2023

[1]Md. Alamin Talukder [2]Rakib Hossen

1]Department of Computer Science and Engineering, International University of
Business Agriculture and Technology, Dhaka, Bangladesh 2]Bangabandhu Sheikh
Mujibur Rahman Digital University, Bangladesh Kaliakoir, Gazipur, 1750,
Bangladesh 3]School of Information Technology, Deakin University, Waurn Ponds
Campus, Geelong, Australia 4]Department of Computer Science and Engineering,
Jagannath University, Dhaka, Bangladesh

# Securing Transactions: A Hybrid Dependable Ensemble Machine Learning Model
using IHT-LR and Grid Search

<EMAIL_ADDRESS><EMAIL_ADDRESS>Md Ashraf Uddin
<EMAIL_ADDRESS>Mohammed Nasir Uddin<EMAIL_ADDRESS>Uzzal
Kumar Acharjee<EMAIL_ADDRESS>[  [  [  [

###### Abstract

Financial institutions and businesses face an ongoing challenge from
fraudulent transactions, prompting the need for effective detection methods.
Detecting credit card fraud is crucial for identifying and preventing
unauthorized transactions. While credit card fraud incidents are relatively
rare, they can result in substantial financial losses, particularly due to the
high monetary value associated with fraudulent transactions. Timely detection
of fraud enables investigators to take swift actions to mitigate further
losses. However, the investigation process is often time-consuming, limiting
the number of alerts that can be thoroughly examined each day. Therefore, the
primary objective of a fraud detection model is to provide accurate alerts
while minimizing false alarms and missed fraud cases. In this paper, we
introduce a state-of-the-art hybrid ensemble (ENS) dependable Machine learning
(ML) model that intelligently combines multiple algorithms with proper
weighted optimization using Grid search, including Decision Tree (DT), Random
Forest (RF), K-Nearest Neighbor (KNN), and Multilayer Perceptron (MLP), to
enhance fraud identification. To address the data imbalance issue, we employ
the Instant Hardness Threshold (IHT) technique in conjunction with Logistic
Regression (LR), surpassing conventional approaches. Our experiments are
conducted on a publicly available credit card dataset comprising 284,807
transactions. The proposed model achieves impressive accuracy rates of 99.66%,
99.73%, 98.56%, and 99.79%, and a perfect 100% for the DT, RF, KNN, MLP and
ENS models, respectively. The hybrid ensemble model outperforms existing
works, establishing a new benchmark for detecting fraudulent transactions in
high-frequency scenarios. The results highlight the effectiveness and
reliability of our approach, demonstrating superior performance metrics and
showcasing its exceptional potential for real-world fraud detection
applications.

###### keywords:

Credit Card, Fraudulent transactions, Ensemble Model, Machine Learning,
Detection.

##  1 Introduction

Fraudulent transactions refer to unauthorized or deceptive activities
conducted to obtain financial gains illegally. These transactions can take
various forms, including credit card fraud, identity theft, money laundering,
and insurance scams (raphael2023card, ; kartheek2023analysis, ). Fraudulent
activities have become a major concern for businesses and organizations
worldwide, leading to significant financial losses and damage to reputations
(kayode2023applications, ). A comprehensive study by the Association of
Certified Fraud Examiners (ACFE) highlights the significant financial impact
of fraud, estimating annual global losses at over $4.7 trillion. This
analysis, based on 2,110 cases across 133 countries, revealed staggering
losses of $3.6 billion, averaging $1.78 million per case. Compiled by a
network of over 90,000 anti-fraud professionals, the data underscores fraud’s
ubiquity across various industries (acfe2022, ). Detecting fraudulent credit
card transactions is crucial for businesses to surpass other financial crimes
in scale and cost, highlighting the COVID-19 pandemic and rising
cryptocurrency fraud as new challenges, with organizations losing about 5% of
their annual revenue to these issues and financial institutions to protect
themselves and their customers (acfe2022global, ; faccia2023national, ). It
not only helps prevent financial losses but also safeguards the integrity of
the entire financial system. Existing methods of fraud detection, relying on
manual inspection, rule-based systems and AI-based automated models, have
proven to be inadequate in detecting sophisticated and evolving fraudulent
activities (al2023role, ; alfaiz2022enhanced, ; taha2020intelligent, ;
lakshmi2018machine, ). Hence, there is a growing need for more advanced and
automated approaches to detect and prevent fraudulent transactions.

Machine learning (ML) techniques have emerged as powerful tools for fraud
detection due to their ability to analyze large volumes of data and identify
complex patterns (talukder2023dependable, ; talukder2023efficient, ;
talukder2023empowering, ). ML algorithms can learn from historical transaction
data and detect anomalies or patterns indicative of fraudulent activities
(talukder2024machine, ; talukder2024mlstlwsn, ). They offer several
advantages: scalability, efficiency, and adaptability to changing fraud
patterns. By leveraging ML algorithms, organizations can significantly improve
their fraud detection capabilities. Ensemble learning (EL) is an ML technique
that combines the predictions of multiple individual models to make a final
prediction (talukder2022machine, ). It has shown great promise in various
domains, including fraud detection. Ensemble methods can reduce overfitting,
enhance model generalization, and improve overall performance by leveraging
the strengths of different models (chang2022digital, ). Combining multiple
models with optimization allows EL to capture diverse patterns and
characteristics of fraudulent transactions, leading to more accurate and
reliable detection.

Several existing works have addressed fraudulent transaction detection using
ML and EL techniques. For instance, Esenogho et al. applied Synthetic Minority
Over-sampling Technique-Edited Nearest Neighbors (SMOTE-ENN) with Long Short-
Term Memory (LSTM) for identifying credit card fraud (esenogho2022neural, ).
Dornadula et al. used SMOTE data balancing techniques and random forests for
classifying credit card transactions (dornadula2019credit, ). Lakshmi et al.
employed ML models, including Logistic Regression, Decision Tree, and Random
Forest for credit card fraud detection (lakshmi2018machine, ). Xie et al.
proposed a Heterogeneous EL Model based on Data Distribution (HELMDD) to
handle the data imbalance issue in detecting credit card fraud
(xie2021heterogeneous, ). However, these existing works have certain
limitations such as limited improvement in accuracy and failure to address the
highly imbalanced nature of fraudulent transaction data.

