A divide-and-conquer method for large scale ν-nonparallel support vector machines

Abstract

Recently, nonparallel support vector machine (NPSVM), a branch of support vector machines (SVMs), is developed and has attracted considerable interest. A kind of developed NPSVM, ν-nonparallel support vector machine (ν-NPSVM), which inherits the advantages of ν-support vector machine (ν-SVM) enables us to achieve higher classification accuracy and less time to tune for parameters. However, applications of ν-NPSVM to large data sets are seriously hampered by their excessive training time. In this paper, we use divide-and-conquer technique for large scale ν-nonparallel support vector machine (DC-νNPSVM) aiming at overcoming this burden. In the division step, we first divide the whole samples into several smaller subsamples and solve smaller subproblems using ν-NPSVM independently. We theoretically and experimentally show that objective function value, solutions, and support vectors solved by (DC-νNPSVM) are likely to those of the whole ν-NPSVM. In the conquer step, subsolutions from subproblems are used as an initial coordinate descent solver which converges to the optimal solution quickly. Moreover, multi-level (DC-νNPSVM) is adopted to balance the accuracy and efficiency. (DC-νNPSVM) can achieve higher accuracy by tuning the parameters in a smaller range and control the number of support vectors efficiently. Quantities of experiments show our (DC-νNPSVM) outperforms state-of-the-art SVM methods for large scale data sets.