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The Comparation And Study On Least Square Method,?-Support Vector Regression And Least Square Support Vector Regression

Posted on:2019-06-22Degree:MasterType:Thesis
Country:ChinaCandidate:Y LiFull Text:PDF
GTID:2428330566460563Subject:Applied Mathematics
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Statistic learning theory is a new machine learning theory built on statistical methods by Vapnik and others.Based on statistical learning theory,a new machine learning method,Support Vector Machines,is developed.For its superiorities in small sample,noliner,high dimention,and local minimun problems,Support Vector Machines have a prospect for research and application.As typical problems in machine learning field,regression problems can be solved by Support Vector Machines.We name the Support Vector Machines applied in regression problems as Support Vector Regression.The essential Support Vector Regression is ?-Support Vector Regression(SVR).In traditional statistics,Least Squares(LS)is the most common and typical method to solve regression problems.Besides,there is an other Support Vector Regression named as Least Squares Support Vector Regression(LS-SVR).In this article,we compare Least Squares,?-Support Vector Regression and Least Squares Support Vector Regression.I believe this can help us understand the distinguishing features of the three means of regression,and betterly apply them to the practical problems.In this article,I do the following researches:1.When the parameter C changes,what the connection is between Least Squares and ?-Support Vector Regression or Least Squares Support Vector Regression.2.Practically,for one variable linear regression problems,linear regression problems with noise points,and multiple linear regression problems,the comparation of results for Least Squares,?-Support Vector Regression and Least Squares Support Vector Regression.3.For nonlinear regression problems,the comparation of results for Least Squares,?-Support Vector Regression and Least Squares Support Vector Regression.I get the following conclusions:1.When C ? 0,for ?-Support Vector Regression(?-SVR)and Least Squares Support Vector Regression(LS-SVR),? ? 0;when C ? ?,Least Squares Support Vector Regression(LS-SVR)equals Least Squares(LS);2.For one one variable linear regression problems,Least Squares(LS)is close to Least Squares Support Vector Regression(LS-SVR),both better than ?-Support Vector Regression(?-SVR);for linear regression problems with noise points,?-Support Vector Regression(?-SVR)has better anti-noise abilities than Least Squares(LS)and Least Squares Support Vector Regression(LS-SVR);for multiple linear regression problems,Least Squares(LS)and Least Squares Support Vector Regression(LS-SVR)are better than ?-Support Vector Regression(?-SVR).3.For nonlinear regression problems,?-Support Vector Regression(?-SVR)is better than Least Squares(LS)and Least Squares Support Vector Regression(LS-SVR).
Keywords/Search Tags:Least Squares Method, ?-Support Vector Regression, Least Squares Support Vector Regression
PDF Full Text Request
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