A three-step combination strategy for addressing outliers and class imbalance in software defect prediction

IAES International Journal of Artificial Intelligence (IJ-AI)
Vol. 13, No. 3, September 2024, pp. 2987~2998
ISSN: 2252-8938, DOI: 10.11591/ijai.v13.i3.pp2987-2998  2987
Journal homepage: http://ijai.iaescore.com
A three-step combination strategy for addressing outliers and
class imbalance in software defect prediction
Muhammad Rizky Pribadi1,2
, Hindriyanto Dwi Purnomo2
, Hendry2
1
Department of Informatics, Faculty of Computer Sciences and Engineering, Universitas Multi Data Palembang, Palembang, Indonesia
2
Department of Computer Science Doctoral, Faculty of Information Technology, Satya Wacana Christian University, Salatiga, Indonesia
Article Info ABSTRACT
Article history:
Received Jan 15, 2024
Revised Feb 2, 2024
Accepted Feb 10, 2024
Software defect prediction often involves datasets with imbalanced
distributions where one or more classes are underrepresented, referred to as
the minority class, while other classes are overrepresented, known as the
majority class. This imbalance can hinder accurate predictions of the
minority class, leading to misclassification. While the synthetic minority
oversampling technique (SMOTE) is a widely used approach to address
imbalanced learning data, it can inadvertently generate synthetic minority
samples that resemble the majority class and are considered outliers. This
study aims to enhance SMOTE by integrating it with an efficient algorithm
designed to identify outliers among synthetic minority samples. The
resulting method, called reduced outliers (RO)-SMOTE, is evaluated using
an imbalanced dataset, and its performance is compared to that of SMOTE.
RO-SMOTE first performs oversampling on the training data using SMOTE
to balance the dataset. Next, it applies the mining outlier algorithm to detect
and eliminate outliers. Finally, RO-SMOTE applies SMOTE again to
rebalance the dataset before introducing it to the underlying classifier. The
experimental results demonstrate that RO-SMOTE achieves higher accuracy,
precision, recall, F1-score, and area under curve (AUC) values compared to
SMOTE.
Keywords:
Classification
Imbalanced data
Outliers
Software defect prediction
Synthetic minority
oversampling technique
This is an open access article under the CC BY-SA license.
Corresponding Author:
Muhammad Rizky Pribadi
Department of Informatics, Faculty of Computer Sciences and Engineering
Universitas Multi Data Palembang
Palembang, Indonesia
Email: rizky@mdp.ac.id
1. INTRODUCTION
The widespread use of devices in our daily lives has heightened our dependence on various software
systems [1]. Any disruption in the operation of software upon which we heavily rely can lead to severe
consequences [2]. To ensure the flawless functioning of such systems, comprehensive testing procedures are
essential. According to Sava [3], an expert in information technology (IT) security and services market
analysis, global IT spending reached $3.8 trillion in 2020 and was expected to increase by approximately
5.1% to about $4.45 trillion in 2022 [3]. In the IT industry, approximately 35% of total development costs are
allocated to quality control and testing [4].
One significant effort to reduce software testing costs is software defect prediction. It has become a
practical approach to enhance the quality, efficiency, and cost-effectiveness of software testing by focusing
on identifying defective software [5]. Recent research has extensively employed machine learning to develop
models for defect prediction. Various methods have been proposed to address this task, relying on historical
defect data, software metrics, and a chosen prediction algorithm. Techniques such as classification,

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clustering, regression, and machine learning algorithms like artificial neural network, K-nearest neighbor
(KNN), naive Bayes, decision tree, and ensemble methods have been utilized in this field [5]. The successful
prediction of defective software allows for more effective resource allocation by prioritizing software that is
predicted to contain defects [6].
However, datasets for software defect prediction often suffer from class imbalance, where very few
defective software instances are available for comparison with non-defective ones [7]. To address this
imbalance, software engineers can employ data-level techniques to manipulate training data and achieve a
more balanced distribution [8]. These techniques include undersampling, which involves removing some data
from the majority class, and oversampling, where new instances are added to the minority class by
duplicating or creating new samples [9]. While undersampling poses the risk of losing important data,
oversampling, particularly when the number of minority class instances is very small, can lead to a
significant reduction in dataset size and potentially limit classifier performance [10]. One solution for
handling imbalance issues using the oversampling method is the synthetic minority oversampling technique
(SMOTE), which involves adding new instances through the KNN approach [11].
Previous studies have shown that SMOTE can be an effective method for addressing data imbalance
in datasets. However, in the context of software defect prediction datasets, the issue goes beyond data
imbalance; it also involves outliers [12]. While SMOTE is capable of mitigating class imbalance, it does not
address the problem of outliers [13]. Research in software defect prediction is critical, as the quality of the
data used directly impacts the model being developed. Software defect prediction datasets often contain noisy
data with outliers and missing values, which can distort the results [14]. This issue is exemplified in a study
[15] that utilized SMOTE to combat class imbalances in National Aeronautic and Space Administration
(NASA) and least square support vector machine (LSSVM) datasets for classification. The study reported a
low F1-score, such as the PC1 dataset achieving only a score of 0.2807, attributed to the substantial number
of outliers in the training data after oversampling [16]. Supervised learning techniques, extensively employed
in software defect prediction research, are highly sensitive to outliers, which can significantly reduce their
accuracy [17].
