Radius-margin based support vector machine with LogDet regularizaron

Theoretically, Support Vector Machine (SVM) has the generalization error bound of radius-margin ratio, while the standard SVM only maximizes the margin. Several SVM variants based on the radius-margin ratio error bound have been proposed. However, most of them either require the form of the transformation matrix to be diagonal, or the optimization is computationally expensive. In this paper, we propose a novel convex radius-margin based SVM model with-LogDet regularization, ie., L-S VM Our model not only takes radius into consideration, but also increases the stability by combing the individual inequality constraints into one integrated inequality constraint. In L-SVM, we introduce a-LogDet regularization term to make the model more effective and get a dosed-form solution of the transformation matrix. Furthermore, we extend the L-SVM model to kernel space for nonlinear cases with the advantages of kernel principal component analysis. The experimental results show that L-SVM achieves significantly better performance both in accuracy and efficiency, compared to the standard SVM and the state-of-the-art radius-margin based SVM methods, e.g., RMM, R-SVM⁺ and R-SVM+ μ.