Under-sampling technique for imbalanced data using minimum sum of euclidean distance in principal component subset

IAES International Journal of Artificial Intelligence (IJ-AI)
Vol. 13, No. 1, March 2024, pp. 305~318
ISSN: 2252-8938, DOI: 10.11591/ijai.v13.i1.pp305-318  305
Journal homepage: http://ijai.iaescore.com
Under-sampling technique for imbalanced data using minimum
sum of euclidean distance in principal component subset
Chatchai Kasemtaweechok1
, Worasait Suwannik2
1
Department of Computer Science and Information, Faculty of Science at Sriracha, Kasetsart University, Chonburi, Thailand
2
Department of Computer Science, Faculty of Science, Kasetsart University, Bangkok, Thailand
Article Info ABSTRACT
Article history:
Received Jan 18, 2023
Revised Apr 26, 2023
Accepted May 7, 2023
Imbalanced datasets are characterized by a substantially smaller number of
data points in the minority class compared to the majority class. This
imbalance often leads to poor predictive performance of classification models
when applied in real-world scenarios. There are three main approaches to
handle imbalanced data: over-sampling, under-sampling, and hybrid
approach. The over-sampling methods duplicate or synthesize data in the
minority class. On the other hand, the under-sampling methods remove
majority class data. Hybrid methods combine the noise-removing benefits of
under-sampling the majority class with the synthetic minority class creation
process of over-sampling. In this research, we applied principal component
(PC) analysis, which is normally used for dimensionality reduction, to reduce
the amount of majority class data. The proposed method was compared with
eight state-of-the-art under-sampling methods across three different
classification models: support vector machine, random forest, and AdaBoost.
In the experiment, conducted on 35 datasets, the proposed method had higher
average values for sensitivity, G-mean, the Matthews correlation coefficient
(MCC), and receiver operating characteristic curve (ROC curve) compared to
the other under-sampling methods.
Keywords:
Classification algorithms
Data preprocessing
Hybrid methods
Imbalanced data
Sampling methods
This is an open access article under the CC BY-SA license.
Corresponding Author:
Chatchai Kasemtaweechok
Department of Computer Science and Information, Faculty of Science at Sriracha, Kasetsart University
199 Moo 6, Sukhumvit Road, Tung Sukla, Sriracha, Chonburi, Thailand
Email: chatchai.ka@ku.th
1. INTRODUCTION
Data mining and machine learning rely on data to train models and make predictions. Thus, the
characteristic of data significantly impacts the performance of machine learning algorithms. An imbalanced
dataset has unequal distribution of classes. There are a small amount of important data represented as positive
class and a large amount of low importance data in in the negative class. This characteristic is frequently
observed in real-world scenarios, such as disease diagnosis [1], fraud monitoring [2], computer network
intrusion [3], and credit risk [4]. Model trained from imbalanced data sets is unable to effectively classify the
minority class data.
There are three approaches that can be used to address the problem of imbalanced data [5]–[8]: cost-
sensitive, algorithm, and sampling. The first approach, cost-sensitive approach, involves assigning different
cost to different class during the training. Misclassifying instances from the minority class has higher cost. As
a result, cost-sensitivity methods will increase the accuracy of the minority class data so that it is higher than
for the accuracy of the majority class data.
The second approach, known as algorithm approach, improves the algorithms currently in use to deal
with imbalanced data by adjusting classification rules to introduce biased against a minority class. Algorithm

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approaches can be divided into two categories: one-side learning and ensemble learning [9]. The first type,
one-side learning algorithms, train a model for only one class. For example, a one-sided fuzzy support vector
machines based on sphere method introduces a hypersphere reduction approach by finding minimal
hypersphere of the majority class to reduce the majority noises [10]. Another example is weighted one class
support vector machine method, where the algorithm assigns higher weight to prediction of the minority class
to minimize the influence of the majority class on support vector machine class classification [11]. The second
type is ensemble learning algorithms. These methods are applied as bagging and boosting algorithms to
improve classification performance in imbalanced data sets such as random under-sampling (RUS) with a
boosting algorithm [12], AdaBoost with clustering algorithm [13], fuzzy rough set theory [14], and bagging
techniques with replacement with the segregation of majority and minority classes [15].