Outliers, or anomalous values, refer to data points that significantly deviate from the norm in a
dataset [18]. They are often considered unexpected values that fall outside a reasonable range, thereby
affecting data analysis and the results of statistical tests [19]. Outliers can arise for various reasons, including
measurement errors, data input errors, or very rare and unusual events that influence measurement outcomes
[20]. For instance, if we have a dataset of human heights and one person’s height deviates significantly from
the rest, we classify that individual as an outlier. The presence of extreme outliers can substantially impact
statistical measures like the mean and standard deviation, rendering these measures unrepresentative of the
true data distribution [20]. Consequently, outliers are often identified and considered for removal before
conducting statistical analysis. However, it’s crucial to exercise caution when removing outliers, as doing so
can alter the data distribution and affect the outcomes of statistical analysis [19].
This article introduces a novel model for addressing the class imbalance problem, termed reduced
outliers (RO)-SMOTE. This innovative approach employs efficient algorithms to identify SMOTE-generated
outliers and eliminate them from the training dataset. Following the removal of outliers, the dataset is
resampled using the SMOTE method to achieve data balance. The primary contributions of this paper are:
‒ The introduction of a novel pre-processing technique for addressing data imbalance, RO-SMOTE, which
leverages efficient algorithms to remove outliers after SMOTE oversampling.
‒ An evaluation of the proposed RO-SMOTE using various classifiers and cross-project datasets for
software defect prediction.
‒ A comparative analysis of classifier performance when combined with RO-SMOTE against their
performance when combined with SMOTE.
The remaining sections of this paper are structured as follows: section 2 provides a review of related
work. In section 3, we introduce the proposed model, beginning with an overview of SMOTE and the
efficient algorithm, followed by a detailed explanation of RO-SMOTE. Section 4 presents the experimental
setup and discusses the obtained results. Finally, section 5 offers conclusions and recommendations for future
research.
2. RELATED WORK
A successful strategy for handling imbalanced dataset classification involves adopting a different
perspective by treating the data as anomalies or noise. This is necessary because the initial dataset may
contain irregularities, and some resampling methods, like SMOTE, may inadvertently introduce more noise,
worsening the imbalance problem. High levels of noise within the training dataset can adversely impact
classifier performance, a perspective that several studies have addressed [16].

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Asniar et al. [21] proposed SMOTE-local outlier factor (LOF), which combined SMOTE for
oversampling with LOF for noise detection in three real-world datasets characterized by low imbalance ratios.
However, its performance across various classifiers, datasets with different imbalance ratios, and dimensions
remains uncertain. Additionally, LOF is computationally intensive compared to other techniques. Some
researchers [22], [23] employed the interquartile range (IQR) for outlier detection in their oversampling
method. Initially, they detected outliers within the imbalanced dataset using the IQR algorithm and then
oversampled these identified outliers with replacement to integrate them into the original dataset. Finally, they
applied SMOTE to balance the dataset. The IQR, however, does not account for variations in data distribution
as it relies solely on the two data points, namely Q1 and Q3, to gauge data spread. Consequently, the IQR may
not accurately represent outliers, especially in datasets with diverse distributions [24].
Another technique, the outlier detection-based oversampling technique (ODBOT) [25], was
introduced for imbalance datasets in multi-class scenarios. It clusters data using weight-based bat algorithm
with k-means (WBBA-KM) to identify dissimilarities between minority and majority classes and then
identifies outliers in the minority class by comparing the relationship of differences between the cluster
centers in the minority and majority classes. Samples are generated according to the best minority cluster
boundary. However, the use of the WBBA-KM algorithm comes with high complexity, primarily due to the
time required to construct the hierarchical tree from large datasets [26]. Another study introduced the
selective oversampling approach (SOA) [27], which identifies outliers in minor classes using a one-class
support vector machine (OCSVM) before removing them and oversampling the data with SMOTE and
adaptive synthetic sampling (ADASYN). However, OCSVM’s accuracy may be compromised when dealing
with limited training data, and it can be time-consuming when applied to large datasets [28].
Furthermore, SMOTE-iterative-partitioning filter (IPF) [28] combines oversampling and noise-
filtering methods. The process commences by augmenting the training data through SMOTE, followed by the
removal of noise and boundary samples using the IPF. Although this method was tested on real-world
datasets featuring up to 19 attributes and a minimum imbalance ratio of 35:301, its effectiveness in scenarios
with lower imbalance ratios or greater dimensions has not been investigated. It is important to highlight that
the evaluation focused solely on the C4.5 classifier, utilizing the area under curve (AUC) metric, and did not
extend the analysis to include other classifiers or metrics.
Puri and Gupta [29] proposed a hybrid model named K-means-SMOTE–edited nearest neighbors
(ENN), which integrates bagging, K-means clustering, ENN, and adaptive boosting (AdBoost). In this
approach, the model begins by clustering the training data within individual subsamples through K-means
clustering [29]. Subsequently, it employs SMOTE to oversample data within each cluster and removes noise
using ENN. The study evaluated this approach using real-world datasets with a maximum of 9 attributes, and
it didn’t assess the model’s performance on datasfets with higher dimensions, primarily due to significant
computational time requirements, which placed it last among the fifteen other approaches it was compared to.
