带惩罚项的自适应非参数回归方法

Method of Non-parametric Regression with Penalty Term to Determine Adaptively the Fitting Function

针对曲线拟合问题,提出了用带惩罚项的自适应非参数回归方法来确定一组数据的拟合函数,并主要讨论了此方法中正则化参数的确定问题,其中包括凭主观选择法和交叉验证法以及通过非线性函数方程来确定正则化参数.最后,采用Matlab编程对一些实际例子进行了试算,其中应用了不同的方法,并且对一个实际问题采用不同方法进行了处理,并做出了比较.通过比较可看出,用带惩罚项的自适应非参数回归方法来确定一组数据的拟合函数的效果良好.

Aiming at curve fitting question, a method of non-parametric regression with penalty term to determine adaptively the fitting function of a group of data is presented, emphasing on the problem of determining the regular parameter of the method, including subjective back-and-forth method and cross validating method. With these methods the regular parameter are determined certainly by means of nonlinear function equations. Fanally, some examples are computed with different methods by Matlab programming. With these actual examples, the results are compared through various methods. This shows these methods are effective.