CART algorithm for spatial data: Application to environmental and ecological data

Most statistical learning techniques such as Classification And Regression Trees (CART) assume independent samples to compute classification rules. This assumption is very practical for estimating quantities involved in the algorithm and for assessing asymptotic properties of estimators. In many environmental or ecological applications, the data under study are a sample of some regionalized variables, which can be modeled as random fields with spatial dependence. When the sampling scheme is very irregular, a direct application of supervised classification algorithms leads to biased discriminant rules due, for example, to the possible oversampling of some areas. The CART algorithm is adapted to the case of spatially dependent samples, focusing on environmental and ecological applications. Two approaches are considered. The first one takes into account the irregularity of the sampling by weighting the data according to their spatial pattern using two existing methods based on Voronoï tessellation and regular grid, and one original method based on kriging. The second one uses spatial estimates of the quantities involved in the construction of the discriminant rule at each step of the algorithm. These methods are tested on simulations and on a classical dataset to highlight their advantages and drawbacks. They are then applied on an ecological data set to explore the relationship between pollen data and presence/absence of tree species, which is an important question for climate reconstruction based on paleoecological data.