In addition, there’s another proposal called noise-adaptive synthetic oversampling technique
(NASOTECH) [30]. NASOTECH makes use of the noise-adaptive synthetic oversampling (NASO) rule,
which involves applying the KNN method to calculate the total distance from each sample in the minority
class to its Kth nearest neighbors. These cumulative distances are then utilized to determine the noise ratio
for each minority class sample, guiding the generation of synthetic samples. The evaluation of this approach
was conducted exclusively with a single classifier, namely the support vector machine (SVM), using
real-world datasets with a maximum of 294 features. However, its performance with other classifiers
employing different operational principles has not been explored.
These research findings illustrate that integrating SMOTE with outlier cleaning methods can
improve the performance of diverse machine learning classifiers. This enhancement is achieved by furnishing
the classifiers with balanced training datasets while minimizing noise. Nevertheless, a few of these studies
have only applied their techniques to a restricted range of classifiers, leaving their effectiveness unexplored
with other classifier types. Furthermore, some studies have neglected the evaluation of crucial performance
metrics. Furthermore, previous research has primarily concentrated on datasets with a restricted number of
attributes. Moreover, none of these studies have tackled datasets with highly severe imbalance ratios.
3. METHOD
This section presents the proposed methodology, which combines SMOTE and efficient algorithms
to address the outlier issue in imbalanced data. Subsection 3.1 describes SMOTE [11] as the basis of the
proposed method. While subsection 3.2 discusses the utilization of efficient algorithms [21] to identify the
outliers generated by SMOTE.

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3.1. Synthetic minority oversampling technique
The SMOTE was initially introduced by Chawla et al. [11]. This method has gained popularity for
addressing class imbalance issues. To tackle class imbalance, the SMOTE technique augments the
underrepresented class with synthetic data, which is generated within the minority class using the KNN
method [5]. SMOTE has been widely adopted by researchers and practitioners, particularly in the context of
software defect prediction, as demonstrated some references [5], [13], [15], [31], [32]. An illustration of the
SMOTE method is presented in Figure 1.
Figure 1. Illustration of SMOTE
SMOTE has two hyperparameters: N, representing the percentage of oversampling for minority
classes (non-defect), and k, which signifies the number of nearest neighbors used to generate synthetic data.
There is no definitive rule for determining the values of k and N. The formula used to generate a new
instance is found in (1). In this way, SMOTE helps optimize the class distribution in the dataset, enhancing
the machine learning model’s ability to recognize and predict the minority class more accurately.
𝑥′
= 𝑥 + 𝑟𝑎𝑛𝑑(0,1) ∗ |𝑥 − 𝑥𝑘| (1)
Algorithm SMOTE(T,N,k)
Input: Number of minority class samples T; Amount of SMOTE N%; Number of nearest neighbors k
Output: (N/100) * T synthetic minority class samples
1. (* If N is less than 100% randomize the minority class samples as only a random percent of them will be SMOTEd.*
2. if N < 100
3. then Randomize the T minority class samples
4. T = (N/100) * T
5. N = 100
6. endif
7. N = (int)(N/100) ( * The amount of SMOTE is assumed to be in integral multiples of 100.*)
8. k = Number of nearest neighbors
9. numattrs = Number of attributes
10. Samples[][]: array for original minority class samples
11. newindex: keeps a count number of synthetic samples generated,
initialized to 0
12. Synthetic[][]: array for synthetic for synthetic samples
(*Compute k nearest neighbors for each minority class sample only.*)
13. for i ← 1 to T
14. Compute k nearest neighbors for i, and save the indices in the nnarray
15. Populate(N, i, nnarray)
16. endfor
Populate(N, i, nnarray) (* Function to generate the synthetic samples. *)
17. while N ≠ 0
18. Choose a random number between 1 and k, call it nn.
This step chooses one of the k nearest neighbors of the k
nearest neighbors of i.
19. for attr ← 1 to numattrs
20. Compute: dif = Sample[nnarray[nn]][attr] – Sample[i][attr]
21. Compute: gap = Random number between 0 and 1
22. Synthetic[newindex][attr] = Sample[i][attr] + gap * dif
23. endfor
24. Newindex++
Synthetic minority oversampling technique

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25. N = N – 1
26. endwhile
27. return (* End of Populate *)
End of Pseudo-Code
3.2. Mining outliers
Outliers are data points or observations that significantly deviate from the expected or typical data
points within a dataset [33]. When the number of outliers increases in an imbalanced dataset, it can lead to a
decline in the performance of the classification algorithm due to reduced model accuracy [25]. In this study,
the identified outliers are primarily derived from synthetic minority class samples created by SMOTE.
This study aims to detect the noise introduced by SMOTE using efficient algorithms, which can
effectively identify outliers based on a point’s distance from its KNN [20]. Another method used for outlier
detection is the LOF. LOF calculates the distance between each data point and other data points within a
specific range to assess the degree of abnormality for each data point in the dataset [34]. However, the LOF
algorithm has some limitations, such as longer execution times and sensitivity to the minimum point value.
The third method used for outlier detection is density-based spatial clustering of applications with noise
(DBSCAN) [35], but it is susceptible to high-dimensional datasets, making it challenging to distinguish
between outlier points and dense points.
The current study seeks to identify outliers generated by SMOTE using an approach recommended
by Ramaswamy et al. [20]. This method offers a more efficient strategy for outlier identification, assigning
distinct outlier levels to each object. It proposes a formulation for recognizing distance-based outliers by
computing the distance between a point and its k-th nearest neighbor. The ranking of each point is
determined by its distance from the k-th nearest neighbor, and the top n points in this ranking are designated
as outliers. Parameters for the number of neighbors (k) and the number of outliers (n) allow for
customization. This approach is grounded in a straightforward and intuitive distance-based outlier criterion,
as articulated by Knorr and Ng: ‘A point p within a dataset is considered an outlier based on two parameters,
k and d, if no more than k points in the dataset are found at a distance of d or less from p’.
This algorithm introduces a new boolean attribute called ‘outlier’ to the provided ExampleSet. If the
‘outlier’ attribute has a true value, it signifies that the corresponding example is an outlier, while a false value
indicates that the example is not an outlier. The ‘outlier’ attribute is set to true for a total of n examples
(where n is determined by the number of outliers parameter). This operator supports various distance
functions, and you can specify your desired distance function by setting it through the distance function
parameter.
Figure 2 illustrates the RO-SMOTE algorithm, which combines SMOTE with the mining outliers
algorithm [20] to obtain training data with minimal outliers before applying it to the learning algorithm. The
core concept involves using SMOTE on imbalanced training data to balance it. However, the results of
balanced SMOTE often contain outliers [36], [37], which can mislead the classifier. Therefore, in the
subsequent step, the mining outliers algorithm [20] is used to remove the detected outliers, resulting in clean
but imbalanced data that is then integrated with the training data. To prepare this data for classifier use,
SMOTE is reapplied to balance it and produce clean, balanced data. Figure 2 offers an overview of this
process.
Figure 2. An overview of the RO-SMOTE mode, illustrating the steps and both the minor and major classes
involved in each step
Figure 3 outlines the specific steps of the proposed process. The process initiated by normalizing the
dataset through Z-score normalization [37]. Subsequently, the normalized dataset underwent resampling
using SMOTE to create balanced data. The outcomes fof data resampling were further refined using an
efficient algorithm since the newly balanced data still contained outliers.

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Figure 3. Flowchart of research process
4. RESULTS AND DISCUSSION
In this section, we discuss the evaluation of RO-SMOTE, which includes assessing its performance
with three different classification algorithms: KNN, SVM, and neural network (NN). We conducted this
evaluation on datasets from 11 cross-projects for software defect prediction, each with varying imbalance
ratios. The evaluation employed multiple metrics, such as balanced accuracy [38], precision, recall, F1-score,
and AUC.
4.1. Datasets
This study utilized datasets from 11 cross-projects for software prediction sourced from NASA and
promise projects. To distribute the dataset, we applied K-fold cross validation (K=10). In this study, one fold
was reserved for testing data, while the remaining nine folds were allocated for training data in each dataset.
Table 1 provides details regarding the number of features, samples, and imbalance ratios for each dataset.
These datasets include attributes like static software metrics that help characterize the presence of defects in
the software.
Table 1. Properties of datasets in 11 projects
Datasets Project #instances #Attributes #defects %defect
NASA MDP CM1 327 38 42 12.84
KC1 2109 22 326 15.4
PC1 679 38 25 10
PROMISE Ant-1.3 125 21 20 16
Ant-1.7 745 21 166 22.28
Camel-1.6 965 21 188 19.48
Ivy-2.0 352 21 40 11.36
Jedit-4.3 492 21 11 2.24
Poi-3.0 442 21 281 63.57
Synapse-1.2 256 21 86 33.59
Velocity-1.6 229 21 78 34.06
4.2. Results discussion for classifier
In this section, we delve into the results of implementing RO-SMOTE with KNN, SVM, and NN
algorithms. The hyperparameters for these classifiers have been optimized using 10-fold grid search, and the
hyperparameter configurations are outlined in Table 2. The inclusion of three distinct algorithms in this paper
serves the purpose of evaluating the compatibility of RO-SMOTE with various algorithms. RO-SMOTE’s
performance was then compared with that of SMOTE to assess the improvement in classifier algorithm

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performance. The performance of each classifier was evaluated based on balanced accuracy,
F1-score, precision, recall, and AUC across all 11 datasets. The results for each classifier are presented in
individual tables. Balanced accuracy score represents an enhanced version of the standard accuracy metric,
specifically tailored to enhance performance on datasets with imbalanced class distributions. It accomplishes
this by calculating the average accuracy for each class individually, as opposed to the aggregation employed
in standard accuracy calculations [38]. The F1-score, on the other hand, is the harmonic mean of precision
and recall from a classification model. In the context of imbalanced datasets, the F1-score serves as a more
reliable alternative to the standard accuracy metric. It provides a more accurate assessment of the model’s
performance, especially when prioritizing the evaluation of minority or critical classes [39].
