Font Size: a A A

Study On Improved High-Dimension And Nonlinear Partial Least-Squares Regression Method And Applications

Posted on:2011-09-02Degree:DoctorType:Dissertation
Country:ChinaCandidate:J X GuoFull Text:PDF
GTID:1119330338483260Subject:Management Science and Engineering
Abstract/Summary:PDF Full Text Request
Partial Least-Squares (PLS) Regression is a new non-parametric regression method based on higher-dimensional projection. It can effectively combine functions of multiple regression analysis, principal component analysis and canonical correlation analysis. That's why it has already been labeled as the second generation of multiple statistical analysis method. Identification method of Specific Sample Points and bitree dimension reduction of a variable set are two important preprocessing of data analysis. Based on PLS regression model and combined with non-linear Kernel Principal Component Analysis and Binary Tree Dimension Reduction methods etc., the dissertation came up with a modified non-linear Partial Least-Squares Regression model. Moreover, dimension reduction method and evaluation methodology for Binary Tree were also presented. Furthermore, Specific Sample Points'identification method was also extended. Main research contents are as follows:An improved non-linear Partial Least-Squares Regression model was proposed. Traditional linear and non-linear PLS regression models calculate linear regression relations between dependent variable set and principal components extracted, without taking into consideration that dependent variable set and principal components may have non-linear relations. In the dissertation, linear regressions of dependent variable set to each principal component was modified to linear or non-linear regression choosing according to concrete conditions. And each principal component was still expressed as linear regression equation of the original independent variable set. The dissertation also elaborated on and further established a non-linear regression model of motor oil consumption and ten other indicators about design and performance.Binary Tree Dimension Reduction methods in higher dimensional space and evaluation methodology for dimension reduced Binary Tree were also proposed. In the dissertation, the traditional method to reduce dimensions on the whole was modified to reduce dimensions from partial sections to overall. If the sample had an oversized variable number, then Principal Component Analysis or Kernel Principal Component Analysis could be implemented between two variables having the strongest correlation: extracting the first component variable to replace the original two variables, the sample variable number would then be reduced to n ?1. This dimension reduction process would be executed circularly until the precision demanded obtained. Depending on evaluation methodology for dimension reduced Binary Tree, the dissertation adopted economic development indicators of each district or county in Tianjin in the year 2008, and made a scientific evaluation on economic development levels of 18 districts or counties in Tianjin. What's more, identification method of Specific Sample Points in higher dimensional space was also extended. Based on analysis technics of PLS regression Specific Sample Points identification, ellipse T~2 recognition method in two dimensional surface was extended to Ellipsoid T~2 in three dimensional surface andHyper ellipsoidal T~2 in higher dimensional surface. In the meanwhile, on the basis of pedigree clustering method,Specific Sample Points identification method based on principal component pedigree chart in higher dimensional surface was brought up and employed to evaluate gasoline and diesel prices in major provinces and cities in China.
Keywords/Search Tags:Partial Least-Squares Regression, Method of Bitree Dimension Reduction, Specific Sample Points Identification, Non-Linear, Principal Component Analysis(PCA), Kernel Principal Component Analysis(KPCA)
PDF Full Text Request
Related items