Large-scale linear nonparallel support vector machine solver

• A novel nonparallel linear classifier avoids computing the inverses of matrices.
• Two problems of L1L1-NPSVM can be solved by the dual coordinate descent method.
• Linear TWSVMs and linear L1L1-SVM are the special cases of linear L1L1-NPSVM.
• L1L1-NPSVM has the similar sparseness with standard SVMs.
• Results show the superiority of L1L1-NPSVM on large-scale problems.

Twin support vector machines (TWSVMs), as the representative nonparallel hyperplane classifiers, have shown the effectiveness over standard SVMs from some aspects. However, they still have some serious defects restricting their further study and real applications: (1) They have to compute and store the inverse matrices before training, it is intractable for many applications where data appear with a huge number of instances as well as features; (2) TWSVMs lost the sparseness by using a quadratic loss function making the proximal hyperplane close enough to the class itself. This paper proposes a Sparse Linear Nonparallel Support Vector Machine, termed as L1L1-NPSVM, to deal with large-scale data based on an efficient solver—dual coordinate descent (DCD) method. Both theoretical analysis and experiments indicate that our method is not only suitable for large scale problems, but also performs as good as TWSVMs and SVMs.