Table 2. Hyperparameter configuration
Classifier Hyperparameters
SMOTE k = 2
NN training cycles = 200, learning rate= 0.01
KNN k = 5
SVM (linear) Kernel cache = 200
SVM (radial) Kernel gamma = 1.0
SVM (poly) Kernel degree = 2.0
Table 3 compares the performance of SMOTE and RO-SMOTE in the NN classifier. From this
table, the performance of RO-SMOTE was superior to SMOTE in terms of balanced accuracy metrics
(0.42%-5.2%), F1-score (1.18%-4.38%), and AUC (0.50%-5.70%). In terms of precision, RO-SMOTE
outperformed SMOTE in six datasets (0.62%-7.3%), while SMOTE excelled in five datasets (0.34%-3.89%).
Regarding recall, RO-SMOTE was superior in 11 datasets (0.26%-12.29%), while SMOTE only excelled in 2
datasets (1.62%-2.17%).
Table 3. Results summary of NN classifier
Dataset
Metrics
Model Balanced accuracy (%) Precision (%) Recall (%) F1-score(%) AUC (%)
CM1 SMOTE 80.63 79.15 84.19 81.59 0.861
RO-SMOTE 83.06 83.64 82.57 83.10 0.888
KC1 SMOTE 73.39 71.94 77.29 74.51 0.818
RO-SMOTE 75.11 70.87 86.60 77.54 0.832
PC1 SMOTE 82.75 78.47 91.12 84.32 0.887
RO-SMOTE 86.06 81.72 93.33 87.13 0.914
Ant-1.3 SMOTE 86.19 85.75 88.73 87.21 0.889
RO-SMOTE 91.39 93.05 89.67 91.32 0.946
Ant-1.7 SMOTE 77.72 78.98 75.67 77.28 0.838
RO-SMOTE 79.15 78.64 81.05 79.82 0.854
Camel-1.6 SMOTE 74.38 71.97 81.04 76.23 0.810
RO-SMOTE 75.03 73.39 78.87 76.03 0.820
Ivy-2.0 SMOTE 83.49 88.47 77.83 82.80 0.910
RO-SMOTE 85.93 85.59 86.79 86.18 0.924
Jedit-4.3 SMOTE 94.18 93.16 95.42 94.27 0.975
RO-SMOTE 94.60 93.78 95.68 95.68 0.980
Poi-3.0 SMOTE 79.19 78.91 80.86 79.87 0.844
RO-SMOTE 79.85 76.56 86.11 81.05 0.807
Synapse-1.2 SMOTE 79.12 79.45 79.41 79.42 0.846
RO-SMOTE 81.52 80.56 84.17 82.32 0.875
Velocity-1.6 SMOTE 77.13 82.00 72.21 76.79 0.841
RO-SMOTE 80.27 78.11 84.50 81.17 0.832
Table 4 compares the performance of SMOTE and RO-SMOTE in the KNN classifier. The
experimental results demonstrated that RO-SMOTE outperformed SMOTE in terms of balanced accuracy in
nine datasets (0.06%-7.81%), while SMOTE excelled in two datasets (0.48%-4.46%). In terms of precision,
RO-SMOTE excelled in six datasets (0.21%-15.43%), while SMOTE excelled in two datasets
(0.19%-10.47%). RO-SMOTE outperformed in recall in seven datasets (0.12%-14.73%), while SMOTE
outperformed in four datasets (0.31%-17.97%). Furthermore, for the results of the F1-score, RO-SMOTE
produced better results than SMOTE in eight datasets (0.11%-5.93%), while SMOTE excelled in three
datasets (0.4%-3.69%). For AUC, RO-SMOTE excelled in eight datasets (0.20%-2.80%), while SMOTE
excelled in three datasets (0.10%-2.20%).

