中文摘要：

径向基函数（Radial Basis Function,RBF）是一种确定性的多维空间插值模型,可以有效逼近任意维度的空间数据。RBF插值模型中,基函数形态参数直接影响插值精度。为了快速求解最佳形态参数,获取准确的插值结果,该文采用改进的逐点交叉验证（Improved Leave One Out Cross Validation,ILOOCV）方法求取最优形态参数,首先从形态参数取值区间内选定初始形态参数α,然后从n个已知点中顺序选出一个点,使用剩下的n-1个已知点构建RBF插值模型,计算被取出点处真实值与插值结果的误差,循环n次,累计交叉验证误差,再依次从形态参数取值区间选取下一个值,重复操作,建立形态参数α与累计交叉验证误差之间的函数映射关系,最后通过最小化交叉验证误差来获取最佳形态参数。以我国东北地区气象观测数据进行实验,对ILOOCV方法进行验证,结果表明ILOOCV方法选取最佳形态参数使其插值结果比较精确,是一种可行的RBF形态参数优化方法。

英文摘要：

Radial Basis Function（RBF）can effectively approximate arbitrary dimension spatial data,which is a deterministic multivariate spatial interpolation method.In RBF interpolation model,the shape parameter in the basis function has a direct impact on the accuracy of the interpolation.In order to get optimal shape parameter which leads to smallest interpolation error and obtains the most accurate interpolated results,the Improved Leave One Out Cross Validation（ILOOCV）approach is applied in this paper.First,the initial shape parameterαis selected from the shape parameter interval which are divided by the step const value,then sequentially choose one point from then known points as the verify point and use the n-1remaining known points to calculate the RBF interpolation model.After that,the interpolated value of the point which are taken away from the n known points by the RBF interpolation model is calculated and compared with the true value of the known point to get the interpolation error,then these operations are repeated for ntimes until all the points are left out to be chosen as the verify point and the cross validation interpolation error is accumulated.After all these steps have been done,another shape parameter from the shape parameter interval is taken according to the step const value and the leave one out cross validation is repeated until all the shape parameters have been used to calculate the accumulated cross validation interpolation error,then the mapping relationship between the selected shape parameter and the accumulated cross validation interpolation error is established.Finally,to minimize the accumulated cross validation interpolation error in each leave one out cross validation process to get the smallest error and take the correspondingαas the optimal shape parameter.The meteorological observation data in Northeast China are taken as examples to verify the feasibility and effectiveness of this approach.Results show that,the optimal shape parameter selected by ILOOCV turns out to be eff