Sparse L0-norm based Kernel-free Quadratic Surface Support Vector Machines

Abstract: Kernel-free quadratic surface support vector machine (SVM) models have gained significant attention in machine learning. However, introducing a quadratic classifier increases the model's complexity by quadratically expanding the number of parameters relative to the dimensionality of the data, exacerbating overfitting. Hence, we propose sparse $\ell_0$-norm based Kernel-free quadratic surface SVMs, designed to mitigate overfitting and enhance interpretability. Given the intractable nature of these models, we present a penalty decomposition algorithm to obtain first-order optimality points efficiently. We demonstrate that the subproblems in our framework either admit closed-form solutions or can leverage duality theory to improve computational efficiency. Through empirical evaluations on real-world datasets, we demonstrate the efficacy and robustness of our approach, showcasing its potential to advance Kernel-free quadratic surface SVMs in practical applications while addressing overfitting concerns. All the implemented models and experiment codes are available at https://github.com/raminzandvakili/L0-QSVM.