IEEE Computational Intelligence Magazine - February 2021 - 91

This study focuses on binary highdimensional unbalanced classification. In
the experiments, ten datasets (gene
expression datasets [44])1 are used to
examine the performance of the proposed method. The details of these datasets are reported in Table 2, including the
number of features and instances, and
class imbalance ratio ( IR = #Maj/#Min,
where #Maj and #Min stand for the
number instances in the majority class
and the minority class, respectively).
According to Table 2, the ten datasets are unbalanced and contain a small
number of instances described by a
large number of features. Therefore, these
datasets may encounter the joint effect of
class imbalance and high-dimensionality.

The Test Process
During the test process, a new classification threshold TH3 is defined as:

1
These datasets are available at http://csse.szu.edu.cn/
staff/zhuzx/Datasets.html;https://schlieplab.org/Stat
ic/Supplements/CompCancer/datasets.htm

	

TH 3 =

We chose the ten datasets because of
the following reasons. First, for each
dataset, its IR is greater than or equal to
2. Second, several of the datasets have
different imbalance ratios (i.e., four
datasets with IR = 2; two datasets with
IR = 3; two datasets with IR = 5; two
datasets with IR = 8). Third, across the
ten datasets, the number of features
varies from hundreds to tens of thousands. Therefore, the performance of
the proposed method could be comprehensively examined to some extent.
Note that gene expression datasets
usually do not have a sufficient number
of instances for both the majority class
and the minority class, so their imbalance
ratios are usually less than 6. In order to
examine the classification p- erformance
of the proposed method on some highly-unbalanced binary datasets, tomlins2006-v1 (5 classes) and Lung (5  classes)
are changed into highly-unbalanced binary datasets. For tomlins-2006-v1, class 5
(12 instances) is used as the minority class,
and the rest of classes are combined
together (92 instances) as the majority
class. For Lung, class 1 is -selected as the
majority class (139 instances), and class 2

instances that are directly predicted
into Min, and max (PMin) is the maximum value in PMin).

Step2: The output value of its right
sub-tree is an evolved cost interval
(C l, C u ), and then C_ max and
C_middle are obtained;
Step3: TH1 and TH2 are calculated
by Eqs. (9) and (10), respectively;
Step4: The constructed classifier (represented by the left sub-tree) uses TH1
and TH2 as classification thresholds to
separately predict Maj and Min. After
that, G_Mean1 and G_Mean2 are calculated and summed together as the
fitness value (according to Eq. (12)).
After the evaluation process, the fitness values are used to select good
individuals by the tournament selection. The genetic operators, e.g., mutation, crossover and elitism, are used to
generate offspring for the new population. The evolutionary learning process
is stopped when a termination criterion is satisfied. Finally, the best individual from the final generation is selected
to make the classification predictions
on a test set.

V. Experiment Design
A. Datasets

C_ min
(13)
C_ min + 1

where C_ min stands for the minimum
cost value in a cost interval. Eq. (13) is
also derived from Eq. (3). TH3 is used
with TH1 and TH2 to predict class labels
of unseen instances. Note that TH3 #
TH 2 # TH 1 (because 0 1 C_ min #
C_middle # C_ max).
Figure 4 explains the classification
process on a test set. For instance x,
❏❏ If p x $ TH1, x is directly classified
to Maj;
❏❏ If p x # TH3 , x is directly classified
to Min;
❏❏ If TH3 1 p x 1 TH1, we use the following rule:
	 If p x $ TH2 and p x is nearer to
min (PMaj) than max (PMin) , then x is
classified into Maj; otherwise it is
classified into Min (where PMaj is a
list of probabilities of instances that
are directly predicted into Maj, and
min (PMaj) is the minimum value in
PMaj; PMin is a list of probabilities of

The Minority Class

TH3

0

The Majority Class

TH2 TH1

1

FIGURE 4 Classification predictions on a test set.

TABLE 2 Dataset description.
DATASET

#FEATURES

#INSTANCES

IR (APPROXIMATION)

ARMSTRONG-2002-V1

1081

72

2

GOLUB-1999-V1

1868

72

2

COLON

2000

62

2

LEUKEMIA (ALL-AML)

7129

72

2

SHIPP-2002-V1

798

77

3

DLBCL

5469

77

3

GORDON-2002

1626

181

5

YEOH-2002-V1

2526

248

5

TOMLINS-2006-V1

2315

104

8

LUNG (BHATTACHARJEE-2001)

12600

156

8

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