The third approach, sampling approach, involves changing the size of either majority or minority class
to achieve a balanced dataset. There are three types of sampling methods: over-sampling, under-sampling, and
hybrid techniques. The oversampling methods add to the synthesized training data by randomly generating a
minority data of the attributes from samples in the minority class. The synthetic minority over-sampling
technique (SMOTE) algorithm is a popular over-sampling method [16]. This method reconstructs the minority
by randomly interpolating between two neighboring minority points. The SMOTE can be improved by
regenerating the minority class only in the border region of minority clusters [17] or in the highest safe area of
the minority class point [18]. Some over-sampling methods combine several clustering techniques to create
minority clusters and then add a new minority class such as DBSCAN, clustering using representatives
(CURE)-SMOTE [19], k-means SMOTE [20], radius-SMOTE [21], and Gaussian Kernels with diagonal
smoothing matrices [22].
Under-sampling methods remove majority data from the training data set using a variety of criteria
such as decision boundary, the redundant majority class groups, and the majority class groups that are close to
or overlapping with the minority class groups. The Tomek link method (TML) [23] removes majority classes
when nearby data is noise or border data. The one-side selection method (OSS) [24] deletes majority classes
when they are redundant data that is far from the data border using Hart’s condensing technique or borderline
data that is close to boundary between majority and minority regions using Tomek link technique. The
neighborhood cleaning rule method (NCR) [25] was introduced to screen most of the data classes minus
Wilson’s editing techniques [26] that find and remove noisy data from the dataset. The instance hardness
threshold method (IHT) [27] was presented for deleting most of the hardness data that are a misclassified from
multiple models. The hardness of a data point can be determined based on three metrics: k disagreeing
neighbors, class likelihood, and class likelihood difference. Finally, the NearMiss method (NRM) [28] was
proposed to remove majority class data that are close to minority class data. The method described above uses
the nearest neighborhood principle to find majority class data that are close to minority class data or a majority
class that is far from other majority class groups as the decision criterion for reducing the size of the data.
Some under-sampling algorithms use clustering techniques to group majority class, and then applying
the majority reduction. A cluster-based instance selection that combines the use of affinity propagation and
k-means techniques to cluster the majority class into subsets and to select representatives from the subsets
using some algorithms: genetic algorithm, instance based learning, and decremental reduction optimization
procedure. The clustering-based undersampling method selects k cluster centers from k-mean algorithm [29].
The DBIG-US algorithm [30] is a two-step process of selecting the majority class clusters. The density-based
spatial clustering of applications with noise (DBSCAN) algorithm screens the noisy majority class in the first
step. The second step selects most representatives of the data using a graph-based procedure. The balanced
data set derived from the DBIG-US algorithm increases the geometric mean of the classification. The
undersampling framework with denoising, fuzzy c-means clustering, and representative sample selection
(UFFDFR) algorithm uses three techniques [31], where the first step removes noisy, boundary, and redundant
data in majority clusters with Tomek links. The second step clusters the majority data based on fuzzy c-means
clustering. The last step selects the most representatives using the max-min concept.
Hybrid methods combine the benefits of both under-sampling and over-sampling by combining the
process of removing noise in the majority classes with the synthetic minority class creation process. Bagging
and boosting ensemble methods have been proposed to optimize the screening of majority classes or to create
new minority classes [32], [33]. The SMOTETomek method [34] uses the SMOTE method to equalize the
minority of the data with the majority, and then uses the Tomek link technique to reduce noise and decision
border data. A balanced data selection method expands the efficiency of discriminating the minority class
through filtering and transforming the noisy majority class to a minority class with relabeling and amplification
techniques [35]. A clustering and density-based hybrid (CDBH) method segments the minority class using the
k-means clustering algorithm [36].
In general, the sampling methods are independent of classifier and have a wide range of applications.
It has been reported that under-sampling methods are more efficient than over-sampling methods because the

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Under-sampling technique for imbalanced data using minimum sum … (Chatchai Kasemtaweechok)
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latter tend to cause over-fitting [37]. However, under-sampling methods can exclude some useful majority
class information from the training data.
To overcome this limitation, this study presents a method for selecting representative instances from
the majority class using principal component analysis (PCA), which is widely used for reducing dimensions
and data clustering [38]–[40]. PCA transforms all numerical columns into principal component (PC) columns,
resulting in a reduced number of columns compared to the original dataset. The primary goal of this analysis
is to preserve the data's variability through new PC axes derived from eigenvectors and eigenvalues of the
covariance matrix. PC columns are sorted in descending order based on the variance of the projected data. PC1
represents the axis with the highest variance, while the subsequent PCs represent progressively lower amounts
of variance [41]–[45].