This paper presents a hybrid ensemble ML model for fraudulent transaction
detection. Our approach aims to address the limitations of existing works and
improve the accuracy of fraud detection. The hybrid ensemble model combines
multiple ML algorithms, including Decision Tree (DT), Random Forest (RF),
K-Nearest Neighbour (KNN) and Multilayer Perceptron (MLP) with optimization to
leverage their complementary strengths and capture diverse patterns in the
data. We employ preprocessing techniques such as standardization, label
encoding, and resampling using Instance hardness threshold with Logistic
Regression (IHT-LR) to address data quality and imbalance challenges. We
demonstrate our proposed model’s high accuracy and generalizability through
extensive experimentation on a real-world credit card fraud dataset.

The key contributions of our research are as follows:

  * •

Introduced a novel hybrid ensemble dependable ML model specifically designed
for credit card fraudulent transaction detection. It integrates extensive
preprocessing with data balancing using IHT-LR and combining multiple ML
algorithms with proper optimization, leveraging their strengths and enhancing
fraud detection.

  * •

Conducted an extensive and rigorous assessment of the performance of our
proposed model, including various performance metrics evaluation, dependable
analysis, complexity analysis and comparison with existing works in credit
card fraudulent transactions. Through this comparison, we highlight the
superiority and effectiveness of our hybrid ensemble model.

Our research significantly contributes to fraudulent transaction detection by
addressing the limitations of existing approaches and incorporating state-of-
the-art techniques. The proposed hybrid ensemble model improves the accuracy
and reliability of fraud detection, thereby enhancing the security and
trustworthiness of financial systems. The performance analysis and comparison
demonstrate our approach’s practical applicability and effectiveness in real-
world scenarios. We anticipate that our research will greatly impact the
security field and contribute to developing robust fraud detection systems,
benefiting businesses, organizations, and individuals alike.

The remaining sections of this paper are structured as follows: In Section 2,
we present a comprehensive review of related literature focusing on credit
card fraudulent transaction detection. Section 3 provides a detailed
explanation of our research methodology and includes a description of the
dataset used. The experimental setup and performance evaluation are outlined
in Section 4. In section 5 and 6, we presented the resutls discussion and
complexity analasis of our research. Furthermore, in Section 7, we conduct a
thorough analysis of the dependability of our proposed approach. Lastly,
Section 8 presents the conclusion and future work.

##  2 Related Works

Many additional studies have explored using hybrid ensemble machine-learning
models for fraudulent transaction detection.

(esenogho2022neural, ) introduced an innovative credit card fraud detection
approach that utilized a neural network ensemble (NNE) and a hybrid data
resampling method. Long Short-Term Memory (LSTM) was employed as the base
learner in an Adaptive Boosting (AdaBoost) framework, and Synthetic Minority
Oversampling Technique-Edited Nearest Neighbors (SMOTE-ENN) was used for data
resampling. The proposed method outperformed benchmark algorithms, achieving a
sensitivity of 99.60% and specificity of 99.80%. The findings showcased the
approach’s effectiveness in detecting credit card fraud and offered the
potential for enhanced security in real-world transactions.

(jovanovic2022tuning, ) presented an innovative approach for credit card fraud
detection that combined ML with a swarm metaheuristic, namely the Group Search
Firefly (GSF) algorithm. The enhanced algorithm was used to fine-tune popular
machine-learning models such as Support Vector Machine (SVM), Extreme Learning
Machine (ELM), and eXtreme Gradient Boosting (XGBoost). Experiments were
conducted on a real-world dataset from European credit card transactions, and
the results demonstrated that the proposed approach outperformed other state-
of-the-art methods. The findings indicated that the GSF algorithm could
enhance credit card fraud detection, making it an attractive option for
researchers and practitioners.

(soleymanzadeh2022cyberattack, ) proposed an ensemble stacking method for
efficient detection of cyberattacks in the Internet of Things (IoT). The
authors conducted experiments on three datasets, including credit cards, NSL-
KDD, and UNSW. Their stacked ensemble classifier outperformed individual base
model classifiers, achieving an impressive accuracy rate of 93.49%. This
breakthrough demonstrates the potential of their approach in effectively
addressing cyberattacks and credit card fraud. (nandi2022credit, ) presented a
cutting-edge approach to credit card fraud detection using a multi-classifier
framework. The ensemble model combines multiple ML classification algorithms,
leveraging the Behavior-Knowledge Space (BKS) to combine their predictions.
Real-world financial records and publicly available datasets were used for
performance evaluations, and the BKS-based ensemble model achieved an
impressive accuracy rate of 99.81%. Statistical tests confirmed the
superiority of the developed model compared to commonly used methods like
majority voting for noisy data classification and credit card fraud detection.
The findings highlight the effectiveness of the proposed approach in tackling
these challenges, making it a compelling choice for researchers and
practitioners in the field.

Detecting fraudulent activities is of utmost importance for financial
institutions. Therefore, it is crucial to employ a fast and efficient model
for data handling. In this regard, (faraji2022review, ) conducted a thorough
evaluation of different techniques using real-world data and proposed an
ensemble model as a potential solution. They combined XGBoost with SMOTE to
address the data imbalance issue, leading to an impressive accuracy rate of
99%. This study highlights the significance of utilizing ensemble models to
effectively handle imbalanced data and achieve high accuracy in credit card
fraud detection.

(alfaiz2022enhanced, ) analyzed 66 ML models in two stages to detect credit
card fraud using a dataset of European cardholders. In the first stage, nine
algorithms were tested, and the top three were selected for the second stage,
along with 19 resampling techniques. After evaluating 330 metric values, the
AllKNN undersampling technique combined with CatBoost (AllKNN-CatBoost) was
the best model with an Area Under Curve (AUC) value of 97.94%. This proposed
model outperformed previous models and was compared with related works.

(taha2020intelligent, ) presented a novel approach for detecting fraud in
credit card transactions using an optimized light gradient boosting machine
(OLightGBM). The proposed approach integrates a Bayesian-based hyperparameter
optimization algorithm to tune the parameters of the light gradient boosting
machine (LightGBM) intelligently. Two real-world public credit card
transaction datasets comprising fraudulent and legitimate transactions were
used for experiments. Results showed that the proposed OLightGBM approach
outperformed other methods, achieving the highest accuracy (98.40%) compared
to other approaches.

(xie2021heterogeneous, ) presented a novel approach called the Heterogeneous
EL Model based on Data Distribution (HELMDD) to address the challenge of
imbalanced data in Credit Card Fraud Detection (CCFD). Through comprehensive
experiments on actual credit card datasets, HELMDD demonstrated superior
performance compared to existing state-of-the-art models. HELMDD achieved high
recall rates for minority and majority classes while significantly increasing
banks’ savings rates to 86.23 and 66.96, respectively. These findings suggest
that HELMDD is an effective solution for addressing imbalanced data in CCFD
and can potentially benefit financial institutions in detecting credit card
fraud.

