Neural Computing and Applications

, Volume 29, Issue 9, pp 497–509 | Cite as

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

  • Xuchan Ju
  • Yingjie TianEmail author
Original Article


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.


Support vector machines ν-Nonparallel support vector machines Large scale data sets Divide-and-conquer 



This work has been partially supported by grants from National Natural Science Foundation of China (Nos.61472390, 11271361, 71331005), Major International (Regional) Joint Research Project (No.71110107026).


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Copyright information

© The Natural Computing Applications Forum 2016

Authors and Affiliations

  1. 1.School of Economics and ManagementTsinghua UniversityBeijingChina
  2. 2.Postdoctoral Programme of Agricultural Bank of ChinaBeijingChina
  3. 3.Research Center on Fictitious Economy and Data ScienceChinese Academy of SciencesBeijingChina
  4. 4.Key Laboratory of Big Data Mining and Knowledge ManagementChinese Academy of SciencesBeijingChina

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