Multivariate Statistical Regression Methods Based On Kernel Function

In order to improve the ability of processing nonlinear data in complex process industry, the kernel partial least-squares regression(KPLSR) and kernel independent component regression(KICR) are put forword. These methods make full use of the advantage of kernel to deal with nonlinear problem in process industry.The paper deduces the KPLSR and KICR algorithm on the basis of PLSR and ICR which deals with linear problem. In the KPLSR algorithm, the kernel function is used to change the training sample data from the lower dimensions of nonlinear mapped to high dimensional linear feature space in which PLSR was used to predict value; genetic algorithm is used to optimize the kernel parameter called C; enter the test sample and the C value in KPLSR algorithm to obtain the prediction. In the KICR algorithm, the kernel function is used to change the training sample data from the lower dimensions of nonlinear mapped to high dimensional linear feature space in which PCA and FastICA were used to obtain KIC; build the the least-squares regression model in which KIC as the independent variable and the real value matrix as the dependent variable; enumeration method is used to optimize the kernel parameter called C; enter the test sample and the C value in KICR algorithm to obtain the prediction.This paper bliud the converter steel-making endpoint temperature prediction model based on KPLSR and KICR method. The predicted results of the them are compared separately with PCR and PLSR and ICR to validate the effectiveness in practical application. Compare the prediction results of the KPLSR and KICR to validate the theory of KPLSR and KICR process data from different aspects.