After the transformation, the majority class representatives in each partition (i.e., subset of instances)
are selected from the data with the smallest sum of Euclidean distances between other data sets within the same
partition. The number of the partition is equal to the number of minority instances. The training data sets
derived from the proposed algorithms are compared with the results from six currently used algorithms using
35 data sets, based on the predictive efficiency of five indicators: sensitivity, specificity, G-mean, Matthew’s
correlation coefficient (MCC) and receiver operating characteristic curve (ROC curve).
2. METHOD
This study introduces a new under-sampling method to keep only majority classes which have the
minimum sum of the Euclidean distance principal component value (PC-MIN) for imbalanced data
classification. The method leverages the minimum sum of Euclidean distances within a principal component
subset (i.e., a column-wise subset in the transformed space). By applying this algorithm, the number of
instances belonging to the majority classes in the training dataset can be significantly reduced, approaching the
quantity of instances in the minority class groups. Following the under-sampling process, the resulting training
dataset with balanced classes is utilized to train three classification models, with performance evaluation of
classification using the imbalanced test data set, as shown in Figure 1.
Figure 1. Process flow of PC-MIN method
In algorithm 1, the PC-MIN pseudocode has three input variables: majority data (MJ), minority data
(MN), and variance ratio (VR). The seven steps of the algorithm can be divided into two parts: data transformation
and selection of representative majority instances. The first four steps belong to the first part. The specific pseudo

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code for each function is omitted due to its well-established nature. In our implementation, we simply call
functions from a library. The 1st
step, Normalize_Standard_Scale normalizes the values in each column to the
standard z-score. The 2nd
step, Transform_PC_Data, converts the z-score to PC columns. The 3rd
step,
Get_PC_Columns, calculates the number of PC columns based on variance ratio within the range of 0 to 1. The
4th
step, Create_PC_Table, creates a data table using the number of PC columns obtained from the previous step.
The second part of Algorithm 1 selects representative of majority instances from each partition.
Sort_Data sorts the majority class instances in ascending order based on their PC values (i.e., starting with
PC1, then PC2, and so on). After that, Split_MajorityData_into_Partition divides the majority class data into
disjoint partitions based on the order of sorted instances.
Algorithm 1. PC-MIN
Input: MJ: Majority Data, MN: Minority Class, VR: Variance Ratio
Output: BS: Balanced Dataset
1: SDF = Normalize_Standard_Scale (MJ)
2: PCD = Transform_PC_Data (SDF)
3: PC_COLS = Get_PC_Columns (PCD, VR)
4: PC_DF = Create_PC_Table (PCD, PC_COLS)
5: PC_DF = Sort_Data(PC_DF)
6: PDF = Split_MajorityData_Into_Partition (PC_DF, Size(MN))
7: RS = [ ]
8: for i = 1 to Size(MN) do
9: REP = Get_Representative (PDFi)
10: Append REP to RS
11: end for
12: BS = Create_Balance_Dateset (RS, MN)
13: return BS
Next, Get_Representative selects majority class representatives of each partition. This selection is
based on identifying data points with a minimum distance from other data points within the same partition.
Algorithm 2 shows the pseudocode for Get_Representative, which takes the PC columns table (PDFi) as input.
First, a square metric table, pdist, is created by calculating pairwise Euclidean distance between n data points
as shown in Table 1. Then, a list of total distance to all instances in the same partition, sumdist, is calculated.
In the set of data points in the partition PDFi, the criteria for selecting representatives can be expressed using
(1). The final step of Algorithm 1 creates a balanced dataset by combining representative of majority data with
minority data. The balanced dataset (BS) is returned as a result by the PC-MIN algorithm.