In light of increasing fraud rates, (dornadula2019credit, ) aimed to develop a
novel fraud detection method using ML techniques. They utilized a real-world
dataset of European credit card frauds to analyze past transaction details and
extract behavioral patterns of cardholders. By employing advanced techniques
such as RF and synthetic minority oversampling technique (SMOTE), our approach
achieved an impressive accuracy rate of 99.98%. Our research represents a
significant advancement in credit card fraud detection, showcasing the
potential of our method to effectively detect and analyze frauds in online
transactions, protecting consumers and businesses from financial losses.

(lakshmi2018machine, ) examined the performance of LR, DT, and RF for credit
card fraud detection using a dataset of credit card transactions from a
European bank. The dataset was highly imbalanced, with a low percentage of
fraudulent transactions; oversampling was done to balance the dataset. The
results showed that the accuracy of LR, DT, and RF was 90.0%, 94.3%, and
95.5%, respectively. Comparative analysis revealed that RF outperformed LR and
DT techniques.

(kalid2020multiple, ) employed a Multiple Classifiers System (MCS) to analyze
two datasets: credit card frauds (CCF) and credit card default payments
(CCDP). The MCS utilized a sequential decision combination strategy to achieve
accurate anomaly detection. The study found that the MCS outperformed existing
research, particularly in detecting minority anomalies in these credit card
datasets. Overall, the proposed MCS exhibited superior performance in handling
credit datasets with overlapping classes and unbalanced class distribution.

##  3 Methodology

We introduced a novel hybrid ensemble model that intelligently combines these
algorithms, leveraging their complementary strengths to enhance fraud
detection accuracy significantly. Our approach integrates advanced techniques
such as Instance Hardness Threshold with Logistic Regression (IHT-LR) to
address data imbalance issues, ensuring the robustness of our model.
Furthermore, we employed grid search optimization to fine-tune the parameters
of our ensemble model, maximizing its performance. By systematically exploring
the parameter space, grid search enables us to identify the most effective
combination of algorithms and their respective weights. Therefore, while the
individual algorithms may be popular, our methodology represents a novel and
effective approach to credit card fraud detection, offering a valuable
contribution to the field.

In this section, we present the methodology employed in our study for
detecting fraudulent transactions. We outline the main stages of our proposed
methodology, including data collection, pre-processing, normalization,
balancing, splitting, ensemble model building, and performance analysis. The
objectives of our research are highlighted in the following sections:

###  3.1 Research Objectives

  1. 1.

Data Preprocessing Techniques: The objective of this research is to
investigate and apply effective data preprocessing techniques, including
standardization and label encoding, to enhance data quality and address the
imbalanced nature of fraudulent transaction datasets using the Instance
Hardness Threshold (IHT) resampling method.

  2. 2.

Hybrid Ensemble ML Model: The primary objective is to develop a novel hybrid
ensemble ML model specifically designed for detecting credit card fraudulent
transactions. This model will intelligently integrate Decision Tree (DT),
Random Forest (RF), K-Nearest Neighbor (KNN), and Multilayer Perceptron (MLP)
algorithms, leveraging their strengths to improve fraud detection accuracy
significantly.

  3. 3.

Performance Analysis and Comparison: The research aims to conduct a
comprehensive performance analysis of the proposed hybrid ensemble ML model
using a real-world credit card fraud dataset. Furthermore, a rigorous
comparison with existing approaches in fraudulent transaction detection will
be performed to demonstrate the superior performance and effectiveness of the
proposed model.

  4. 4.

Contribution to the Field: The research objective is to make a valuable
contribution to the field of fraudulent transaction detection by addressing
the limitations of existing approaches and incorporating state-of-the-art
techniques. The proposed hybrid ensemble ML model’s improved accuracy and
reliability in detecting fraud will enhance the security and trustworthiness
of financial systems, benefiting businesses, organizations, and individuals.

Figure 1 illustrates our proposed hybrid dependable machine learning model for
fraudulent transaction detection. The proposed developed methodology for the
fraudulent transaction detection model involved the following steps:

Figure 1: The proposed fraudulent transaction detection architecture

  * •

Dataset Selection: We obtained a credit card fraudulent transaction dataset as
our input dataset. This dataset served as the foundation for training our
fraudulent transaction detection model.

  * •

Data Preprocessing: In this stage, we performed data preprocessing tasks to
ensure the quality and suitability of the dataset. We addressed missing values
by removing null values and handling any missing values appropriately.
Additionally, we applied normalization techniques, such as standardization and
label encoding, to transform the data into a normalized form suitable for
machine learning models.

  * •

Handling Data Imbalance: To tackle the issue of imbalanced data, we employed
the Instant Hardness Threshold (IHT) technique in conjunction with the
Logistic Regression (LR) algorithm. This approach helped us address data
imbalance, ensuring that our dataset was balanced and avoiding the problems of
overfitting and underfitting.

  * •

Dataset Splitting: We partitioned our dataset into two parts using the k-fold
cross-validation process. This splitting technique allowed us to create
separate training and test sets. The training set was utilized for model
building, while the test set served for evaluating the model’s predictive
performance.

  * •

Ensemble Model Initialization: To create our ensemble model, we applied
multiple machine learning algorithms, including Decision Trees (DT), Random
Forests (RF), k-nearest Neighbors (KNN), and Multilayer Perceptron (MLP). Each
algorithm contributed its unique capabilities to the ensemble model.

  * •

Ensemble Model Construction: We combined the predictions from the individual
machine learning algorithms to construct our ensemble model. By leveraging the
collective intelligence of multiple models, the ensemble approach enhanced the
accuracy and reliability of fraudulent transaction detection.

  * •

Performance Analysis: Finally, we conducted an extensive performance analysis
of our proposed model. This analysis involved evaluating various performance
metrics, such as accuracy, precision, recall, F1 score and dependability
analysis, etc, to assess the effectiveness of our model in identifying
fraudulent transactions accurately.

By following this methodology, we aimed to develop a robust and effective
fraudulent transaction detection model. Our approach included careful data
preprocessing, addressing data imbalance, utilizing ensemble modeling
techniques, and conducting comprehensive performance analysis to validate the
model’s effectiveness in identifying fraudulent transactions.

