• Nguyen The Cuong Faculty of Basic, Telecommunications University, Nha Trang, Khanh Hoa.
  • Huynh The Phung Department of Mathematics, College of Sciences, Hue University.




Support Vector Machine, Twin Support Vector Machine, Structural Twin Support Vector Machine, Weighted Structural - Support Vector Machine


In binary classification problems, two classes of data seem to be different from each other. It is expected to be more complicated due to the clusters in each class also tend to be different. Traditional algorithms as Support Vector Machine (SVM) or Twin Support Vector Machine (TWSVM) cannot sufficiently exploit structural information with cluster granularity of the data, cause limitation on the capability of simulation of data trends. Structural Twin Support Vector Machine (S-TWSVM) sufficiently exploits structural information with cluster granularity for learning a represented hyperplane. Therefore, the capability of S-TWSVM’s data simulation is better than that of TWSVM. However, for the datasets where each class consists of clusters of different trends, the S-TWSVM’s data simulation capability seems restricted. Besides, the training time of S-TWSVM has not been improved compared to TWSVM. This paper proposes a new Weighted Structural - Support Vector Machine (called WS-SVM) for binary classification problems with a class-vs-clusters strategy. Experimental results show that WS-SVM could describe the tendency of the distribution of cluster information. Furthermore, both the theory and experiment show that the training time of the WS-SVM for classification problem has significantly improved compared to S-TWSVM.


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V.N. Vapnik, The natural of statistical learning theory. Springer, New York, 1995.

G.H Golub and C.F Van Loan, Matrix computations, third ed., pp. 50. The John Hopkins Univ,

Press, 1996.

G. Fung and O. L Mangasarian, "Proximal support vector machine," Proc. Seventh Int’l Conf.

Knowledge discovery and Data mining. pp. 77-86, 2001.

B. Scholkopf and A. Smola, Learning with kernel. Cambridge, Mass.: MIT Press, 2002.

W.S. Noble, Support vector machine applications in computational Biology. MIT Press.

O. L. Mangasarian and E. W. Wild, "Multisurface proximal support vector classification via

generalized eigenvalues", IEEE Trans. Pattern analysis and machine learning. Vol. 28, No. 1,

pp. 69-74, 2006.

Jayadeva, R. Khemchandani and S. Chandra, "Twin support vector machines for pattern classification". IEEE Transactions on Pattern Analysis and Machine intelligence, Vol. 29, No. 5,

D. Yeung, D. Wang, W. Ng. E. Tsang, X. Wang, "Structured large margin machines: sensitive

to data distribution", Machine Learning, Vol. 68, pp. 171-200, 2007.

M.M. Adankon, M. Cheriet, "Model selection for the LS-SVM. Application to handwriting recognition", Pattern Recognition, Vol. 42, pp. 3264-3270, 2009.

H. Xue, S. Chen, Q. Yang, "Structural regularized support vector machine: a framework for structural large margin classifier",IEEE Transactions on Neural Networks, Vol. 22, No. 4, pp.

-587, 2011.

Y. Tian, Y. Shi, X. Liu, "Recent advances on support vector machines research", Technological

and Economic development of Economy, Vol. 18, 5-33, 2012.

Z. Qi, Y. Tian, Y. Shi, "Structural twin support vector machine for classification", KnowledgeBase Systems, Vol. 43, pp. 74-81, 2013.

Divya Tomar, Sonali Agarwal, "Twin Support Vector Machine: A review from 2007 to 2014",

Egyptian Informatics Journal, No.16, pp. 55-69, 2015.

X. Pan, Y. Luo, Y. Xu, "K-nearest neighbor based structural twin support vector machine",

Knowl. Based Syst. 88, pp. 34{44, 2015.

X. Xie, S. Sun, "Multitask centroid twin support vector machines", Neurocomputing. 149, pp.

{1091, 2015.

B. Mei and Y. Xu, "Multi-task least squares twin support vector machine for classification",

Neurocomputing. DOI: 10.1016/j.neucom.2018.12.079, 2019.

Jair Cervantes, Farid Garcia-Lamont, Lisbeth Rodr´ıguez-Mazahua, Asdrubal Lopez, "A comprehensive survey on support vector machine classification: Applications, challenges and trends",

Vol. 408, pp. 189-215, 2020.