Research On Kernel-free Quadratic Surface Support Vector Regression

Machine learning has become a hot topic.As a classical machine learning algorithm,support vector regression(SVR)is widely used in stock prediction,air quality prediction,cancer risk prediction and other fields.SVR solves nonlinear problems by introducing kernel function,but the nonlinear decision function is not interpretable,so this paper studies the kernel-free quadratic surface support vector regression.The algorithm does not need to introduce kernel function,so it avoids the selection of kernel parameters and does not lose the interpretability of decision function.The details are as follows:First,?-kernel-free soft quadratic surface support vector regression(SQSSVR)is proposed.By finding a quadratic function with a given training set,the concept of ?-band is further given,and the sample points are distributed in the ?-band as much as possible,so as to construct an optimization problem.Since the unknown quantity of the optimization problem contains matrix,it is difficult to solve it,so this paper uses matrix vectorization to transform the optimization problem into a quadratic programming problem.This paper also discusses the consistency relation between optimization problem and classification model.The artificial datasets and the UCI datasets further verify that the algorithm has better fitting performance and less timeSecond,an asymmetric v-kernel-free quadratic surface support vector regression(Asy-v-QSSVR)is proposed.By introducing the pinball loss function,the training points above and below the ?-band are given different penalties,so the better regression function is obtained.Furthermore,we theoretically prove that the parameter p and v control the up-per bound of the number of the training point classified incorrectly above and below the ?-band.When p=0.5,the method is degenerated into a symmetric v-kernel-free quadratic surface support vector regression,and the number of support vectors can be controlled by parameter v is also proved.The numerical experiment shows that the proposed approach has better fitting performance and less time consumption,and the parameter p will not increase the computational cost.