Research And Application Of Twin Least Squares Support Vector Regression Model

Twin Least Square Support Vector Regression(TLSSVR)is a new machine learning method based on Least Square Support Vector Regression.It corrects the inequality constraints of Quadratic Programming Problem in Twin Support Vector Regression(TSVR)into equality constraints,which greatly reduces the computational time complexity.Compared with the SVR,The calculation efficiency of TLSSVR has been greatly improved.In view of the good learning performance of TLSSVR,it has become a research hotspot in the fields of machine learning and data mining.However,TLSSVR is not perfect in many aspects,such as lack of sparsity,and needs further research and improvement.This paper mainly studies the regression task with noise characteristics,uses the Bayesian strategy and the maximizing posterior probability method to solve the loss function with noise characteristics,applies optimization theory and statistical learning theory,and proposes two extended models of LSSVR.The main work and innovations of this paper are as follows:(1)Study on TLSSVR model with Heteroscedastic Gaussian Noise.The classic LSSVR model assumes that noise has a Gaussian distribution with zero mean and homoscedasticity.However,in some practical applications,the noise characteristic satisfies a Gaussian distribution with zero mean and heteroscedasticity.In this paper,using the twin LSSVR regression model framework,the optimal loss function with heteroscedastic Gaussian noise is introduced,and the twin least squares support vector regression model with heteroscedastic Gaussian noise(TLSSVR-HGN)is constructed.Due to the lack of sparseness of TLSSVR-HGN,in order to analyze the generalization ability of the proposed model,a sparse TLSSVR-HGN with simple mechanism is proposed.The proposed model was tested on artificial data sets,several UCI data sets and actual wind speed data.Experimental results show that in terms of prediction accuracy,the TLSSVR-HGN model has better prediction accuracy than other models discussed in this article.(2)Study on TLSSVR model with Gauss-Laplace Mixed Noise.In some practical applications,the noise cannot satisfy a single distribution including Gaussian and Laplace,but a mixed distribution.In this paper,using the TLSSVR regression model framework and introducing the characteristics of Gauss-Laplace mixed noise,the twin least squares support vector regression model with Gauss-Laplace mixed noise(GL-TLSSVR)is proposed.Then,the proposed model is solved by the Augmented Lagrange Method.Finally,the simulation results on the short-term wind speed data set show that the proposed GL-TLSSVR model can make up for the shortcomings of other models discussed in this article and improve the prediction accuracy of this model.