摘要： 提出了一种新的基于分类的SVM非线性回归算法(CSVR),首先将Y扩展为Y+ε和Y-ε两个数据集,再将n维输入空间X中的数据连同Y+ε和Y-ε组成n+1维空间χ中的两类数据,并用Z∈{+1,-1}来标识两类数据,再利用标准的SVM二分类算法求解。利用该算法对一系列的基准函数进行测试,取得了令人满意的结果。该算法对噪声数据不敏感,具有较好的鲁棒性,并且可以根据实际需要设定ε的大小,防止出现过拟合现象。该算法由于不需要先验地建立一个参数未知的回归模型,因此可以用在其他传统统计回归算法失效的场合。

关键词: 非线性, 回归算法, 支持向量机

Abstract: A novel SVM nonlinear regression algorithm based on classification(CSVR) is proposed to solve the difficult problem of obtaining nonlinear regression function Y =f(X) under the condition of having no knowledge about regression model.First,Y is extended into two data sets,Y + ε and Y-ε.Then two n+1 dimension data sets labeled with Z∈{+1,-1} are achieved by adding n-dimension data of input space X to those two data sets.Next the two nonlinear unclassified data sets are transformed to linear classified data sets in a higher dimension feature space by a particular mapping function Φ.Finally,the paper trains the data sets with standard SVM two classification algorithm.Experiment is conducted on a series of benchmark functions and the result shows that the approach is satisfactory.This algorithm is robust and insensitive to noise.It can prevents from over-fitting by setting the value of ε empirically.Since the algorithm does not require a prior regression model with unknown variables,it can be utilized in the circumstances where other traditional statistical regression algorithms fail.

中图分类号: 

• TP18