Digital Signal Processing Reference
In-Depth Information
2.2
Case Study
Suppose that there are 3 base classifiers in the ensemble. We consider several repre-
sentative cases as shown in Fig. 1.
a) (0,0,0)
b) (2/3,2/3,0)
c) (1,1,0)
d) (2/3,2/3,1/3)
e) (2/3,2/3,2/3)
f) (2/3,2/3,2/3)
g) (2/3,2/3,1)
h) (2/3,2/3,2/3)
i) (2/3,2/3,1)
j) (2/3,1,1)
k) (1,1,1)
Fig. 1.
Case study of the diversity measures, supposing that the ensemble comprises of 3 base
classifiers. The shade stands for the part of objects misclassified and the number in the paren-
theses denotes the classification accuracy of each base classifier.
The values of the diversity measures can be calculated according to the formulas
listed in the precedent section and the results are shown in Table 1. The up/down
arrow in the table means that the bigger/smaller value the measure has, the more di-
verse the base classifiers are. From the table, we can get the following observations.
1.
The values of E and KW are proportional to those of Dis
av
, while the change of θ
is very similar to that of
. In fact, it is pointed out by Kuncheva
[17]
that KW
differs from Dis
av
only by a coefficient. We imagine that other measures may have
similar internal relation between them.
2.
None of the measures can differentiate all the cases. For example, Q
av
can not dif-
ferentiate case d) and f), nor can it differentiate case g) and j). Though these cases
are obviously different, Q
av
takes the same value for them.
3.
All the diversity measures except DF
av
is irrelevant to the accuracies of the base
classifiers.
ρ
Due to the defect of the discussed diversity measures as described in observation 2,
one can not expect too much for obtaining an accurate description of the practical
diversity among the base classifiers by them.