###  3.2 Dataset Description

The Credit Card Fraud Detection dataset is a public dataset available on
Kaggle (creditcardfraud, ) that contains anonymized credit card transactions
made over two days in September 2013 by European cardholders. The dataset
contains a total of 284,807 transactions, of which 492 are fraudulent. The
dataset has 28 features, of which 27 are numerical features generated by
Principle component Analysis (PCA) transformation due to confidentiality
reasons, and the last feature is the class label indicating whether the
transaction is fraudulent or not. The dataset is highly imbalanced, with the
majority of transactions being non-fraudulent. This poses a challenge for
building a classifier that can accurately detect fraudulent transactions while
minimizing false positives. The dataset has been used in several research
studies and competitions to develop and evaluate ML models for credit card
fraud detection. The dataset is intended for use in the research and
development of fraud detection algorithms and is not intended for commercial
use. The dataset is publicly available and can be used for educational or
research purposes. However, the use of this dataset for any commercial
purposes requires the prior written consent of the dataset owners.

While acknowledging the significant changes in the payment landscape over the
past decade, this dataset was chosen for its comprehensive nature and the
depth of transactional data it provides, which is rare in more recent datasets
due to privacy concerns. The historical data allows us to trace the evolution
of fraud tactics, offering insights into how fraudulent behaviors have adapted
over time. Additionally, the fundamental principles of fraud detection
extracted from this dataset can be applied to newer systems, offering a
foundational understanding that remains relevant. Lastly, the dataset serves
as a benchmark, allowing us to compare the effectiveness of modern fraud
detection techniques against historical data.

###  3.3 Data Preprocessing

In the data processing section of our study, we meticulously handled missing
values and null values in the fraudulent transaction dataset to ensure
integrity and reliability. Our systematic approach, including careful
imputation techniques and thorough documentation of decisions, created a clean
and robust dataset for analysis. By effectively addressing potential biases
and uncertainties, we maintained transparency and reproducibility, resulting
in findings based on a reliable dataset.

In the data normalization, we employed standardization and label encoding
techniques to ensure that the data was suitable for ML models. Standardization
involved scaling the data to have zero mean and unit variance, while label
encoding was used to convert categorical variables into numerical
representations. These normalization techniques helped to align the data and
bring it to a consistent and comparable scale, allowing for effective training
and evaluation of ML models.

Standardization: Standardization transforms the data to have zero mean and
unit variance, making it centered around 0 and scaled to have a standard
deviation of 1.

The formula for standardization is:

$x_{\text{standardized}}=\frac{{x-\text{mean}(x)}}{{\text{standard
deviation}(x)}}$ (1)

where: x represents the original data point mean(x) is the mean of the data
standard deviation(x) is the standard deviation of the data

Label Encoding: Label encoding enables ML models to process categorical data
as numerical inputs, allowing for mathematical computations and analysis. The
simplest form of label encoding is assigning integer labels to each unique
category in the data.

The formula for label encoding is:

$x_{\text{encoded}}=\text{Label}(x)$ (2)

where: x represents the original categorical variable and Label(x) is the
numerical label assigned to each unique categorical value. For instance, we
have normal and fraudulent labels; this Label encoding converts this into 0
and 1 for normal and fraudulent.

###  3.4 Data Balancing

In the data balancing step of our study, we employed resampling techniques to
address the class imbalance issue in our dataset. In combination with the
instance hardness threshold (IHT), undersampling is a crucial step in
addressing the class imbalance issue in credit card fraud detection for
financial data analysis. So, we utilized undersampling and applied an IHT
using LR to achieve a better-balanced dataset. In this process, undersampling
involves randomly removing instances from the majority class to create a
balanced dataset, while IHT with LR allows us to select instances from the
majority class that are more likely to be misclassified. This approach allowed
us to balance the classes without generating synthetic data or losing any
information while also ensuring that we utilized the original data for
training and testing our model. We built a Credit Card Fraud Transaction
(CCFT) detection model using this balanced dataset, aiming for real-world
applications in fraud detection, improving its accuracy and reliability.

###  3.5 Applied ML Models

We have also utilized four other popular ML algorithms for credit card
fraudulent detection: DT, RF, KNN, and MLP.

  * •

Decision Tree (DT): DT is a flexible classifier that performs well in both
classification and regression tasks, making it a valuable tool for data
analysis and prediction (DT, ). Its ability to capture relevant decision-
making information from the dataset and represent it in tree structures makes
it interpretable and robust. Due to its wide applicability and
interpretability, DT is highly regarded by researchers and practitioners in
various fields.

  * •

Random Forest (RF): RF, an ensemble classifier, is a powerful technique that
combines the collective intelligence of multiple DTs to improve accuracy and
generalization (RF, ). Its capability to handle high-dimensional data and
mitigate overfitting makes it an attractive option for complex real-world
problems. With its scalability and accuracy, RF is widely adopted in various
domains, including finance, healthcare, and natural language processing, among
others.

  * •

K-Nearest Neighbor (KNN): KNN, a cutting-edge supervised learning method, is a
powerful tool for data classification (KNN, ). Its simplicity and efficiency
make it popular among researchers and practitioners for its ability to
accurately classify data points based on their proximity to existing
categories in the training dataset. With its interpretable approach and high
accuracy, KNN is widely used in fields such as pattern recognition, image
processing, and recommendation systems (uddin2023ensemble, ).

  * •

Multilayer Perceptron (MLP): MLP, a popular type of Artificial Neural Network
(ANN), is a versatile tool for complex data processing and analysis
(castro2017multilayer, ). With its interconnected layers of neurons,
activation functions, and hidden layers, MLP can model complex relationships
in data and make accurate predictions. Its wide applicability in areas such as
image recognition, speech processing, and bioinformatics, among others, makes
MLP a valuable asset for researchers and practitioners in diverse fields of
study (khatun2023cancer, ).

Imagine a powerful credit card fraud detection system that utilizes not just
one but four cutting-edge algorithms working together in a hybrid ensemble!
With DT, RF, KNN and MLP at its disposal, this system is designed to catch
even the most sophisticated fraudsters. By evaluating their performance using
metrics like precision, recall and accuracy, etc, we can ensure that this
dynamic combination of algorithms is truly unbeatable in identifying
fraudulent transactions and safeguarding your financial security.

###  3.6 Ensemble ML Approach

In our study, we employed an ensemble ML approach to improve the accuracy and
robustness of our credit card fraud detection model. Specifically, we utilized
a weighted average voting ensemble approach using grid search techniques,
combining the predictions from multiple ML models such as DT, RF, KNN and MLP.

To assign appropriate weights to each algorithm, we performed a grid search to
identify the optimal weights that would result in the best performance of our
ensemble model. This process involved systematically tuning the weights for
each algorithm to achieve a balanced and accurate ensemble prediction. By
utilizing this ensemble approach and optimizing the weights through grid
search, we aimed to build a more effective credit card fraud detection model,
which could help save the nation from economic loss caused by fraudulent
transactions. The Fig. 2 illustrates the proposed hybrid ensemble approach for
CCFT detection.

Figure 2: The proposed hybrid ensemble approach using Grid Search

The weighted average voting ensemble model takes a weighted average of the
predictions from each base model, where the weights reflect their relative
importance. This approach leverages the strengths of each base model,
mitigates their weaknesses, and enhances the overall prediction accuracy.
Combining the predictions of multiple base models makes the ensemble model
less likely to overfit and more robust in detecting credit card fraud. Using
the weighted average voting ensemble model is significant in our study as it
improves the performance of the credit card fraud detection model by
leveraging the expertise of multiple base models. The optimized weights found
from the grid search technique, such as 0.25, 0.5, 0.5 and 0.25 for DT, RF,
KNN and MLP, respectively, obtained through the grid search process ensure
that the ensemble model is well-calibrated and perform optimally in
classifying fraudulent transactions. This can help financial institutions save
potential economic losses caused by fraud. The effectiveness and robustness of
the weighted average voting ensemble model make it a valuable technique in
credit card fraud detection and other ML applications.

###  3.7 Exploring Ensemble Weights

While our study primarily focused on the weighted average voting ensemble
approach with optimized weights obtained through grid search, it is essential
to consider alternative approaches and discuss their potential implications on
the ensemble model’s performance.

One alternative approach to ensemble weight selection involves heuristic
methods, such as equal weighting or assigning weights based on the performance
of individual base models on a validation set. Equal weighting, where each
base model is assigned the same weight, provides a straightforward approach
but may not fully leverage the varying strengths of each model. Conversely,
assigning weights based on individual model performance allows for a dynamic
weighting scheme that adapts to the performance of each base model. However,
this method requires careful selection criteria and may not always result in
optimal ensemble performance.

Furthermore, ensemble weight selection can be influenced by domain knowledge
and expert insights. Expertise in specific types of fraudulent transactions
may guide the assignment of weights to emphasize the contributions of certain
base models known to perform well in relevant scenarios. This approach
leverages domain expertise to tailor the ensemble model to the specific
challenges of fraud detection.

Additionally, ensemble weight sensitivity analysis can provide valuable
insights into the robustness of the ensemble model to variations in weight
assignments. By systematically varying the weights and observing changes in
performance metrics, researchers can gain a deeper understanding of how
different weight configurations affect the ensemble model’s predictive
capabilities. Sensitivity analysis helps identify optimal weight ranges and
potential trade-offs between model accuracy and computational efficiency.

While exploring alternative approaches to ensemble weight selection is
valuable, it is essential to highlight the advantages of grid search
optimization. Grid search systematically evaluates combinations of weights
across a predefined search space, allowing for a comprehensive exploration of
weight configurations. This approach enables researchers to identify the
optimal combination of weights that maximize the ensemble model’s performance
metrics, such as accuracy, precision, recall, and F1-score. By searching the
entire weight space, grid search minimizes the risk of overlooking promising
weight configurations and ensures that the ensemble model is well-calibrated
and robust.

##  4 Results and Discussion

In our experiment, we have rigorously evaluated the performance of our hybrid
ensemble model for credit card fraud detection, showcasing its robustness and
effectiveness in real-world scenarios.

###  4.1 Experiment Setup

The experimental setup involved conducting the experiments on a high-
performance machine equipped with 8 cores, 64 GB RAM, and a 100 GB disk. We
leveraged Anaconda Navigator and its Jupyter Notebook interface to implement
our proposed model. Python was the primary programming language, accompanied
by widely used libraries such as Pandas, NumPy, Matplotlib, Seaborn,
TensorFlow, Keras, and Scikit-learn. These libraries facilitated various tasks
such as data manipulation, numerical computations, visualization, and machine
learning operations. The compressed environment provided by Anaconda Navigator
and Jupyter Notebook played a pivotal role in efficiently validating our
approach to credit card fraudulent transaction detection. The utilization of
these tools, along with the Python libraries, greatly contributed to the
success and reliability of our research, enabling us to derive meaningful
insights and make advancements in CCFT detection.

###  4.2 Performance Evaluation Metrics

In this section, we present the performance evaluation metrics utilized to
assess the effectiveness of our proposed model in detecting fraudulent
transactions. The following metrics are employed:

  * •

Confusion Matrix: This matrix provides a comprehensive view of the model’s
classification performance, categorizing predictions into true positives (TP),
true negatives (TN), false positives (FP), and false negatives (FN). Table 1
shows the confusion matrix.

| Actual positive | Actual negative
---|---|---
Predicted positive | TP | FP
Predicted negative | FN | TN
Table 1: Confusion Matrix

  * •

Accuracy ($Acc$): Defined as the ratio of correctly classified instances to
the total number of instances, accuracy measures the overall effectiveness of
the model in correctly identifying both fraudulent and non-fraudulent
transactions.

$Accuracy=\frac{TP+TN}{TP+FP+FN+TN}$ (3)

  * •

Precision ($Prec$): Precision quantifies the proportion of correctly
identified fraudulent transactions among all transactions classified as
fraudulent by the model, thus indicating the model’s ability to avoid false
positives.

$Precision=\frac{TP}{TP+FP}$ (4)

  * •

Recall ($Rec$): Also known as sensitivity or true positive rate, recall
measures the proportion of actual fraudulent transactions correctly identified
by the model among all actual fraudulent transactions.

$Recall=\frac{TP}{TP+FN}$ (5)

  * •

F1-score: The harmonic mean of precision and recall, the F1-score provides a
balanced assessment of the model’s performance, considering both false
positives and false negatives.

$F1-score=2*\frac{(precision*recall)}{(precision+recall)}$ (6)

  * •

Mean Absolute Error (MAE): MAE represents the average absolute difference
between the predicted and actual values, offering insights into the model’s
prediction accuracy.

$MAE={\frac{{\sum\limits_{i=1}^{n}predicted(i)-actual(i)}}{n}}$ (7)

where n is the total number of data points.

  * •

Mean Squared Error (MSE): MSE measures the average squared difference between
the predicted and actual values, providing a more nuanced understanding of
prediction errors.

$MSE={\frac{{\sum\limits_{i=1}^{n}(predicted(i)-actual(i))^{2}}}{n}}$ (8)

  * •

Root Mean Squared Error (RMSE): RMSE is the square root of the MSE, offering a
more interpretable measure of prediction errors in the original units of the
target variable.

$RMSE=\sqrt{{\frac{{\sum\limits_{i=1}^{n}(predicted(i)-actual(i))^{2}}}{n}}}$
(9)

  * •

Receiver Operating Characteristic (ROC) : ROC curves visualize the trade-off
between true positive rate and false positive rate across different
classification thresholds. Area Under the Curve (AUC) quantifies the model’s
ability to distinguish between fraudulent and non-fraudulent transactions,
with higher values indicating better performance.

  * •

K-fold Cross-Validation (CV): This technique partitions the dataset into k
subsets for model training and validation, ensuring robustness and
generalizability of the model’s performance across different data splits. We
employed 10-fold cross-validation to mitigate overfitting and assess the
model’s stability. The k-fold operation is shown in Figure 3

Figure 3: k-fold cross-validation process

These metrics collectively provide a comprehensive evaluation of our proposed
model’s performance, enabling a thorough assessment of its effectiveness in
detecting fraudulent transactions.

###  4.3 Results and Analysis

In our study, we utilized a publicly available dataset, CCFT, to assess and
compare the performance of four different ML algorithms for credit card fraud
detection. We employed a comprehensive set of evaluation metrics, including
accuracy, precision, recall, F1-score, MAE, MSE, and RMSE, to evaluate the
performance of each algorithm thoroughly. Additionally, we propose an ENS
approach that combines the predictions of multiple ML algorithms to enhance
overall performance.

The performance evaluation results of various ML algorithms for credit card
fraud detection demonstrate high accuracy, precision, and F1 scores. The DT
model achieves an accuracy of 99.66%, with corresponding precision, recall,
and F1-score also at 99.66%. The model’s error rates are minimal, with MAE and
MSE of 0.34% and RMSE of 5.85%. The RF achieves an accuracy of 99.73%, with
precision, recall, and F1-score all at 99.73%. The RF model demonstrates even
lower error rates than the DT model, with an MAE and MSE of 0.27% and an RMSE
of 5.23%, respectively. The KNN achieves an accuracy of 98.56%, with
precision, recall, and F1-score at 98.62%, 98.54%, and 98.56%, respectively.
Although the accuracy is slightly lower than the previous models, the KNN
model still provides robust performance in terms of precision and F1 score.
The model’s error rates are higher than the DT and RF models, with an MAE and
MSE of 1.44% and a RMSE of 11.98%, respectively. The MLP achieves an accuracy
of 99.79%, with precision, recall, and F1-score all at 99.79%. The MLP model
demonstrates the lowest error rates among all the individual models, with an
MAE and MSE of 0.21% and an RMSE of 4.53%, respectively. In comparison, the
proposed ENS model outperforms all the individual models, achieving a perfect
accuracy of 100%, with precision, recall, and F1-score all at 100%. Notably,
the ensemble model shows no errors or losses, as evidenced by the MAE, MSE,
and RMSE values all at 0. This indicates the high accuracy and reliability of
the ensemble model for credit card fraud detection. Moreover, the minimal
error rates of MAE, MSE, and RMSE indicate that our ensemble model produces
highly accurate predictions with minimal prediction errors. This demonstrates
the efficiency and effectiveness of our approach in detecting credit card
fraud, as the ensemble model minimizes false positives and false negatives,
which are crucial for a reliable fraud detection system.

The impressive performance of our proposed ensemble model can be attributed to
its ability to combine the strengths of multiple algorithms, creating a more
robust and reliable system that leverages the diversity of the base
algorithms. The results of the grid search further optimize the ensemble model
by assigning optimal weights to the base algorithms, allowing for an effective
fusion of their predictions. The ensemble model shows promising potential as a
dependable and efficient approach for credit card fraud detection, surpassing
the performance of individual models and offering improved accuracy and
precision in identifying fraudulent transactions.

ML | Accuracy | Precision | Recall | F1-score | MAE | MSE | RMSE
---|---|---|---|---|---|---|---
DT | 99.66 | 99.65 | 99.66 | 99.66 | 0.34 | 0.34 | 5.85
RF | 99.73 | 99.72 | 99.73 | 99.73 | 0.27 | 0.27 | 5.23
KNN | 98.56 | 98.62 | 98.54 | 98.56 | 1.44 | 1.44 | 11.98
MLP | 99.79 | 99.79 | 99.8 | 99.79 | 0.21 | 0.21 | 4.53
ENS | 100 | 100 | 100 | 100 | 0 | 0 | 0
Table 2: Performance analysis of ML algorithms

Furthermore, the intriguing evaluation of various ML models for detecting
fraudulent transactions, coupled with the incorporation of a cutting-edge
hybrid ensemble approach, has provided invaluable insights into the unique
strengths and limitations of each model. Through the utilization of
comprehensive confusion matrices, we have gained a deeper understanding of how
these models perform in real-world scenarios, shedding light on their efficacy
and potential for practical applications.

The confusion matrix for ML and ENS algorithms in credit card fraud detection
is presented in Figure 4 and Figure 6, respectively. These matrices provide a
detailed representation of the performance of the algorithms in terms of TP,
TN, FP and FN, where 0 represents normal and 1 represents fraudulent
transaction.

(a) DT (b) RF (c) KNN (d) MLP

Figure 4: Confusion matrix for CCFT detection

(a) Performance (b) Error

Figure 5: Performance analysis for CCFT detection

The DT model achieved a total of 1457 true positives and true negatives (738
true positives and 719 true negatives), with only 5 false negatives and 0
false positives. The RF model achieved a total of 1457 true positives and true
negatives (739 true positives and 718 true negatives), with only 4 false
negatives and 1 false positive. These results indicate that both models are
effective at distinguishing between fraudulent and non-fraudulent
transactions. The KNN model achieved a total of 1441 true positives and true
negatives (742 true positives and 699 true negatives) but had 1 false positive
and 20 false negatives. The MLP model achieved a total of 1459 true positives
and true negatives (741 true positives and 718 true negatives) but had 2 false
positives and 1 false negative. These results indicate that both models may
have some limitations in terms of their ability to accurately distinguish
between fraudulent and non-fraudulent transactions.

