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Spatial CART classification trees

Author

Listed:
  • Avner Bar-Hen

    (Cnam)

  • Servane Gey

    (Univ. Paris)

  • Jean-Michel Poggi

    (Univ. Paris-Saclay
    Univ. Paris)

Abstract

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.

Suggested Citation

  • Avner Bar-Hen & Servane Gey & Jean-Michel Poggi, 2021. "Spatial CART classification trees," Computational Statistics, Springer, vol. 36(4), pages 2591-2613, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01091-6
    DOI: 10.1007/s00180-021-01091-6
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    References listed on IDEAS

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    3. Avner Bar-Hen & Nicolas Picard, 2006. "Simulation study of dissimilarity between point process," Computational Statistics, Springer, vol. 21(3), pages 487-507, December.
    4. Wagner Martin & Zeileis Achim, 2019. "Heterogeneity and Spatial Dependence of Regional Growth in the EU: A Recursive Partitioning Approach," German Economic Review, De Gruyter, vol. 20(1), pages 67-82, February.
    5. Luc Anselin & Arthur Getis, 2010. "Spatial Statistical Analysis and Geographic Information Systems," Advances in Spatial Science, in: Luc Anselin & Sergio J. Rey (ed.), Perspectives on Spatial Data Analysis, chapter 0, pages 35-47, Springer.
    6. Bel, L. & Allard, D. & Laurent, J.M. & Cheddadi, R. & Bar-Hen, A., 2009. "CART algorithm for spatial data: Application to environmental and ecological data," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 3082-3093, June.
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