Weighted CART with spatially split rules: A new kernel-based approach in spatial classification trees

Machine learning algorithms are commonly utilized for independent observations and may not be efficient for analyzing spatial data sets since dependency is present in all directions. In spatial data sets, due to spatial correlations between observations, the independence assumption is violated; thus, some modifications are necessary for accurate analysis. In this article, the well-known CART algorithm is adapted to the spatial domain by proposing two new approaches, namely kernel-based weighted CART and kernel-based weighted CART with spatially split rules. The first approach suggests kernel-based weights as a new method for weighting the observations according to their spatial locations. The weights are inversely proportional to the density of the data location. We also use the Voronoi and Kriging weights, all of which assign less weight to clustered data than others. The second approach is defined based on spatial entropy as an impurity criterion in the weighted CART to achieve a more accurate algorithm. Findings are evaluated by conducting simulation studies and analyzing a real data set to highlight the advantages and limitations of the proposed approaches. The numerical results indicate that the proposed W-CART-SSR algorithm with class-based kernel weight outperforms other algorithms in terms of accuracy, tree structure, and implementation time.