回归问题中的k近邻加权方法研究

Research into the Weighted k-nearest Neighbor Method for Regression

针对回归问题分析了常用的k近邻加权回归算法的特点,给出一种基于k近邻的改进加权方法.根据每个样本在整个样本空间中所处的位置的不同来计算不同的权重值,更好地描述了样本点的局部性质.理论上,我们给出了改进方法与原始计算权重方法所得的权重值之间的关系,证明了我们的改进方法能够更好的描述离群点和具有重要局部性质的样本点.另外,我们还将这种新的加权方法推广到支持向量回归机和最小二乘支持向量回归机中,实验验证了所提方法的有效性.

In this paper,we analyze the unreasonable parts of the common k nearest neighbor weighted regression algorithm,and give a reasonable k nearest neighbor weighted regression algorithm. Especially we accurate the different weight value precisely according to each sample＇s position in the whole sample space,so as to much better describe the local property of the sample points.Through the theorem form of this paper,we describe the relationship of weight value which is given by our improved method and the original weight value,and then the theorem proves that the improved method can be better describe outliers and sample points which has important local property. In addition,we will also generalize this newmethod to support vector regression machine and least squares support vector regression machine,the experiment verified the effectiveness of this weighted way.