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

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  • Bel, L.
  • Allard, D.
  • Laurent, J.M.
  • Cheddadi, R.
  • Bar-Hen, A.

Abstract

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 Vorono 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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:8:p:3082-3093
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    References listed on IDEAS

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    1. Hennig, Christian & Hausdorf, Bernhard, 2004. "Distance-based parametric bootstrap tests for clustering of species ranges," Computational Statistics & Data Analysis, Elsevier, vol. 45(4), pages 875-895, May.
    2. Gey, Servane & Poggi, Jean-Michel, 2006. "Boosting and instability for regression trees," Computational Statistics & Data Analysis, Elsevier, vol. 50(2), pages 533-550, January.
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    Cited by:

    1. LeSage, James & Banerjee, Sudipto & Fischer, Manfred M. & Congdon, Peter, 2009. "Spatial statistics: Methods, models & computation," Computational Statistics & Data Analysis, Elsevier, vol. 53(8), pages 2781-2785, June.
    2. Avner Bar-Hen & Servane Gey & Jean-Michel Poggi, 2021. "Spatial CART classification trees," Computational Statistics, Springer, vol. 36(4), pages 2591-2613, December.
    3. Hossein Haroonabadi, 2014. "Islanding Detection in Micro-grids using Sum of Voltage and Current Wavelet Coefficients Energy before the Main Circuit Breaker Side," Asian Engineering Review, Asian Online Journal Publishing Group, vol. 1(1), pages 1-12.
    4. Avner Bar-Hen & Servane Gey & Jean-Michel Poggi, 2015. "Influence Measures for CART Classification Trees," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 21-45, April.
    5. Sophie Dabo-Niang & Camille Ternynck & Anne-Françoise Yao, 2016. "Nonparametric prediction of spatial multivariate data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 428-458, June.

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