𝑅𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑎𝑡𝑖𝑣𝑒 = 𝑎𝑟𝑔 𝑚𝑖𝑛
𝑥𝑖,𝑦∈𝑃𝐷𝐹𝑖
∑ 𝑑(𝑥𝑖 − 𝑦)
𝑛
𝑖=1 (1)
Algorithm 2. Get_Representative
Input: PDFi : a set of majority data in partition i
Output: REP : a representative of partition i
1: pdist = Create_PairwiseDistances_Metric(PDFi)
2: mindist = MaxFloatValue()
3: for i = 1 to Size(PDFi) do
4: if sumdist(i) < mindist
5: REP = Get_Majority_Data(i)
6: mindist = sumdist(i)
7: end if
8: end for
9: return REP
Figure 2 visualizes how to partition and select representatives in PC-MIN algorithm. The algorithm
takes advantage of PCA to reduce the dimensionality of the data. Figure 2(a) shows the dataset that was
transformed from high dimension to 2 dimensions, PC1 and PC2, from the six datasets: abalone, libras_move,
ozone_level, wine_quality, breast-cancer, and colon-cancer. In this experiment, the PC-MIN algorithm uses
only the 2-dimensional PC to capture the essence of higher dimensions in 19 datasets.
In Figure 2(b), the representives have minimum sum of distance in each partition. To ensure clarity and avoid
confusion, we have chosen a subset of the dataset and limited the number of partitions to fewer than 20.

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(a) (b)
Figure 2. Scatter plots of PC1 and PC2 for (a) data points of assigned partitions (colored dot) and
(b) representative (colored star) of the six datasets

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Table 1. Pairwise distances between n data points in m -dimensional space
Distance metric x1 x2 … xi … xn Sumdist
y1 𝑑(𝑥1 − 𝑦1) 𝑑(𝑥2 − 𝑦1) … 𝑑(𝑥𝑖 − 𝑦1) … 𝑑(𝑥𝑛 − 𝑦1) Sumdist(1) = ∑ 𝑑(𝑥𝑖 − 𝑦1)
𝑛
𝑖=1
y2 𝑑(𝑥1 − 𝑦2) 𝑑(𝑥2 − 𝑦2) … 𝑑(𝑥𝑖 − 𝑦2) … 𝑑(𝑥𝑛 − 𝑦2) Sumdist(2) = ∑ 𝑑(𝑥𝑖 − 𝑦2)
𝑛
𝑖=1
… … … … … … … …
yi 𝑑(𝑥1 − 𝑦𝑖) 𝑑(𝑥2 − 𝑦𝑖) … 𝑑(𝑥𝑖 − 𝑦𝑖) … 𝑑(𝑥𝑛 − 𝑦𝑖) Sumdist(i) = ∑ 𝑑(𝑥𝑖 − 𝑦𝑖)
𝑛
𝑖=1
… … … … … … … …
yn 𝑑(𝑥1 − 𝑦𝑛) 𝑑(𝑥2 − 𝑦𝑛) … 𝑑(𝑥𝑖 − 𝑦𝑛) … 𝑑(𝑥𝑛 − 𝑦𝑛) Sumdist(n) = ∑ 𝑑(𝑥𝑖 − 𝑦𝑛)
𝑛
𝑖=1
3. RESULTS AND DISCUSSION
A test was conducted to determine the performance of the PC-MIN algorithm based on comparisons
with six currently used algorithms obtained from the imbalanced-learn library [46]: IHT, NRM, NCR, OSS,
RUS, and TML. Table 2 lists the undersampling algorithms compared and the parameters used in testing each
method. Additionally, the baseline model was trained from the original imbalanced data set (FULL) to be
normalized in this experiment.
Table 2. List of compared methods
Methods Parameters
IHT sampling_strategy = auto, random_state = 42, cv = 5, estimator = RandomForestClassifier
NRM n neighbors = 3
NCR threshold_cleaning = 0.5, n_neighbors = 3, kind_sel = all
OSS random_state = 42, n_seeds = 1
RUS sampling_strategy = auto, random_state = 42, replacement = False
TML random_state = 42
The PC-MIN algorithm that appears in algorithm 1 has three input variables: majority class (MS),
variance ratio (VR), and minority class (MR). The two variables MS and MR have values and data items that
depend on the data set used in the test and as such cannot be adjusted. Therefore, in this experiment, the PC-
MIN algorithm was adjusted for the required coverage variance (VR) using five values: 0.5 (PC-MIN50), 0.4
(PC-MIN40), 0.3 (PC-MIN30), 0.2 (PC-MIN20), and 0.1 (PC-MIN10).
Table 3 shows the details of the 35 test data sets. The data were sorted by data set name [47]–[49]. In
Table 3, the fifth column shows the number of principal component columns used by the PC-MIN30 algorithm.
