A New Class of e-Piecewise Smooth SupportVector Regressions

ε-support vector regression (ε-SVR) can be converted into an unconstrained convex and non-smooth quadratic programming problem. It is not solved by the traditional algorithm. In order to solve this non-smooth problem, a class of piecewise smooth functions is introduced to approximate the ε-insensitive loss function of ε-SVR, which generates a ε-piecewise smooth support vector regression (ε-dPWSSVR) model. The fast Newton-Armijo algorithm is used to solve the ε-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 ε-dPWSSVR for massive datasets. Experimental results show that the proposed ε-dPWSSVR has the better regression performance and the learning efficiency than other competitive baselines.