Application Research Of Based On Different Penalty Function Constraint Partial Least Squares

With the development of science and technology, the handling problem of high dimensional data increasingly attract people's attention. It will encounter various problems in the analysis process of high dimensional data, such as multi variables but little samples. Using the traditional multivariate statistical methods to deal with data will lead to the phenomenon of excessive fitting, so traditional multivariate statistical methods couldn't solve the problems at present. Although Partial Least Squares Regression method can solve the problem of multi variables but little samples, it will not automatically select variable. If we can find a method that makes some coefficients of unimportant variable to be zero, and only pick out the important variables, which can achieve the purpose of the variable selection and minimize the prediction error at the same time. Then it will have a very important significance for high-dimensional data processing problems. Therefore, this article mainly studies the following contents:The first part we mainly introduces the background, purpose and meaning of the research,and the research of the improvement on the Partial Least Squares algorithm at home and abroad.The second part we introduces the principle and properties of the multivariate linear regression model, and studies several penalty functions which constrains least squares,including ridge regression penalty, LASSO penalty, the elastic net penalty, the SCAD penalty, then studies their algorithm and parameter selection in detail. At the same time we introduces the modeling steps of partial least squares and the selection problem of principal component number.The third part through the improvement of the Partial Least Squares regression, we join three different penalty function in the process of modeling: LASSO penalty, the elastic net penalty and the SCAD penalty, and research their algorithm. At the same time we carry on a comparison between three kinds of algorithms through real corn light data, concludethat LASSO penalty constraint Partial Least Square regression method is better than the other two penalty function constraint Partial Least Squares method.The fourth part discusses the Partial Least Squares regression algorithm based on convex constraints, we introduce a formal framework to improve the algorithm, and by solving a relaxed SIMPLS punishment to optimize problem, and make a detailed research on the steps and algorithm of Regularized Partial Least Squares. Finally we put the sensitivity and specificity as evaluation standard, carries on the comparative study through the simulated data,and concluded that the convex constrained Partial Least Squares algorithm is superior to other methods.