In this paper, we propose a novel nonparallel hyperplane classifier, named ν-nonparallel support vector machine (ν-NPSVM), for binary classification. Based on our recently proposed method, i.e., nonparallel support vector machine (NPSVM), which has been proved superior to the twin support vector machines, ν-NPSVM is parameterized by the quantity ν to let ones effectively control the number of support vectors. By combining the ν-support vector classification and the ν-support vector regression together to construct the primal problems, ν-NPSVM inherits the advantages of ν-support vector machine so that enables us to eliminate one of the other free parameters of the NPSVM: the accuracy parameter ε and the regularization constant C. We describe the algorithm, give some theoretical results concerning the meaning and the choice of ν, and also report the experimental results on lots of data sets to show the effectiveness of our method.
Support vector machine Twin support vector machines Nonparallel Structural risk minimization principle Sparseness
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This work has been partially supported by grants from National Natural Science Foundation of China (Nos. 11271361, 71331005), the CAS/SAFEA International Partnership Program for Creative Research Teams, Major International (Regional) Joint Research Project (No. 71110107026), and the Ministry of water resources’ special funds for scientific research on public causes (No. 201301094).
Burges C (1998) A tutorial on support vector machines for pattern recognition. Data Min Knowl Disc 2:121–167CrossRefGoogle Scholar
Deng NY, Tian YJ, Zhang CH (2012) Support vector machines: optimization based theory, algorithms, and extensions. Chapman and Hall/CRC, LondonGoogle Scholar
Trafalis TB, Ince H (2000) Support vector machine for regression and applications to financial forecasting. In: Proceedings of IEEE-INNSENNS international joint conference neural networks, vol 6, pp 348–353Google Scholar
Li S, Kwok JT, Zhu H, Wang Y (2003) Texture classification using the support vector machines. Pattern Recogn 36(12):2883–2893CrossRefzbMATHGoogle Scholar
Wu YC, Lee YS, Yang JC (2008) Robust and efficient multiclass SVM models for phrase pattern recognition. Pattern Recogn 41(9):2874–2889CrossRefzbMATHGoogle Scholar
Isa D, Lee LH, Kallimani VP, RajKumar R (2008) Text document preprocessing with the Bayes formula for classification using the support vector machine. IEEE Trans Knowl Data Eng 20(9):1264–1272CrossRefGoogle Scholar
Karsten MB (2011) Kernel methods
in bioinformatics. Handb Stat Bioinform Part 3:317–334Google Scholar
Wang XY, Wang T, Bu J (2011) Color image segmentation using pixel wise support vector machine classification. Pattern Recogn 44(4):777–787CrossRefzbMATHGoogle Scholar
Khan N, Ksantini R, Ahmad I, Boufama B (2012) A novel SVM+ NDA model for classification with an application to face recognition. Pattern Recogn 45(1):66–79CrossRefzbMATHGoogle Scholar
Mangasarian OL, Wild EW (2006) Multisurface proximal support vector classification via generalized eigenvalues. IEEE Trans Pattern Anal Mach Intell 28(1):69–74CrossRefGoogle Scholar
Jayadeva RK, Khemchandani R, Chandra S (2007) Twin support vector machines for pattern classification. IEEE Trans Pattern Anal Mach Intell 29(5):905–910CrossRefGoogle Scholar
Kumar MA, Gopal M (2008) Application of smoothing technique on twin support vector machines. Pattern Recogn Lett 29(13):1842–1848CrossRefGoogle Scholar
Platt J (2000) Fast training of support vector machines using sequential minimal optimization. In: Schölkopf B, Burges CJC, Smola AJ (eds) Advances in kernel methods—support vector learning. MIT Press, CambridgeGoogle Scholar
Williamson RC, Scholkopf B, Smola A, Bartlett PL (2000) New support vector algorithms. Neural Comput 12:1207–1245CrossRefGoogle Scholar