L-SVM: A radius-margin-based SVM algorithm with LogDet regularization

Theoretically, support vector machines (SVMs) have general error bounds along a radius-margin ratio, while conventional SVMs consider only the maximization of the margin and ignore the minimization of the radius, which is sensitive to affine data transformations. Thus, conventional SVMs can be improved by controlling both the radius and the margin. Several SVM variants based on radius-margin ratio error bounds have been proposed to integrate the radius and margin. However, most of these either require a diagonal transformation matrix or are computationally expensive to optimize. In this paper, we propose a novel radius-margin-based SVM model with LogDet regularization called L-SVM. In our model, we consider the radius and introduce a negative LogDet term to improve the model accuracy. We also adopt a two-step alternating minimization strategy to obtain an optimal solution, which leads to impressive computational improvements. Our experimental results validate the performance of the L-SVM and show that the L-SVM achieves significantly higher accuracy and efficiency compared to conventional SVMs and some other state-of-the-art radius-margin-based SVM methods. In addition, we apply our proposed L-SVM to solve transaction fraud problems and propose a framework for an L-SVM-based fraud detection system.