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t -Test Results a,b
Methods in Group 1
Table 4.4
Methods in Group 2
12-7-11
Under-Ada
Under-RF
14-6-10
Over-Ada
9-7-14
Over-RF
8-11-11
SMOTE
15-8-7
15-7-8
26-12-12
Chan
17-0-13
24-4-22
BRF
7-11-12
12-15-23
Asym
13-7-10
18-18-14
SMB
20-7-3
40-7-3
Easy
17-5-8
29-9-12
Cascade
a Data is derived from [6].
b The table shows the win-tie-lose counts of method in row versus method
in column.
Ensemble methods for CIL (Group 3) are generally better than standard meth-
ods (Group 1) and methods in Group 2, except Asym . The bad performance of
Asym may be due to the fact that it is a heuristic boosting method designed
for cost-sensitive problems. Among these methods, Chan , Easy ,and Cascade
perform better than the others.
Among these CIL methods, SMB and over-sampling are most time consuming,
as the data samples they use to generate classifiers are the largest. While BRF ,
Chan , Easy ,and Cascade are least time consuming, they are as efficient as
under-sampling.
It is worth noting that although stacking is a popular combination strategy for
ensemble learning, it could be harmful when handling imbalanced data. Liu et
al. [6] reported a significant decrease in the performance of EasyEnsemble and
BalanceCascade when they use stacking to combine base learners. In imbalanced
data, the minority class examples are often rare when they are used for multiple
times as in EasyEnsemble and BalanceCascade; stacking has a great chance to
over-fit.
4.5 CONCLUDING REMARKS
Ensemble learning is an important paradigm in machine learning, which uses a
set of classifiers to make predictions. The generalization ability of an ensemble
is generally much stronger than individual ensemble members.
Ensemble learning is very useful when designing CIL methods. The ensemble
methods are roughly categorized into Bagging-style methods, such as UnderBag-
ging, OverBagging, SMOTEBagging, and Chan; boosting-based methods, such
as SMOTEBoost, RUSBoost, and DataBoost-IM; and hybrid ensemble methods,
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