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Journal of Information Science and Engineering, Vol. 31 No. 5, pp. 1813-1828 (September 2015)


A New Class of e-Piecewise Smooth Support Vector Regressions*


QING WU
School of Automation
Xi'an University of Posts and Telecommunications
Xi'an, Shaanxi, 710121 P.R. China

e-support vector regression (e-SVR) can be converted into an unconstrained convex and non-smooth quadratic programming problem. It is not solved by the typical algorithm. In order to solve this non-smooth problem, a class of piecewise smooth functions is introduced to approximate the e-insensitive loss function of e-SVR, which generates a e-piecewise smooth support vector regression (e-dPWSSVR) model. The fast Newton-Armijo algorithm is used to solve the e-dPWSSVR. The piecewise functions can get higher and higher approximation accuracy as required with increase of parameter d. The reduced kernel technique is applied to avoid the computational difficulties in nonlinear e-dPWSSVR for massive datasets. Experimental results show that the proposed e-dPWSSVR has the better regression performance and the learning efficiency than other competitive baselines.

Keywords: support vector regression, smooth technique, piecewise function, Newton-Armijo method

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Received August 7, 2014; revised September 29, 2014; accepted November 13, 2014.
Communicated by Hsuan-Tien Lin.
* This work was supported by the National Natural Science Foundation of China (61100165, 61100231, 512- 0309, 61472307), Natural Science Foundation of Shaanxi Province (2010JQ8004, 2012JQ8044, 2014JM-8313) and Foundation of Education Department of Shaanxi Province (2013JK1096).