Paysages virtuels et analyse de scénarios pour évaluer les impacts ...

eached. The graphical structure of DTs makes them easy to read, to interpret or to design, in comparison to
black-box classifiers like neural networks, generalized linear models or maximal likelihood classifiers (Pal
and Mather, 2003). Such DTs are deterministic, so that two instances carrying the same values for their
attributes will be routed by the same test nodes to identical decision leaf.
DT do not require to be built with expert knowledge and they can be extracted from a learning dataset. We
used the C4.5 algorithm (Quinlan, 1993) because it can handle both discrete (the 10 crop classes, the three
soil waterlogging classes) and continuous attributes (distance-to-farmstead and field area are real numbers)
without making any assumption on the distribution of the input attributes (Friedl and Brodley, 1997). The
learning dataset supplied to C4.5 must contain instances characterized by explanatory attributes (the
observed current crop, field area, field distance-to-farmstead, soil waterlogging class) and one target
attribute (the observed next crop). The learning process starts with the “tree growing” phase, which
recursively subdivides the learning dataset into smaller partitions, by testing the values of explanatory
attributes and maximizing the information gain ratio. The information carried by a dataset partition is
evaluated by an indicator derived from the Shannon entropy index (Shannon, 1948):
m
infoT =−∑ p log j/ T 2 p j/T , withp = j/T
j=1
n j/T
m
where info(T) is the information entropy of data partition T, log2 is the logarithm function to base 2, m is the
number of crop classes, pj/T is the proportion of instances in T carrying the crop class j. Pj/T is therefore the
ratio between nj/T, the number of instances carrying class j in T, and the total number of instances of T.
Given a test X that partitions T into n outcomes, the total information content after applying X is the sum of
the information of the sub-partitions weighted by the number of instances in each sub-partition:
m
n ∑ n j/T i
j=1
infoX T =∑ infoT i
i=1
m
∑ n j/T
j=1
The information gained by splitting T using X is:
gain X =infoT −info X T (10)
∑ j=1
The gain criteria selects the test for which gain(X) is maximum.
III. Stochastree, un modèle de successions de cultures basé sur des arbres de décision stochastique – p. 80
n j/ T
(8)
(9)