In recent years, nonparallel support vector machine (NPSVM) is proposed as a nonparallel hyperplane classifier with superior performance than standard SVM and existing nonparallel classifiers such as the twin support vector machine (TWSVM). With the perfect theoretical underpinnings and great practical success, NPSVM has been used to dealing with the classification tasks on different scales. Tackling large-scale classification problem is a challenge yet significant work. Although large-scale linear NPSVM model has already been efficiently solved by the dual coordinate descent (DCD) algorithm or alternating direction method of multipliers (ADMM), we present a new strategy to solve the primal form of linear NPSVM different from existing work in this paper. Our algorithm is designed in the framework of the stochastic gradient descent (SGD), which is well suited to large-scale problem. Experiments are conducted on five large-scale data sets to confirm the effectiveness of our method.

A new kernel-based learning algorithm called kernel affine subspace nearest point (KASNP) approach is proposed in this paper. Inspired by the geometrical explanation of support vector machines (SVMs) and its nearest point problem in convex hulls, we extend the convex hull of each class to its corresponding affine subspace in high dimensional space induced by kernel. In two class affine subspaces, KASNP finds the nearest points and then constructs a separating hyperplane, which bisects the line segment joining them. The nearest point problem of KASNP is only an unconstrained optimal problem whose solution can be directly computed. Compared with SVM, KASNP avoids solving convex quadratic programming. Experiments on two-spiral dataset, two UCI credit datasets, and face recognition datasets show that our proposed KASNP is effective for data classification.