Research On Twin Support Vector Regression Algorithm And Its Unconstrained Solution

The Twin Support Vector Regression Algorithm is a new regression algorithm based on the Twin Support Vector Machine(TSVM)proposed by Jayadeva et al.It has been successfully applied in the fields of pattern recognition,speech recognition and image processing.The basic idea of TSVM is to construct a pair of non-parallel hyperplanes,which respectively determine the insensitive upper and lower bound functions of the target regression function,and the final objective function is taken as the average of the upper and lower bound functions.The principle of Twin Support Vector Regression(TSVR)is similar to that of TSVM,but TSVR still has room for improvement in terms of algorithm efficiency.For these problems,this paper has done systematic research.The following are the main research contents:Some scholars have proposed the ?-TSVR algorithm by adding a regular term in TSVR.Compared with the traditional TSVR,this algorithm not only considers the empirical risk minimization but also considers the structural risk minimization,but it does not consider the location feature of the sample.Aiming at this shortcoming,this paper adds a wavelet weight diagonal matrix D to give different punishments to different sample points.A wavelet-based ?-twin support vector regression machine model(WW-?-TSVR)is proposed.In order to remove the constraint and solve the problem in the primal space,the additive function is introduced,but because the plus function can not be derived,three kinds of smooth functions are introduced to replace the non-smooth plus function.In this way,a pair of unconstrained minimization problems can be solved directly in the primal space,which is much faster than that in the dual space.Finally,in order to solve this pair of unconstrained minimization problems,we apply the Newton iteration method and the generalized gradient iteration method to each smoothing function to obtain an approximate solution,and obtain several more detailed algorithms.The experimental results on several artificial and UCI datasets indicatethat our proposed method not only gives similar or better generalization performancewith other popular methods such as TSVR and ?-TSVR,but also requires less computational time,and therefore clearly indicates the effectiveness and applicability of ourmethod.