Bound estimation-based safe acceleration for maximum margin of twin spheres machine with pinball loss

Abstract

Maximum margin of twin spheres support vector machine (MMTSSVM) is an efficient method for imbalanced data classification. As an extension to enhance noise insensitivity of MMTSSVM, MMTSSVM with pinball loss (Pin-MMTSM) has a good generalization performance. However, it is not efficient enough for large-scale data. Inspired by the sparse solution of SVMs, in this paper, we propose a safe accelerative approach to reduce the computational cost. Unlike the existing safe screening rules, where only one variable changes with the parameters. We utilize bound estimation-based to derive the upper and lower bounds of center and radius. With our approach, the inactive samples are discarded before solving the problem, thus it can reduce the computational cost. One important advantage of our approach is safety, i.e., we can obtain the same solution as solving original problem both in linear and non-linear cases. Moreover, it is obvious that our acceleration approach is independent of the solver. To further accelerate the computational speed, a decomposition method is employed. Experiments on three artificial datasets and twelve benchmark datasets clearly demonstrate the effectiveness of our approach. At last, we extend bound estimation-based method to ν-SVM, theoretical analysis and experimental results both verify its feasibility and effectiveness.