Kernel Principal Component Regression Method On Feature Extraction And Prediction Also Its Application In Medicine

In medical research, we often encounter that response variables and explanatory variables show non-linear relationship or impossible to establish the exact function of them. There are two traditional way to extract the functional relationship between response variables and explanatory variables from sample. One is observing the scatter plot of them, then determining the relationship, but it is hard to implement with numerous variables and complicated relation of them. The other is describing non-liner relationship or complicated relation approximately by liner relationship, however, this method is infeasible when obviously non-liner relationship between them and impossible to establish approximate linear relationship by variable transform.For non-linear variables, we can transform them into high-dimensional space linear variables in order to find optimal separating surface in transform space. However, it is usually difficult to accomplish. Fortunately, we can transform the original problem into the dual problem. Both optimizing function and classification function are only involve with inner product operation between the training samples, so the method of calculation in high-dimensional space is only require inner product operation. Thus the computational complexity is no longer depend on space dimension, but the number of samples, especially the number of support vectors in each sample. These characteristics make it possible to overcome problems among high-dimensional, because inner product operation can be achieved from the function of the original space, which even do not need form transformation. According to the relevant functional theory, if the kernel function satisfies the Mercer condition, it will correspond to an inner product in a transform space.Principal component regression is a combination of principal component analysis (PCA) and multiple linear regression analysis method, which mainly use to solve problems of high-dimensional linear. In this study, principal component analysis of kernel functions were used to extract characteristics of the complexed data, meanwhile, principal component regression model which based on chaotic time series were used to predict regresstion of non-liner data, as a result, function of principal component analysis were extend from liner data processing to non-liner. This method has great advantages. First, it overcomes the limitation of principal component analysis which only can process liner data by mapping non-liner data to liner data in high dimensional space. Second, it can make full advantage of the information of sample distribution to establish model of the relationship between response variable and explanatory variable, which can greatly improve the fitting precision and prediction accuracy of the model.In this study, SAS8.0, MATLAB7.1 and LIBSVM2.91 sofewar were used to program and analyze, then get reasonable regression model and expanation. At last we verificated it in case application of medical statistics. Meanwhile, it was comparied with other methods of characteristic extraction and prediction, which indicated that Kernel principal component regression was better at non-linear and complex relationships. Thus, it provides a new way in medical statistical research.