Page 91 - Contributed Paper Session (CPS) - Volume 2

CPS1440 Avner Bar-Hen et al.
So, we first use two simulated examples to check that CART and SpatCART
behave as expected: (a) a control example where the Bayes classifier is a
classification tree. In this case, the two algorithms must find a partition close
to the partition defined by the underlying model. (b) an example where the
classification problem is trivial, and where the interaction between marks plays
an important role. In this case, SpatCART must produce splits significantly
different from those produced by CART.

b. An application
We applied these methods to a tropical rain-forest located at Paracou, 40
km west from Kourou in French Guiana (5°15'N, 52°55'W). It is an experimental
site that is devoted to studying the effects of logging damage on stock
recovery. A more precise description of the Paracou plots may be found in [7].
We focus on two species Vouacapoua americana and Oxandra asbeckii
selected at Paracou because their spatial distribution is linked to the relief:
they are both located on hill tops and slopes. Elevation is the environmental
factor that drives their spatial distribution and this creates a strong interaction
between both repartitions. The data consists of seventy lines (one per tree)
and four columns: the 3-D coordinates (longitude, latitude and elevation) as
well as the specie indication.
SpatCART highlights the presence of Oxandra asbeckii at the hill of left top
of the plot as well as the competition between both species for the hill at the
bottom of the plot. A contrario, CART results are really poor with only two
leaves. Basically it separates the hill at the bottom of the plot from the rest but
cannot catch the mixed structure of species with this hill or the hill at the top
left of the plot. The spatial structure as well as the ecology of the two species
on this plot cannot be inferred from CART results.

4. Discussion and Conclusion
For a marked spatial point process, we consider the problem to segment
the space into homogeneous areas for interaction between marks. The original
CART constructs homogeneous zones with respect to the distribution of the
variable of interest (here, the mark) conditionally to the explanatory variables
(here, the position in space). By modifying the splitting criterion in the CART
algorithm, using an empirical version of the intertype function, we obtain a
new procedure, called SpatCART, adapted to the problem at hand. The
intertype function itself depends on a parameter r which must be carefully
chosen: not to set it once and for all, but rather to start from a rather large
value (at the root of the tree) and gradually decrease it as the tree is built by
SpatCART.
Let us now sketch some perspectives for future work.

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