In almost all of the datasets in this experiment, this number is less than 10 columns, with the exceptions of the
gisette and madelon datasets. For high dimensionality performance tests, we tested methods performance using
the six data sets [50]: breast-cancer [51], colon-cancer [52], gisette [53], leukemia [54], madelon [53], and w1a
[55]. The current study used a 5-folds cross-validation test. The resulting data sets of each method were used
to train three classification models (support vector machine, random forest, and AdaBoost).
In this study, the performance of the classification models trained with training data from all methods
was compared based on five indicators [56]. The first two sensitivity (recall) or true positive rate (TPR)
measured the effectiveness of the classification of the model in each class. The positive class classification
accuracy rate, was calculated using (2). The specificity or true negative rate (TNR) metric indicates the rate of
accuracy in classifying negative classes, as shown in (3). The false positive rate (FPR) is the proportion of all
negatives that be predicted positive by model, as shown in (4).
In this experiment, positive classes were represented as minority class groups and negative classes
were majority class groups.
𝑠𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦 =
𝑇𝑃
(𝑇𝑃+𝐹𝑁)
(2)
𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 =
𝑇𝑁
(𝑇𝑁+𝐹𝑃)
(3)
𝑓𝑎𝑙𝑠𝑒 𝑝𝑜𝑠𝑖𝑡𝑖𝑣𝑒 𝑟𝑎𝑡𝑒 =
𝐹𝑃
(𝐹𝑃+𝑇𝑁)
(4)
Where true positive (TP) is the number of correctly predicted responses in the positive class, false positive
(FP) is the number of incorrectly predicted response in the positive class, true negative (TN) is the number of
correctly predicted responses in the negative class, and false negative (FN) is the number of incorrectly
predicted responses in the negative class. Additionally, this study used three indicators to assess the efficacy
of a balanced classification model that weighed two classes. The first was the Matthews correlation coefficient

311
(MCC) is a measure of association for true and predicted values, as shown in (5). The G-means indicator is
commonly used in this area of research and is defined as the average between sensitivity and specificity as
shown in (6). The measure of the ROC curve shows the probability that a classification model predicts a true-
positive class is higher than for a false-positive class, as shown in (7).
𝑀𝐶𝐶 =
(𝑇𝑃 ∙𝑇𝑁)−(𝐹𝑃 ∙ 𝐹𝑁)
√(𝐹𝑃+𝑇𝑃)(𝑇𝑃+𝐹𝑁)(𝑇𝑁+𝐹𝑃)(𝑇𝑁+𝐹𝑁)
(5)
𝐺 − 𝑚𝑒𝑎𝑛 = √𝑠𝑒𝑛𝑡𝑖𝑣𝑖𝑡𝑦 × 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑖𝑡𝑦 (6)
𝑅𝑂𝐶 𝑐𝑢𝑟𝑣𝑒 =
1 +𝑇𝑃𝑅−𝐹𝑃𝑅
2
(7)
To compare the performance based on MCC, G-means, and A, we used a t-test between the PC-MIN
algorithm’s average and the compared algorithm. This was divided into two hypotheses. In the benchmark
comparison test, MCC, G-means, and ROC curve test assumed the null hypothesis H0: the averages of the PC-
MIN algorithm and the compared algorithm are not significantly different. The alternative hypothesis was H1:
the average for the PC-MIN algorithm is higher than the average for the compared algorithm at a significance
level of 0.1.
Table 3. Data set information
Dataset Imbalance ratio Number of samples Number of features PC-MIN30 columns
abalone 9.7:1 4,177 10 2
abalone19 130:1 4,177 10 2
arrhythmia 17:1 452 278 5
breast-cancer 4.2:1 26 7,129 2
car_eval34 12:1 1,728 21 5
car_eval4 26:1 1,728 21 5
coil_2000 16:1 9,822 85 6
colon_cancer 8:1 45 2,000 2
credit_card 577.8:1 284,807 29 8
drunk 26.4:1 595,212 57 9
ecoli 8.6:1 336 7 2
gisette 100:1 3,030 5,000 53
isolet 12:1 7,797 617 3
letter_img 26:1 20,000 16 2
leukemia 3.8:1 24 7,129 2
libras_move 10:1 360 90 2
madelon 12:1 1,728 20,958 62
mammography 42:1 11,183 6 2
oil 22:1 937 49 2
optical_digits 9.1:1 5,620 64 4
ozone_level 34:1 2,536 72 2
pen_digits 9.4:1 10,992 16 2
protein_homo 111:1 145,751 74 2
satimage 9.3:1 6,435 36 2
scene 13:1 2,407 294 3
sick_euthyroid 9.8:1 3,163 42 2
solar_flare_m0 19:1 1,389 32 3
spectrometer 11:1 531 93 2
thyroid_sick 15:1 3,772 52 4
us_crime 12:1 1,994 100 2
w1a 649:1 3,900 300 10
webpage 33:1 34,780 300 8
wine_quality 26:1 4,898 11 2
yeast_me2 28:1 1,484 8 2
yeast_ml8 13:1 2,417 1,031 5
3.1. Individual class classification performance
In Figure 3 shows the average sensitivity and specificity of the PC-MIN algorithm and the eight
algorithms compared in the three models. The average sensitivity of the models obtained from the four PC-
MIN algorithms was greater than 80%, which was higher than for all the methods compared in Figure 3(a).
