$p$SVM: Soft-margin SVMs with $p$-norm Hinge Loss
This work addresses improving SVM performance for classification tasks, but it appears incremental as it builds on existing hinge loss SVMs with a modified loss function.
The paper tackles the problem of enhancing Support Vector Machines (SVMs) by introducing $p$SVMs with $p$-norm hinge loss, deriving generalization bounds, formulating dual optimization, and proposing a $p$SMO training algorithm, with experiments showing effectiveness on binary and multi-class classification tasks.
Support Vector Machines (SVMs) based on hinge loss have been extensively discussed and applied to various binary classification tasks. These SVMs achieve a balance between margin maximization and the minimization of slack due to outliers. Although many efforts have been dedicated to enhancing the performance of SVMs with hinge loss, studies on $p$SVMs, soft-margin SVMs with $p$-norm hinge loss, remain relatively scarce. In this paper, we explore the properties, performance, and training algorithms of $p$SVMs. We first derive the generalization bound of $p$SVMs, then formulate the dual optimization problem, comparing it with the traditional approach. Furthermore, we discuss a generalized version of the Sequential Minimal Optimization (SMO) algorithm, $p$SMO, to train our $p$SVM model. Comparative experiments on various datasets, including binary and multi-class classification tasks, demonstrate the effectiveness and advantages of our $p$SVM model and the $p$SMO method. Code is available at https://github.com/CoderBak/pSVM.