剔除支持向量回归中异常数据算法

定义了回归问题中异常数据及其不满足回归映射关系差异程度的度量，分析了回归问题中理论映射模式与回归估计模式关系，提出并证明了回归问题中逐个剔除异常数据，建立回归估计模式逐步逼近理论模式的逐步逼近定理，并构建了以逐步逼近定理为理论依据的剔除支持向量回归中异常数据算法，理论分析了算法的收敛性和有效性。然后，引入逐步搜索算法改进剔除异常数据算法以解决大规模样本的支持向量回归中异常数据剔除问题，理论分析显示改进算法也是收敛的和有效的。最后，应用给定已知函数生成样本和UCI机器学习数据库样本数据仿真实验，结果显示算法是有效的和鲁棒的。

Algorithm of removing outliers in SVR

The outlier and the measurement that an outlier does not fit the theoretical model in the regression problems are defined. The relationship between the theoretical model and the regression model in the regression problem is analyzed. An approximate theorem is proposed and verified by deleting outlier one by one to construct SVR to approximate the theoretical model. An algorithm of detecting outliers in the SVR problems is constructed based on the approximate theorem. The theoretical analysis of the convergence and effectiveness of the proposed algorithm is given. Then, the step-by-step search algorithm is introduced to improve the outlier removing algorithm to remove outliers in SVR with large-scale samples. The theoretical analysis shows that the improved algorithm is convergent and effective. Finally, the samples produced by two test functions and the samples in UCI data set are used for simulation, and the results show that the proposed algorithm is effective and robust.