Spatial CART Classification Trees

Avner Bar-Hen (1) , Servane Gey (2) , Jean-Michel Poggi (3)

1 CEDRIC - MSDMA - CEDRIC. Méthodes statistiques de data-mining et apprentissage
2 MAP5 - UMR 8145 - Mathématiques Appliquées Paris 5
3 LMO - Laboratoire de Mathématiques d'Orsay

Based on links between partitions induced by CART classification trees and marked point processes, we propose a variant of spatial CART method, SpatCART, focusing on the two populations case. While usual CART tree considers marginal distribution of the response variable at each node, we propose to take into account the spatial location of the observations. 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 heterogene-ity function consistent with the CART original algorithm. Then different pruning strategies, including the classical pruning step using the misclassification rate, are performed. The proposed procedure is implemented, illustrated on classical examples and compared to natural competitors. SpatCART is finally applied to a tropical forest example.

Mots clés: CART; Bivariate Marked Point Process; Spatial CART; Ripley's intertype Kfunction

Domaines: Statistiques [math.ST]

Avner Bar-Hen, Servane Gey, Jean-Michel Poggi. Spatial CART Classification Trees. 2020. ⟨hal-01837065v2⟩