These results indicated that the classification models obtained from all the PC-MIN algorithms could predict
the positive class data with an accuracy of more than 80% of the total number of positive class data.
Figure 3(b) shows the average specificity of the PC-MIN algorithm and the compared algorithms. The average
specificity of the PC-MIN algorithm was less than the values for the FULL, NCR, OSS, and TML algorithms.

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The results showed that the negative class data were correctly classified by the PC-MIN algorithm for
approximately 80% of all negative class data. The average sensitivity values of the FULL, NCR, OSS, and
TML methods were lower than 50% while these models had high specificity rates of 90%. The NCR, OSS, and
TML methods removed few majority classes so the number of majority classes from these methods was not
different from that of the original dataset (FULL). Due to the substantially larger size of the majority class data,
the specificity rates of the NCR, OSS, and TML algorithms were much higher than their sensitivity rates.
Otherwise, the NRM, IHT, and RUS methods achieved a balance between sensitivity and specificity.
RUS had the second-highest sensitivity rate, while also having a high specificity rate. The average sensitivity
and specificity values of the PC-MIN algorithm were greater than those for the RUS, IHT, and NRM methods.
Considering both values simultaneously as shown in Figure 4, all PCMIN algorithms and the RUS, IHT, and
NRM algorithms provided sensitivity close to the specificity, while the PC-MIN30 algorithm provided a higher
level of sensitivity than those of the IHT, NRM, and RUS algorithms by approximately 15%, 10%, and 3%,
respectively. Furthermore, the remaining three algorithms (NCR, OSS, and TML) provided much higher
specificity than sensitivity because they selected data sets that caused the classification model to weigh the
accuracy of the negative class predictions over the positive class predictions based on the asymmetric nature
of the data set.
(a) (b)
Figure 3. Average (a) sensitivity and (b) specificity of PC-MIN and compared methods using three
classification models
Figure 4. Average sensitivity and specificity comparison of PC-MIN30 and compared methods

313
Figure 5(a) shows that the PC-MIN30 algorithm had the highest sensitivity among all the algorithms
evaluated. In contrast, Figure 5(b) shows that the specificity distribution of the FULL, NCR, OSS, and TML
methods had very small variances and high values, while the specificity of the PC-MIN algorithms was
lower. However, the PC-MIN30 algorithm had a better balance between both sensitivity and specificity than
the other algorithms.
(a) (b)
Figure 5. The distributions of compared methods for (a) sensitivity and (b) specificity
3.2. Overall classification performance
Figure 6 shows the average MCC value of the PC-MIN algorithm was higher than the average of the
other algorithms for the three classification models, except for the NCR, OSS, and TML algorithms using the
AdaBoost model. The model obtained from the PC-MIN algorithm was able to give a higher association of
true and predicted values than the other algorithms. Figure 7 shows the average G-Mean of the PC-MIN
algorithm was higher than the other algorithms. These results indicated that the classification models based on
the PC-MIN method could predict both classes with a higher balance than the other algorithms. Figure 8 shows
the average ROC curve value of the PC-MIN algorithm was higher than the average of the other algorithms for
the three classification models. The model obtained from the PC-MIN algorithm had a higher ratio of true
positive rate prediction to the false positive rate than the other algorithms.