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Table 4. Results summary of KNN classifier
Dataset
Metrics
CM1 SMOTE 88.09 82.33 97.32 89.20 0.942
RO-SMOTE 88.75 97.76 79.35 87.60 0.954
KC1 SMOTE 85.45 81.21 92.32 86.41 0.928
RO-SMOTE 85.51 81.02 92.81 86.52 0.935
PC1 SMOTE 93.17 89.20 98.35 93.55 0.972
RO-SMOTE 92.69 88.72 98.04 93.15 0.971
Ant-1.3 SMOTE 85.24 80.62 95.18 87.30 0.928
RO-SMOTE 93.05 94.49 92.00 93.23 0.956
Ant-1.7 SMOTE 84.63 79.66 93.44 86.00 0.920
RO-SMOTE 85.80 82.22 91.79 86.74 0.920
Camel-1.6 SMOTE 80.05 74.06 92.53 82.27 0.880
RO-SMOTE 79.95 73.74 93.40 82.41 0.889
Ivy-2.0 SMOTE 90.39 96.06 84.43 89.87 0.946
RO-SMOTE 85.93 85.59 86.79 86.18 0.924
Jedit-4.3 SMOTE 94.08 91.47 97.30 94.29 0.984
RO-SMOTE 95.05 93.13 97.42 95.23 0.986
Poi-3.0 SMOTE 82.20 81.51 84.72 83.08 0.886
RO-SMOTE 83.33 81.72 86.04 83.82 0.914
Synapse-1.2 SMOTE 80.88 85.61 74.71 79.79 0.902
RO-SMOTE 82.27 84.68 81.08 82.84 0.899
Velocity-1.6 SMOTE 77.49 83.60 68.75 75.45 0.872
RO-SMOTE 80.41 78.97 83.48 81.16 0.854
Table 5 presents a comparison of the experimental results of SMOTE and RO-SMOTE in the SVM
classifier on the linear kernel. For balanced accuracy, RO-SMOTE provided better results than SMOTE in
eight datasets (0.18%-6.94%), while SMOTE excelled in two datasets (0.26%-0.28%). In terms of precision,
RO-SMOTE excelled in eight datasets (0.15%-10.42%), while SMOTE excelled in three datasets
(0.23%-1.73%). As for recall, RO-SMOTE excelled in 10 datasets (0.19%-9.02%), while SMOTE excelled in
only one dataset (0.82%). For the F1-Score, RO-SMOTE produced better results in 10 datasets
(0.17%-8.06%), while SMOTE was only superior in one dataset (0.57%). In terms of AUC value,
RO-SMOTE outperformed SMOTE in eight datasets (0.40%-10.90%), while SMOTE excelled in three
datasets (0.40%-0.70%).
Table 5. Results summary of SVM (linear) classifier
Dataset
Metrics
CM1 SMOTE 79.29 79.09 79.98 79.53 0.858
RO-SMOTE 80.86 80.44 81.43 80.93 0.873
KC1 SMOTE 72.46 72.93 71.51 72.21 0.815
RO-SMOTE 72.64 73.08 71.70 72.38 0.811
PC1 SMOTE 80.48 77.77 85.85 81.61 0.852
RO-SMOTE 81.40 77.23 89.31 82.83 0.856
Ant-1.3 SMOTE 82.38 79.11 89.45 83.96 0.867
RO-SMOTE 91.57 89.53 95.00 92.18 0.976
Ant-1.7 SMOTE 76.08 80.09 69.75 74.56 0.827
RO-SMOTE 75.80 79.86 68.93 73.99 0.820
Camel-1.6 SMOTE 65.64 67.90 59.60 63.48 0.719
RO-SMOTE 66.36 68.29 61.35 64.63 0.733
Ivy-2.0 SMOTE 81.26 80.04 83.68 81.82 0.871
RO-SMOTE 83.44 81.25 87.82 84.41 0.889
Jedit-4.3 SMOTE 83.07 84.76 80.73 82.70 0.906
RO-SMOTE 86.13 87.56 84.51 86.01 0.925
Poi-3.0 SMOTE 78.47 76.73 82.18 79.36 0.850
RO-SMOTE 78.21 75.00 85.40 79.86 0.844
Synapse-1.2 SMOTE 75.29 73.71 78.82 76.18 0.802
RO-SMOTE 75.29 72.74 84.33 78.11 0.808
Velocity-1.6 SMOTE 73.52 74.89 70.79 72.78 0.800
RO-SMOTE 80.46 81.90 79.81 80.84 0.845
Table 6 compares the performance of SMOTE and RO-SMOTE in the Radial kernel SVM classifier.
The experimental results show that, in terms of balanced accuracy, RO-SMOTE was superior in eight
datasets (0.16%-3.05%), while SMOTE excelled in three datasets (0.42%-0.61%). For precision,
RO-SMOTE excelled in six datasets (0.42%-5.36%), while SMOTE excelled in five datasets (1.10%-4.32%).
In terms of recall, RO-SMOTE outperformed in seven datasets (1.07%-9.21%), while SMOTE excelled in
four datasets (0.83%-4.06%). Furthermore, in terms of F1-score, RO-SMOTE produced better results than

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SMOTE in seven datasets (0.12%-3.73%), while SMOTE excelled in four datasets (0.16%-1.28%). Finally,
for AUC, RO-SMOTE excelled in eight datasets (0.10%-2.80%), while SMOTE excelled in three datasets
(0.30%-1.20%).
Table 6. Results summary of SVM (radial) classifier
Dataset
Metrics
CM1 SMOTE 88.31 90.10 86.44 88.23 0.948
RO-SMOTE 89.21 92.32 85.61 88.84 0.945
KC1 SMOTE 79.25 77.26 83.01 80.03 0.872
RO-SMOTE 78.64 78.55 78.95 78.75 0.860
PC1 SMOTE 91.57 89.62 94.09 91.80 0.969
RO-SMOTE 94.60 93.09 96.46 94.75 0.974
Ant-1.3 SMOTE 89.52 96.09 82.91 89.01 0.947
RO-SMOTE 91.57 93.76 89.00 91.32 0.948
Ant-1.7 SMOTE 86.27 82.72 92.38 87.28 0.939
RO-SMOTE 86.43 81.62 94.29 87.50 0.950
Camel-1.6 SMOTE 82.37 83.98 80.19 82.04 0.898
RO-SMOTE 81.86 82.50 81.26 81.88 0.886
Ivy-2.0 SMOTE 88.79 88.62 89.45 89.03 0.944
RO-SMOTE 89.37 91.57 86.86 89.15 0.950
Jedit-4.3 SMOTE 93.97 94.78 93.13 93.95 0.980
RO-SMOTE 93.55 92.51 94.82 93.65 0.968
Poi-3.0 SMOTE 83.98 86.37 80.79 83.49 0.906
RO-SMOTE 85.91 91.73 79.09 84.94 0.924
Synapse-1.2 SMOTE 81.76 89.25 72.94 80.27 0.892
RO-SMOTE 84.81 89.67 79.00 84.00 0.920
Velocity-1.6 SMOTE 80.45 80.46 82.71 81.57 0.902
RO-SMOTE 81.11 76.14 91.92 83.29 0.915
Table 7 compares the performance of SMOTE and RO-SMOTE in the SVM kernel poly classifier.
