facet | Yongqi Zhu Zhixia Yang Junyou Ye Yongxing Hu |
| author_sort | Yongqi Zhu |
| collection | DOAJ |
| description | 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 <inline-formula> <tex-math notation="LaTeX">$L_{2,p}$ </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-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. |
| format | Article |
| id | doaj-art-97141b5b80824e63b9dafeb3297d897f |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-97141b5b80824e63b9dafeb3297d897f2025-01-29T00:01:15ZengIEEEIEEE Access2169-35362025-01-0113163621637910.1109/ACCESS.2025.353248310848070Robust and Sparse Kernel-Free Quadratic Surface LSR via L<sub>2,p</sub>-Norm With Feature Selection for Multi-Class Image ClassificationYongqi Zhu0https://orcid.org/0009-0000-1042-2838Zhixia Yang1https://orcid.org/0000-0003-0446-4278Junyou Ye2Yongxing Hu3College of Mathematics and Systems Science, Xinjiang University, Ürümqi, ChinaCollege of Mathematics and Systems Science, Xinjiang University, Ürümqi, ChinaCollege of Mathematics and Systems Science, Xinjiang University, Ürümqi, ChinaCollege of Mathematics and Systems Science, Xinjiang University, Ürümqi, ChinaLeast 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 <inline-formula> <tex-math notation="LaTeX">$L_{2,p}$ </tex-math></inline-formula>-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 <inline-formula> <tex-math notation="LaTeX">$\epsilon $ </tex-math></inline-formula>-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.https://ieeexplore.ieee.org/document/10848070/Multi-class classification learningManifold regularizationSparse learningKernel-freeL2,p-norm |
| spellingShingle | Yongqi Zhu Zhixia Yang Junyou Ye Yongxing Hu Robust and Sparse Kernel-Free Quadratic Surface LSR via L<sub>2,p</sub>-Norm With Feature Selection for Multi-Class Image Classification IEEE Access Multi-class classification learning Manifold regularization Sparse learning Kernel-free L2,p-norm |
| title | Robust and Sparse Kernel-Free Quadratic Surface LSR via L<sub>2,p</sub>-Norm With Feature Selection for Multi-Class Image Classification |
| title_full | Robust and Sparse Kernel-Free Quadratic Surface LSR via L<sub>2,p</sub>-Norm With Feature Selection for Multi-Class Image Classification |
| title_fullStr | Robust and Sparse Kernel-Free Quadratic Surface LSR via L<sub>2,p</sub>-Norm With Feature Selection for Multi-Class Image Classification |
| title_full_unstemmed | Robust and Sparse Kernel-Free Quadratic Surface LSR via L<sub>2,p</sub>-Norm With Feature Selection for Multi-Class Image Classification |
| title_short | Robust and Sparse Kernel-Free Quadratic Surface LSR via L<sub>2,p</sub>-Norm With Feature Selection for Multi-Class Image Classification |
| title_sort | robust and sparse kernel free quadratic surface lsr via l sub 2 p sub norm with feature selection for multi class image classification |
| topic | Multi-class classification learning Manifold regularization Sparse learning Kernel-free L2,p-norm |
| url | https://ieeexplore.ieee.org/document/10848070/ |
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