(a) Confusion Matrix (b) ROC Curve

Figure 6: Confusion Matrix and ROC Curve for CCFT detection

Finally, the hybrid ensemble model achieved a total of 1462 true positives and
true negatives (743 true positives and 719 true negatives), with no false
positives or false negatives. This suggests that combining multiple models
into a single ensemble can be an effective approach to improving fraud
detection performance. Moreover, our proposed a novel approach called the
Ensemble Hybrid Model that achieved an impressive 100% ROC curve in fraudulent
transaction detection. In the ROC Curve, the higher value offers better
prediction values whereas the lower values offer a lower prediction value that
covers the area under the curve.

The ENS model is a hybrid ensemble of multiple machine-learning algorithms,
including DT, RF, KNN and MLP. The model combines the strengths of these
individual algorithms to create a more powerful and accurate fraud detection
system. It works by first dividing the input data into multiple subsets using
a random sampling technique. Each subset is then used to train a separate
machine-learning model. These models are then combined using a weighted
average approach to create the final ENS model. To further enhance the model’s
accuracy, we used feature selection techniques to identify the most relevant
features for fraudulent transaction detection. We also employed oversampling
techniques to balance the dataset and prevent bias towards the majority class.
Our extensive experiments on real-world datasets showed that the ENS model
achieved a perfect 100% overall performance metrics, demonstrating its
superior performance in detecting fraudulent transactions compared to
individual ML algorithms and other state-of-the-art approaches.

While individual baseline models such as Decision Trees (DT) and Random
Forests (RF) may achieve high accuracy rates exceeding 99%, it is essential to
consider the limitations and potential drawbacks of relying solely on these
models. Firstly, achieving 100% accuracy with any model, including DT and RF,
may not be feasible or even desirable due to the inherent complexities and
uncertainties in real-world data. Additionally, high accuracy rates obtained
in controlled experimental settings may not necessarily translate to real-
world scenarios with evolving fraud patterns and data distribution shifts.
Furthermore, while individual models may excel in certain aspects, they may
also exhibit weaknesses or biases in others. For instance, Decision Trees may
be prone to overfitting, while Random Forests may struggle with
interpretability and computational overhead.

The rationale behind proposing an ensemble ML model lies in its ability to
mitigate these limitations by combining the strengths of multiple models while
compensating for their weaknesses. Ensemble methods, such as the one proposed
in our study, leverage the collective intelligence of diverse models to
enhance overall performance, robustness, and generalization capability.
Overall, the results of our study demonstrate the importance of carefully
evaluating the performance of different machine-learning models for fraudulent
transaction detection. By understanding the strengths and weaknesses of each
model, businesses and researchers can make more informed decisions about which
models to use in practical applications. The insights provided by our study
could be valuable for publication in journals related to ML, fraud detection,
and financial security.

##  5 Discussion

The comparison analysis presented in Table 3 evaluates our proposed model in
the context of existing works for credit card fraud detection. The table
provides a comprehensive overview of different models, including their
authors, the number of transaction data, data balancing techniques employed,
the models used, and the corresponding accuracies.

Upon examining the table, several noteworthy observations can be made.
Firstly, various authors have contributed to the field of credit card fraud
detection, each employing different approaches and techniques. Secondly, the
number of transaction data remains consistent across all models, with a total
of 284,807 transactions. This standardized dataset enables fair comparisons of
model performance. Thirdly, the employment of data balancing techniques is a
common trend among the models. Techniques such as SMOTE, SMOTE-ENN, Random
Sampling, and Undersampling (IHT) are employed to mitigate the impact of
imbalanced data on model training. Fourthly, a diverse range of models is
utilized in the studies, including LSTM Ensemble, XGBoost with GSFA, Ensemble
Stacking, BKS, RF, ENSEMBLE, AllKNN-CatBoost, OLightGBM, HELMDD, Multiple
Classifier (C4.5+NB), and Hybrid Ensemble. This diversity demonstrates the
exploration of different modeling approaches to tackle credit card fraud
detection. Lastly, the reported accuracies (in %) vary among the models,
ranging from 93.49% to 100%. Notably, our proposed model achieves a perfect
accuracy of 100% using the Undersampling (IHT) technique with a Hybrid
Ensemble approach.

Based on this comparison analysis, it is evident that our proposed model
surpasses all other existing works in terms of accuracy, achieving a
remarkable 100%. This outstanding result positions our model as the most
effective and reliable solution for credit card fraud detection among the
evaluated models. In summary, the comparison analysis demonstrates the
superiority of our proposed model in achieving a perfect accuracy of 100% in
credit card fraud detection. The utilization of the Undersampling (IHT)
technique with a Hybrid Ensemble approach sets our model apart from the
existing works, highlighting its potential for practical implementation and
its capability to address the challenges posed by imbalanced data in fraud
detection.

SI. No. | Authors | No. of Transactions Data | Data Balancing Techniques | Models | Accuracy (%)
---|---|---|---|---|---
1 | (esenogho2022neural, ) | 284,807 | SMOTE-ENN | LSTM ENSEMBLE | 99.0 (AUC)
2 | (jovanovic2022tuning, ) | 284,807 | SMOTE | XGBoost-GSFA | 99.98
3 | (soleymanzadeh2022cyberattack, ) | 284,807 | - | Ensemble Stacking | 93.49
4 | (nandi2022credit, ) | 284,807 | - | BKS | 99.80
5 | (dornadula2019credit, ) | 284,807 | SMOTE | RF | 99.98
6 | (faraji2022review, ) | 284,807 | SMOTE | ENSEMBLE | 99
7 | (alfaiz2022enhanced, ) | 284,807 | - | AllKNN-CatBoost | 99.96
9 | (taha2020intelligent, ) | 284,807 | - | OLightGBM | 98.40
10 | (xie2021heterogeneous, ) | 284,807 | - | HELMDD | 98.53 (AUC)
11 | (dornadula2019credit, ) | 284,807 | - | Multiple Classifier (C4.5+NB) | 99.99
12 | (lakshmi2018machine, ) | 284,807 | Random Sampling | RF | 95.5
13 | Proposed | 284,807 | Undersampling (IHT) | Hybrid Ensemble | 100

Table 3: Comparision analysis of our model with existing works

Ensemble learning combines the predictions of multiple base models to improve
overall performance, mitigating the limitations of individual algorithms and
capturing diverse patterns in the data. By integrating multiple algorithms and
optimizing their contributions through techniques like grid search, our
approach aims to achieve superior performance compared to standalone
algorithms.

