IEEE Computational Intelligence Magazine - February 2021 - 97

Therefore, cost-sensitive learning
could help GP to address its performance
bias issue and improve its c- lassification
performance in unbalanced classification. As acknowledged, in cost-sensitive
learning, when the cost information
is unknown, the acquirement of a cost
matrix is essential but difficult. In this
regard, ICS-GP does not require a manually designed cost matrix, and can
automatically obtain and determine the
needed cost intervals to build the costsensitive classifiers.
We have presented a method where
cost intervals are co-learned with classifiers. However, in ICS-GP, for a GP individual, the learned cost interval could
not be decoupled from the classifier
which has been evolved together. In the
future, we will explore how the generality of the learned cost information can be
improved by using ensemble learning
with ICS-GP, i.e., how the learned cost
information can be used by different
kinds of classifiers, how the performance
of these cost-sensitive classifiers can be
evaluated and be effectively combined to
improve the overall performance.

whether there is a direct or indirect relationship between IR and the evolved
cost information.
VIII. Conclusions and Future Work

In this paper, we investigated how GP is
used to automatically learn cost intervals
for constructing cost-sensitive classifiers
in high-dimensional unbalanced classification. In the proposed GP method
(ICS-GP), a new tree representation, terminal and function sets were designed to
make a GP individual with the capability to construct a classifier and learn a
cost interval simultaneously. For each
tree in a population, the cost interval
represented by its right sub-tree will be
later used by the classifier represented by
its left sub-tree in the evaluation to
make this algorithm sensitive to different
classification mistakes.
In the experiments, we tested the
effectiveness of ICS-GP on ten highdimensional unbalanced datasets. The
experimental results show a good classification performance of ICS-GP. By comparing ICS-GP with the baseline GP
methods, ICS-GP achieves significantly
better or similar performance in almost
all cases. Compared with GPAucw that
often achieves a very good performance
in unbalanced classification, ICS-GP has
an obvious advantage in efficiency when
achieving significantly better or similar
performance as GPAucw in 9 out of 10
datasets. In addition, by comparing ICSGP with other non-GP methods, ICSGP also achieves similar or significantly
better performance in most cases.

Acknowledgment

This work was supported in part by the
Marsden Fund of New Zealand government under contracts VUW1509 and
VUW1615, the Science for Technological Innovation Challenge (SfTI)
fund under grant E3603/2903, the
University Research Fund at Victoria
U n ive r sity of Wellington (g rant
number 223805/3986), MBIE Data

Cost-Sensitive Classifier

Classifier

T_Cost

f245

AddCost
AddCost

(1.79, 1.69)

(1.58, 1.32)

MulCost

(1.80, 1.63)

FIGURE 6 An evolved tree by ICS-GP on Armstrong-2002-v1.

(1.20, 1.56)

Science SSIF Fund under the contract
RTVU1914, and National Natural Science Foundation of China (NSFC),
under grant 61876169, 61672276 and
51975294. Wenbin Pei was supported by
China Scholarship Council/Victoria
University Scholarship.
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