In this table, the performance of RO-SMOTE was superior to SMOTE in the balanced accuracy metric
(0.01%-17.60%). Regarding precision, RO-SMOTE was better in five datasets (1.62%-22.13%), while
SMOTE excelled in six datasets (0.08%-30.66%). In terms of recall, RO-SMOTE excelled in six datasets
(4.76%-82.37%), while SMOTE only excelled in five datasets (0.10%-7.09%). For the F1-score,
RO-SMOTE measurements produced better results in nine datasets (0.39%-43.83%), while SMOTE was
only superior in two datasets (0.24%-3.14%). Finally, in the AUC value, RO-SMOTE outperformed SMOTE
in 10 datasets (3.00%-27.30%), while SMOTE excelled in one dataset (6.30%).
Table 7. Results summary of SVM (poly) classifier
Dataset
Metrics
CM1 SMOTE 57.13 87.05 16.71 28.04 0.502
RO-SMOTE 61.14 56.39 99.08 71.87 0.775
KC1 SMOTE 61.81 81.04 39.82 53.40 0.756
RO-SMOTE 64.35 83.54 35.94 50.26 0.793
PC1 SMOTE 64.78 85.43 35.57 50.23 0.655
RO-SMOTE 65.55 81.35 40.33 53.93 0.769
Ant-1.3 SMOTE 67.14 61.74 96.36 75.26 0.763
RO-SMOTE 84.74 83.87 89.27 86.49 0.915
Ant-1.7 SMOTE 69.17 74.21 61.23 67.10 0.788
RO-SMOTE 71.96 68.32 82.32 74.67 0.813
Camel-1.6 SMOTE 66.15 61.74 85.85 71.83 0.728
RO-SMOTE 68.21 64.33 82.32 72.22 0.761
Ivy-2.0 SMOTE 72.10 90.39 49.63 64.08 0.872
RO-SMOTE 77.87 92.01 61.15 73.47 0.898
Jedit-4.3 SMOTE 78.48 71.06 97.08 82.06 0.925
RO-SMOTE 86.02 79.69 96.98 87.49 0.955
Poi-3.0 SMOTE 67.80 71.13 66.58 68.78 0.799
RO-SMOTE 74.19 68.37 90.44 77.87 0.736
Synapse-1.2 SMOTE 69.41 63.15 95.29 75.96 0.783
RO-SMOTE 69.42 63.07 94.71 75.72 0.813
Velocity-1.6 SMOTE 63.53 83.52 33.83 48.15 0.719
RO-SMOTE 70.62 72.08 73.82 72.94 0.800

 ISSN: 2252-8938
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After conducting experiments on all selected datasets and classifiers, involving 11 datasets and 5
classifiers, a total of 110 experiments were performed. The results demonstrate that the proposed
RO-SMOTE approach can significantly enhance classification performance in predicting software defects.
According to the experimental results, RO-SMOTE outperformed SMOTE 47 times, while SMOTE
outperformed RO-SMOTE only 8 times in terms of balanced accuracy measurements. Furthermore,
RO-SMOTE excelled 36 times in precision measurements, 40 times in recall, 45 times in F1-score, and 42
times in the AUC value. The average F1-score values in Figure 4 indicate that RO-SMOTE’s F1-score is
consistently higher, highlighting a balance between the model’s ability to identify true positives (precision)
and its ability to detect all true positive cases (recall). RO-SMOTE improves the performance of all the
classifiers used when compared to using SMOTE. RO-SMOTE enhances the performance of NN by 9.44%,
KNN by 8%, linear SVM by 10%, radial SVM by 8%, and poly SVM by 14%.
In the NN classifier, RO-SMOTE consistently improves balanced accuracy, F1-score, and AUC
across all 11 datasets. Therefore, selecting the right parameters for the NN classifier can notably enhance the
performance of the resulting software defect prediction model. When it comes to SVM with three different
kernels-linear, radial, and poly, the radial kernel achieved the highest balanced accuracy at 94.60% in the
PC1 dataset. This demonstrates that the radial kernel is the most suitable for classifying software defect
predictions using SVM. In contrast, using the poly kernel in SVM resulted in a decrease in classification
performance compared to the radial kernel. For instance, in the PC1 dataset, the balanced accuracy decreased
by 29.05%. However, implementing RO-SMOTE on the poly kernel of SVM led to a significant increase in
recall compared to SMOTE, as seen in the CM1 dataset, where the recall increased by 82.37%. This, in turn,
boosted the F1-score to 71.87%, representing a 43.83% increase. A higher F1-score value indicates a balance
between the model’s precision and recall.
