Spatial CART classification trees

We propose to extend CART for bivariate marked point processes to provide a segmentation of the space into homogeneous areas for interaction between marks. While usual CART tree considers marginal distribution of the response variable at each node, the proposed algorithm, SpatCART, takes into account the spatial location of the observations in the splitting criterion. We introduce a dissimilarity index based on Ripley’s intertype K-function quantifying the interaction between two populations. This index used for the growing step of the CART strategy, leads to a heterogeneity function consistent with the original CART algorithm. Therefore the new variant is a way to explore spatial data as a bivariate marked point process using binary classification trees. The proposed procedure is implemented in an R package, and illustrated on simulated examples. SpatCART is finally applied to a tropical forest example.