Partial Least Squares Regression Models And Algorithms Research

Partial least squares regression is a new multivariate statistical data analysis method, and it is mainly a result of the study about multy-to-multy regression modeling. Partial least squares regression method is especially much more effective when there are multiple correlations among the variables. What’s more, partial least squares regression solves the issues that the number of samples may be less than the number of variables and other case. So, statisticians regard this method as the second generation regression analysis.In this paper, we firstly described the hazards when there are multiple correlation among variables in regression modeling, and then outlined the test methods of multiple correlation, which is the preliminary work before the partial least squares regression modeling. Secondly, we summarized and described the procedures of partial least squares regression modeling and the test method for solving model adaptation systematically. The former is a kind of integrated application of multiple regression analysis, principal component analysis and canonical correlation analysis. And on the above basis, we proposed a much more concise way---component extraction method of partial least squares regression. We proved the nature of partial least squares regression by analysis and illustrated the reasons that the PLS (the abbreviations of partial least squares) method can overcome multiple correlation. When it comes to the interpretation of coefficients carried out by PLS method, what should be noted is that coefficients of the regression equations are no longer marginal effects of independent variables on the dependent variables. Therefore the coefficients can not be explained by ordinary PLS regression, instead, they can be analyzed from the point of view of their contribution rate to the construction of the equation. After that, we designed the program of relative algorithm with MATLAB, which in more detail is the general calculation program showing the indicators in the mathematical model of water resources carrying capacity. The model is a mathematical model of a river basin water resources carrying capacity calculation, according to the data information, we used PLS to calculate and get the indexes of water resources carrying capacity. The indexes include:surplus of water in the basin, carrying population of basin water resources, the total water supply guaranteed rate under optimal configuration. And we got their mathematical expression and the regression model, then analyzed the results of the model calculations.