Figure 6. Average values for MCC of PC-MIN and
compared methods using three classification models
Figure 7. Average G-mean of PC-MIN and compared
methods using three classification models

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Among the three classification models from the PC-MIN30 algorithm, the averages for random forest
were higher than for the AdaBoost and support vector machine models. This difference is indicative of the
random forest model's effective utilization of selected data, resulting in 10% more accurate decision trees
compared to those generated by the random forest using the FULL. Similarly, the support vector machine
model using the PC-MIN30 algorithm showed classification performance that was 5% superior to that of the
support vector machine using the FULL. However, the performance of the AdaBoost model using the PC-
MIN30 algorithm did not differ significantly from that of the AdaBoost model using the FULL. Consequently,
the under-sampling algorithm provided a smaller training dataset that facilitated the creation of decision trees
capable of more efficient classification compared to the other two models.
Figure 8. Average ROC curve of PC-MIN and compared methods using three classification models
The average G-mean of all algorithms are presented in Figure 9(a). The PC-MIN30 algorithm clearly
had smaller G-mean distribution boxes than the other methods. This could be attributed to the fact that the
classification models based on the PC-MIN30 algorithm provided more stable sensitivity and specificity
metrics than did the other algorithms across all test datasets. Specifically, the PC-MIN30 algorithm had the
highest ROC curve, with lower variance in Figure 9(b), indicating that the balanced datasets generated by the
PC-MIN30 algorithm improved the predictive performance in the positive class of classification models.
Table 4 shows the average values for MCC, G-mean, and ROC curve of the classification models
using the PC-MIN30 algorithm were significantly greater than those of the classification models based on the
other algorithms. From these statistical comparison results, PC-MIN30 provides higher MCC, G-mean, and
ROC curve values than almost compared algorithms, except for MCC of NRM. These results showed that the
classification models from PC-MIN30 correctly classified most of the minority classes while the majority
prediction rate was high. When handling high-dimensional datasets, PC-MIN30 had lower average specificity
values than FULL, NCR, and TML; however, for other metrics it had higher performance values than those for
other under-sampling methods, and FULL as shown in Table 5.
Three algorithms could be used to reduce the small amount of majority class data and create an
imbalanced dataset: NCR, TML, and OSS. The NCR algorithm screens most of the data classes minus Wilson’s
editing techniques that find and remove noisy data from the dataset. The TML algorithm removes majority
classes when nearby data are noise or border data. The OSS algorithm removes majority classes when they are
redundant data that are far from the data border (using Hart’s condensing technique) or borderline data that are
close to the boundary between majority and minority regions (using the TML technique). By using these
techniques, The NCR, OSS, and TML algorithms can remove a few majority classes, so the number of majority
classes from these methods is not different from that of the original dataset (FULL). Due to the substantially
larger size of the majority class data, the specificity rates of the NCR, OSS, and TML algorithms were much
higher than their sensitivity rates. For this reason, the MCC and G-mean values of these algorithms were nearly
equal to that of PC-MIN30. On the other hand, their AUC values were lower than that of PC-MIN30.

315
The remaining compared algorithms created balanced datasets by reducing most of the majority class
data. First, the IHT method deleted most of the hardness data that were misclassified by multiple models.
Second, the NRM method removed majority class data close to minority class data. The method described
above used the nearest neighborhood principle to find majority class data close to minority class data or a
majority class that was far from other majority class groups as the decision criterion for reducing the size of
the data. Both methods balanced datasets by removing majority class data near the decision boundary based on
the nearest neighbor. This technique may work well with dense majority class groups. The MCC and G-mean
values of both methods were lower than those of PC-MIN and other methods due to low sensitivity and
specificity. However, their AUC values were comparable to those of other methods except for PC-MIN30.
Lastly, RUS create a balanced dataset by randomly selecting majority class data without replacement.
In RUS, each majority data point was chosen with an equal and fair probability. Due to high sensitivity and
specificity, the G-mean and AUC values of RUS were high compared to the other methods because the random
selection process of RUS selected majority class data that were widely spread over the distribution of the
majority data. However, all performance indicators of RUS were quite lower than those of PC-MIN30 because
RUS may have encountered limitations when dealing with some high-dimensional datasets. By using PCA to
reduce the dimensionality of the data, only the first few principal components are retained, and a lower-
dimensional plane is identified that captures the information of the dataset. This results in closer proximity of
the PC majority data partitions, which reduces the complexity of majority data selection. The small size of data
in selected PC columns could capture the information of the majority of the data so the PC-MIN30 algorithm
conveniently selected the appropriate set of majority class representatives.
