An Adaptive IDW Algorithm Involving Spatial Heterogeneity

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 (kAIDW) algorithm can take both spatial correlation and heterogeneity into account simultaneously without the needs of parameters input for users.Firstly, kAIDW 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 kAIDW can effectively improve the accuracy of the IDW interpolation algorithm without the user providing any empirical parameters.