顾及空间异质性的自适应IDW插值算法

An Adaptive IDW Algorithm Involving Spatial Heterogeneity

传统的反距离加权(inverse distance weighted,IDW)插值法存在以假设空间过程平稳为前提,且插值过程需要用户提供初始化参数如分区数目、参考样点个数等的问题,因此提出一种顾及空间异质性的自适应IDW插值算法。该算法首先根据样点待插值属性数据的数理统计特征自适应设定分类阈值,将全部样点按照属性值大小分成高、中、低三类,其次利用机器学习算法k近邻法(k-nearest neighbor,k-NN)判定待插值点所属类别,然后根据分类结果自适应为待插值点一阶邻近样点,并设置相应的权重调和因子,最后构造出一个集空间相关与空间异质性于一体的IDW插值算法模型。实验结果表明,顾及空间异质性算法无需用户提供任何经验参数,其抗粗差的能力较另3种经典IDW插值算法更强,能够有效提高IDW插值算法的精准度。

An adaptive inverse distance weighted(IDW)algorithm involving spatial heterogeneity to solve some problems existed in the classical IDW is proposed.The first problem is that classical IDW algorithms are heavily dependent on the spatial stability.Another one is that the initial parameters are determined by the users empirically,such as the number of stratums or sample points.The k-nearest neighbor IDW(k AIDW)algorithm can take both spatial correlation and heterogeneity into account simultaneously without the needs of parameters input for users.Firstly,k AIDW sets the classification threshold adaptively for each sample point according to the statistical characteristics of the sample data and then divides the reference points into high,medium and low categories.Secondly,the k-nearest neighbor algorithm is used to determine the category of the interpolation point.According to the classification result,different weight adjustment coefficients are adaptively determined for the first-order neighboring samples of the point to be interpolated.Finally,an IDW interpolation algorithm model integrating spatial correlation and heterogeneity is constructed.In order to validate the effectiveness of the algorithm,two different practical applications are adopted.By comparing with three classical IDW algorithms,we find out that the k AIDW can effectively improve the accuracy of the IDW interpolation algorithm without the user providing any empirical parameters.