(a) (b)
Figure 9. The distributions of compared methods for (a) G-mean and (b) ROC curve
Table 4. Results of the t-test for MCC, G-mean, and ROC curve comparisons
Compared methods MCC G-mean ROC curve
p-value Result p-value Result p-value Result
PC-MIN30 vs. FULL 0.0774 Reject H0 4.9607e-10 Reject H0 2.1558e-11 Reject H0
PC-MIN30 vs. IHT 3.3326e-05 Reject H0 9.9963e-10 Reject H0 4.5422e-09 Reject H0
PC-MIN30 vs. NRM 5.1105e-06 Reject H0 3.3991e-07 Reject H0 6.3678e-07 Reject H0
PC-MIN30 vs. NCR 0.1025 Accept H0 6.6343e-09 Reject H0 5.3936e-11 Reject H0
PC-MIN30 vs. OSS 0.0944 Reject H0 1.4221e-09 Reject H0 1.3223e-10 Reject H0
PC-MIN30 vs. RUS 0.0015 Reject H0 8.3600e-04 Reject H0 4.0531e-04 Reject H0
PC-MIN30 vs. TML 0.0846 Reject H0 3.0199e-09 Reject H0 2.8340e-11 Reject H0
Table 5. Results of five performance measures for PC-MIN30 compared to the other methods for high-
dimensioned datasets
Measures Methods
PC-MIN30 FULL IHT NRM NCR OSS RUS TML
Sensitivity 75.17 39.49 59.8 62.73 40.94 44.38 69.12 41.51
Specificity 83.91 91.34 59.87 71.18 91.17 89.74 76.34 90.49
G-mean 78.09 54.29 36.08 41.88 56.25 50.8 71.68 52.5
MCC 0.432 0.387 0.267 0.296 0.39 0.389 0.369 0.386
ROC curve 0.794 0.629 0.593 0.671 0.634 0.645 0.727 0.621

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4. CONCLUSION
This experiment presented a method called ‘PC-MIN’ that reduced most of the data set by selecting
the majority class with the smallest sum of Euclidean distances between other majority classes within the
similarity group. The PC-MIN30 algorithm produced a balanced training data set to train classification models
that generated more balanced and stable predictions of sensitivity and specificity than from using other
algorithms. The values for sensitivity, MCC, G-mean, and ROC curve of the PC-MIN algorithm were higher
than for other methods. However, the PC-MIN algorithm had lower specificity than many of the algorithms
compared in the experiment because those algorithms aim to increase or decrease the amount of data generated
that could classify almost all minority class data but could only partially correctly classify majority class data
in order to achieve better results for sensitivity, G-mean, and ROC curve. In contrast, the PC-MIN algorithm
selected data sets that generated highly sensitive classifying models for a minority class by selecting majority
data at the center of the majority class. Consequently, the classification models derived from the PC-MIN
algorithm predicted a smaller majority class and increased the likelihood of predicting minority classes.
Therefore, the PC-MIN algorithm is suitable for tasks that require higher sensitivity than specificity, such as
investment analysis involving high profit potential with low investment and pre-diagnosis screening of patients.
The PC-MIN algorithm is limited in use where there are large outlier and noisy data sets because selecting
majority data that is at the center of the data group may result in the PC-MIN algorithm selecting some of the
outlier or noisy data. The PC-MIN algorithm can continue to evolve in parallel computing and distributing
processing architectures for improved efficiency in processing and handling large data sets.
ACKNOWLEDGEMENTS
This research was also supported by the Faculty of Science at Sriracha, Kasetsart University under
Grant Sci-Src01/2564. We would like to give thankful to Research and Development Institute, Kasetsart
University for supporting proofreading services.
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BIOGRAPHIES OF AUTHORS
Chatchai Kasemtaweechok received the Ph.D. degree in computer science from
Kasetsart University. He was programmer and senior programmer with IBM software partner
for ten years. He is lecturer with the Computer Science and Information Department, Faculty
of Science at Sriracha, Kasetsart University Sriracha Campus. His research interests include
data pre-processing, data reduction, and parallel computing techniques. He can be contacted at
email: chatchai.ka@ku.th.
Worasait Suwannik received the Ph.D. degree in computer engineering from
Chulalongkorn University, Thailand. He is an Associate Professor at the Faculty of Science,
Kasetsart University. He is an industry-certified security professional (CISSP, CISA). His
research interests include artificial intelligence and parallel programming. He can be contacted
at email: worasait.suwannik@gmail.com.

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