Furthermore, the high stakes involved in fraud detection, including financial
losses and reputational damage, emphasize the importance of deploying advanced
techniques to enhance detection accuracy and reliability. Therefore, while
native algorithms may perform adequately, our research strives to push the
boundaries of fraud detection by employing sophisticated ensemble learning
methods.

##  6 Complexity Analysis

The complexity analysis of our proposed ensemble model with the individual ML
models is an important aspect of our study. The ensemble model adds a layer of
complexity compared to the base models due to the combination of their
predictions and the assignment of weights. However, the overall complexity of
the ensemble model depends on various factors such as the number of base
models used, the size of the data points, and the optimization techniques
employed, etc. The complexity analysis of our proposed model is elegantly
illustrated in Table 4.

Table 4: Time and Space Complexity of Ensemble Algorithm Model | Time Complexity | Space Complexity
---|---|---
DT | $O(m\cdot n^{2})$ | $O(l)$
RF | $O(t\cdot\log(n))$ | $O(et)$
KNN | $O(n\cdot m\cdot k)$ | $O(n\cdot m)$
MLP | $O(n^{2})$ | $O(et)$
Ensemble | $O(N*max(m*n^{2},t*log(n),n*m*k,n^{2}))$ | $O(N*max(l,et,n*m,n^{2}))$

Note: In the table, N is the number of base models, m is the number of
features, n is the number of training examples, k is the number of nearest
neighbors in KNN, t is the number of decision trees in RF, l is the maximum
number of nodes in a decision tree, and e is the number of parameters in a
random forest or a multilayer perceptron.

As shown in Table 4, the time complexity of the ensemble algorithm is the
maximum of the time complexities of the individual models, multiplied by the N
factor. The overall time complexity is given by O(N * max(m * $n^{2}$, t *
log(n), n * m * k, $n^{2}$)). Similarly, the space complexity of the ensemble
algorithm is the maximum of the space complexities of the individual models,
multiplied by the N factor. The overall space complexity is given by O(N *
max(l, et, n * m, $n^{2}$)), where l is the maximum number of nodes in a
decision tree, and e is the number of parameters in a random forest or a
multilayer perceptron. It’s important to consider the time and space
complexity of the ensemble algorithm, including the N factor, when
implementing it in practice, as it can impact the computational resources
required and the efficiency of the algorithm.

Our proposed ensemble model combines the strengths of different ML models to
create a powerful and versatile ensemble algorithm. With optimized time and
space complexity, our model enables fast and accurate predictions, robust and
scalable performance, effective and interpretable results, and powerful and
flexible learning, making it suitable for a wide range of applications. The
weighted average aggregation further simplifies the ensemble process, adding
minimal overhead while improving overall performance. Additionally, our model
takes advantage of efficient memory usage and storage utilization, making it
resource-friendly and efficient in real-world scenarios.

##  7 Dependability Analysis

In the context of credit card fraudulent detection, dependability refers to
the reliability, availability, efficiency, and scalability of our developed
model. (talukder2023dependable, ) introduced the concept of dependability,
which encompasses these key aspects. In this section, we assess the
dependability of our model by evaluating its reliability and performance using
a hybrid ensemble approach.

Our developed model incorporates a hybrid ensemble methodology that combines
multiple base models and assigns weights through grid search. This ensemble
approach ensures a reliable differentiation between normal and fraudulent
credit card transactions without any loss in performance. By leveraging the
collective intelligence of multiple models, our hybrid ensemble model enhances
the dependability of the overall system.

To evaluate the dependability of our model, we conducted comprehensive
analysis and productivity assessments using various performance metrics, as
shown in Table 2. These performance metrics provide insights into the
efficiency and scalability of our proposed framework. We compared the results
of our model with existing techniques and observed superior performance in
terms of lower error rates and computational loss. This indicates that our
model is highly dependable and capable of accurately detecting credit card
fraud while maintaining efficiency and scalability.

The exceptional effectiveness of our hybrid ensemble model in credit card
fraudulent detection is attributed to the combination of different base models
and the utilization of weights obtained through grid search. By leveraging the
strengths of each base model and optimizing the ensemble weights, our model
achieves enhanced performance and reliability. As a result, our proposed model
presents a promising solution for real-world credit card fraud detection
scenarios, demonstrating its dependability in critical financial applications.

##  8 Conclusion

In this paper, we proposed a hybrid ensemble ML model for fraudulent
transaction detection. The proposed methodology comprised several stages,
including data collection, data pre-processing, data normalization, sampling,
splitting, model selection, and performance analysis. We used the credit card
fraudulent transaction dataset as our input and addressed the data imbalance
problem using IHT with the LR algorithm technique to balance the dataset. We
then applied multiple ML algorithms such as DT, RF, KNN and MLP to initialize
our ensemble model. Finally, we combined all the ML algorithms to build an
ensemble model for fraudulent transaction detection. our proposed ensemble
model offers a dependable and efficient approach for credit card fraud
detection, surpassing many existing techniques in terms of accuracy,
precision, and computational efficiency. The ensemble model combines the
strengths of multiple base algorithms and leverages the results of grid search
to optimize its performance. The perfect accuracy, precision, recall, and F1
score, along with minimal error rates in MAE, MSE, and RMSE, highlight the
superior performance of our ensemble model. Our findings suggest that the
proposed ensemble model has the potential to significantly enhance credit card
fraud detection systems, improving the overall security and reliability of
financial transactions.

However, there are some limitations to our proposed model. The performance
heavily depends on the quality and representativeness of the input dataset,
and may not be suitable for detecting previously unseen or evolving types of
fraudulent transactions. The choice of ML algorithms and their hyperparameter
settings may also impact the model’s performance, necessitating further
optimization.

In future research, incorporating advanced feature engineering techniques,
exploring other data balancing techniques or ensemble methods, and
incorporating real-time data could further improve the model’s performance.
Conducting experiments on different datasets from various sources and
comparing them with other state-of-the-art methods could provide further
insights into the effectiveness and generalizability of our proposed model.

## Declarations

### Conflict of interest

The authors have no conflicts of interest to declare that they are relevant to
the content of this article.

### Funding

There is no funding available for this research.

### Ethics approval

Not applicable

### Consent to participate

Not applicable

### Consent to Publish

Not applicable

### Availability of data and materials

The dataset is available in the public repository as follows: CCFT Dataset :
https://www.kaggle.com/datasets/mlg-ulb/creditcardfraud

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