11institutetext:  1Department of Production and Operation Management, Faculty
of Management, University of Tehran, Tehran, Iran
2School of Science, Engineering and Environment, University of Salford, United
Kingdom
3Department of Information Technology, Duisburg-Essen University, Duisburg,
Germany
4Process and Data Science Chair, RWTH Aachen University, