Over the past two decades, support vector machines (SVMs) have become a popular supervised machine learning model, and plenty of distinct algorithms are designed separately based on different KKT conditions of the SVM model for classification/regression with different losses, including convex and or nonconvex loss. In this paper, we propose an algorithm that can train different SVM models in a unified scheme. First, we introduce a definition of the least squares type of difference of convex loss (LS-DC) and show that the most commonly used losses in the SVM community are LS-DC loss or can be approximated by LS-DC loss. Based on the difference of convex algorithm (DCA), we then propose a unified algorithm called UniSVM which can solve the SVM model with any convex or nonconvex LS-DC loss, wherein only a vector is computed by the specifically chosen loss. UniSVM has a dominant advantage over all existing algorithms for training robust SVM models with nonconvex losses because it has a closed-form solution per iteration, while the existing algorithms always need to solve an L1SVM/L2SVM per iteration. Furthermore, by the low-rank approximation of the kernel matrix, UniSVM can solve large-scale nonlinear problems efficiently. To verify the efficacy and feasibility of the proposed algorithm, we perform many experiments on small artificial problems and large benchmark tasks both with and without outliers for classification and regression for comparison with state-of-the-art algorithms. The experimental results demonstrate that UniSVM can achieve comparable performance in less training time. The foremost advantage of UniSVM is that its core code in Matlab is less than 10 lines; hence, it can be easily grasped by users or researchers.

在过去的二十年里，支持向量机 (SVM) 已经成为一种流行的监督机器学习模型，并且基于 SVM 模型的不同 KKT 条件分别设计了许多不同的算法，用于具有不同损失的分类/回归，包括凸和或非凸损失。在本文中，我们提出了一种可以在统一方案中训练不同 SVM 模型的算法。首先，我们介绍了最小二乘类型的凸损失差 (LS-DC) 的定义，并表明 SVM 社区中最常用的损失是 LS-DC 损失或可以通过 LS-DC 损失来近似。基于凸算法（DCA）的差异，我们提出了一种统一的算法，称为UniSVM它可以求解具有任何凸或非凸 LS-DC 损失的 SVM 模型，其中仅通过特定选择的损失计算向量。UniSVM 在训练具有非凸损失的鲁棒 SVM 模型方面优于所有现有算法，因为它每次迭代都有一个封闭形式的解决方案，而现有算法每次迭代总是需要求解 L1SVM/L2SVM。此外，通过核矩阵的低秩逼近，UniSVM 可以有效地解决大规模非线性问题。为了验证所提出算法的有效性和可行性，我们对带有和不带有用于分类和回归的异常值的小型人工问题和大型基准任务进行了许多实验，以与最先进的算法进行比较。实验结果表明 UniSVM 可以在更短的训练时间内达到可比的性能。UniSVM 的最大优势是它在 Matlab 中的核心代码不到 10 行；因此，它可以被用户或研究人员轻松掌握。