Unified SVM algorithm based on LS-DC Loss

Over the past two decades, Support Vector Machine (SVM) has been 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 the distinct losses, including the convex loss or non-convex loss. This paper proposes an algorithm that can train different SVM models in a \emph{unified} scheme. Firstly, we introduce a definition of the \emph{LS-DC} (least-squares type of difference of convex) loss 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 DCA (difference of convex algorithm), we propose a unified algorithm, called \emph{UniSVM}, which can solve the SVM model with any convex or non-convex LS-DC loss, in which only a vector will be changed according to the specifically chosen loss. Notably, for training robust SVM models with non-convex losses, UniSVM has a dominant advantage over all the existing algorithms because it has a closed-form solution per iteration while the existing ones always need to solve an L1SVM/L2SVM per iteration. Furthermore, by the low-rank approximation of the kernel matrix, UniSVM can solve the large-scale nonlinear problems efficiently. To verify the efficacy and feasibility of the proposed algorithm, we perform many experiments on some small artificial problems and some large benchmark tasks with/without outliers for classification and regression to compare it with some state-of-the-art algorithms. The experimental results support that UniSVM can obtain the comparable performance within less training time. The highlight advantage of UniSVM is that its core code in Matlab is less than ten lines, hence it can be easily grasped by users or researchers