Robust Regression Based On Maximum Correntropy Criterion Under Multiple Kernels Space

This paper aims to study the robust modeling problem for complex data,and proposes a robust regression learning algorithm based on multiple kernel functions(RR-MCCMK).On the one hand,the single kernel methods encounter the challenges when modeling data of non-flat distribution.On the other hand,the performance of the regression learning algorithm established by the least squares method is not good when the samples contain non-Gaussian noises or outliers,that is,the robustness of the model is poor.Therefore,in this paper,the hypothesis space of regression learning is constructed by multiple kernel functions,which is a linear combination of base kernel functions.And the loss function in the regression learning optimization strategy is replaced by the squares loss function to the maximum correntropy-induced loss function.Then the paper establishes a regression learning algorithm under the framework of structural risk minimization.After that,the theoretical analysis of the proposed algorithm is given.Based on a new error decomposition method and some appropriate assumptions,the learning rate of the proposed algorithm is obtained by establishing its excess error bound.The experiments on the two simulated data sets and two real data sets evaluate the performance of the proposed algorithm and prove the superiority of the proposed algorithm compared to the two comparison algorithms.