Moreover, the outcomes of these experiments suggest that RO-SMOTE outperforms SMOTE in
both balanced accuracy and F1-score across all the datasets examined. In instances where datasets have a
larger volume of data and more significant imbalance, as observed in the Jedit dataset, the RO-SMOTE
method exhibits superior balanced accuracy compared to SMOTE. Conversely, for datasets containing fewer
data samples, such as synapse-1.2 and velocity-1.6, SMOTE consistently achieves substantially better
balanced accuracy, especially when combined with different classifiers. This poses a challenge for future
research, as it will require testing the proposed method on alternative datasets with varying combinations of
data sample quantities and imbalance ratios.
Figure 4. Comparison of average performance F1-scores between SMOTE and RO-SMOTE
4.3. Comparison with the current state of art
In this section, we assess the effectiveness of RO-SMOTE in comparison to the current
state-of-the-art method, SMOTE-LOF using Ant-1.3 dataset [21]. KNN classifiers have been used for this
comparisson. The metrics considered for comparison include Accuracy, F1-score, and AUC. The
classifications undergo training and evaluation through 10-fold cross-validation. Only the most optimal
results for the SMOTE-LOF model are included in the analysis. In the case of the Ant-1.3 dataset, the
findings demonstrated that the KNN classifier, when assessed based on Accuracy, AUC and F1-score metrics
with RO-SMOTE, surpassed the performance of SMOTE-LOF by 7.81%, 0.028 and 5.93%, respectively.
5. CONCLUSION
This paper introduces a model for classifying imbalanced datasets in software defect prediction. The
model employs three steps: first, oversampling the training data using SMOTE, second, removing noise from
the resulting oversampled data using the efficient algorithm, and finally, combining the cleaned data with the
original training data and rebalancing using SMOTE. Evaluation experiments were conducted on 11 datasets
74.32%
79%
70%
79%
58%
83.76%
87%
80%
87%
72%
N N K - N N S V M ( L I N E A R ) S V M ( R A D I A L ) S V M ( P O L Y )
SMOTE RO-SMOTE

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for software defect prediction, utilizing five different classifiers and five evaluation metrics. The results
indicate that all classifiers demonstrated improved performance when the proposed RO-SMOTE model was
implemented, as opposed to using SMOTE alone. The extent of performance improvement varied across
datasets, classifiers, and metrics. NN classification consistently delivered strong performance, while other
classifiers showed high performance when combined with RO-SMOTE across various metrics for one or
more datasets. Compared to SMOTE, RO-SMOTE demonstrated performance improvements of up to 7.8%
in balanced accuracy, 22.13% in precision, 82.37% in recall, 43.83% in F1 metrics, and an increase of
27.30% in AUC. In the future, our research will expand to include multiclass imbalanced datasets.
Additionally, we plan to leverage deep learning models, such as AutoML and other deep learning
approaches, for noise detection and removal. These models will be combined with various resampling
techniques. Moreover, we intend to utilize deep learning models for data resampling to address the
limitations of existing techniques.
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BIOGRAPHIES OF AUTHORS
Muhammad Rizky Pribadi is a doctoral student at Satya Wacara Christian
University, and lecturer at Universitas Multi Data Palembang, Indonesia. He got masater from
Universitas Indonesia in 2014 and graduate from Universitas Multi Data Palembang in 2011,
both computer science. His research interest inculude machine learning, information retrieval,
text mining, and computer vision. He can be contacted at email: rizky@mdp.ac.id.
Hindriyanto Dwi Purnomo is a professor at Department of Information
Technology, Satya Wacana Christian University, Indonesia. He received his Bachelor degree
in Engineering Physics, from Gadjah Mada University, Indonesia, in 2005, Magister of
Information Technology from The University of Melbourne, Australia in 2009 and Doctor of
Philosophy in Industrial and System Engineering from Chung Yuan Christian University,
Taiwan, in 2013. He was a visiting scholar at Sophia University, Japan, in 2022. He has
received several recognitions and awards for his academic achievement. He also has
published many articles in reputable journals, conferences and books. His research interests
are in the field of metaheuristics, soft computing, machine learning, and deep learning. He
can be contacted at email: hindriyanto.purnomo@uksw.edu.
Hendry received a B.S. degree in Information Technology from Technology
School of Surabaya, in 2005, an M.S. degree in Information Technology from 10 November
Institute of Technology, Surabaya, in 2009, and a Ph.D. degree in Information Management
from Chaoyang University of Technology in 2018. From 2012-2014 he was the Director of
the Business and Technology Incubator at Satya Wacana Christian University. He is now a
lecturer in Faculty of Information Technology, Satya Wacana Christian University, Central
Java, Indonesia. His research interests include domain ontology, recommendation systems,
knowledge engineering, and applications of artificial intelligence. He can be contacted at
email: hendry@uksw.edu.

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