Kernel Principal Component Coefficients In The Multiple Linear Model Estimation And Selection

Kernel Principal Component Analysis as a good nonlinear problem processing tools, has been widely used in various fields. It combines principal component analysis with kernel function. When using it to solve the information redundancy it can ensure the integrity of the original information at the same time. As an extension of the principal component analysis, it broadens the range of application of principal component analysis method.LS estimate is widely used in the linear model regression coefficient of the unbiased estimation. When there are more independent variables or existing non-linear relationship, multiple linear regression model is unstable. The effect of frequently used estimation methods, such as ridge estimation, principal component estimation and partial least squares estimation fitting is not ideal. The kernel principal component estimate is also a biased estimate. The same as Ridge estimation, Stein estimation, it is built on the basis of principal component analysis. Firstly, a full study of principal component analysis and kernel principal component analysis was made. Then, the use of kernel principal component estimation from the nonlinear perspective was proposed. Finally, the concrete implementation steps of kernel principal component estimation was given, and some important conclusions from discussing of kernel principal composition screening guidelines were introduced.The empirical analysis shows that, it successfully avoided the problem of multicollinearity, because the kernel principal component orthogonal to each other. The kernel principal component analysis method effectively solved the problems of existing non-linear regression model or more complex relationships among variables. And the application of kernel principal component selection criteria, which makes the kernel principal component extraction more standardization.