Abstract：Twin support vector regression (TSVR) efficiently determines its objective regression function by optimizing a pair of smaller sized SVM-type problems. The objective functions of TSVR in the primal space are directly optimized by introducing the well-known Newton algorithm. This method effectively overcomes the shortcoming of TSVR that its regressor is approximated by the dual quadratic programming problems. Numerical studies show that the proposed method provides good performance and obtains less learning time compared with TSVR.
[1] Vapnik V N. The Nature of Statistical Learning Theory. New York, USA: Springer, 1995 [2] Vapnik V N. Statistical Learning Theory. New York, USA: Wiley, 1998 [3] Burges C J C. A Tutorial on Support Vector Machines for Pattern Recognition. Data Mining and Knowledge Discovery, 1998, 2(2): 121-167 [4] Christianini V, Shawe-Taylor J. An Introduction to Support Vector Machines. Cambridge, UK: Cambridge University Press, 2002 [5] Jayadeva, Khemchandani R, Chandra S. Twin Support Vector Machines for Pattern Classification. IEEE Trans on Pattern Analysis and Machine Intelligence, 2007, 29(5): 905-910 [6] Peng Xinjun. TSVR: An Efficient Twin Support Vector Machine for Regression. Neural Networks, 2010, 23(3): 365-372 [7] Chapelle O. Training a Support Vector Machine in the Primal [EB/OL]. [2006-08-30]. http://www.kyb.mpg.de/publications/primal_[o].pdf [8] Eubank R L. Statistics: Textbooks and Monographs: Nonparametric Regression and Spline Smoothing. 2nd Edition. New York, USA: Marcel Dekker, 1999 [9] Blake C I, Merz C J. UCI Repository for Machine Learning Databases [DB/OL]. [2009-10-25]. http://www.ics.uci.edu/ ~mlearn/ML-Repository.html [10] Suykens J A K, Vandewalle J. Least Squares Support Vector Machine Classifiers. Neural Processing Letters, 1999, 9(3): 293-300 [11] Suykens J A K, Lukas L, van Dooren P, et al. Least Squares Support Vector Machine Classifiers: A Large Scale Algorithm // Proc of European Conference on Circuit Theory and Design. Stresa, Italy, 1999: 839-842 [12] The MathWorks [DB/OL]. [2009-10-25]. http://www.mathworks.com
2011, Vol. 24 
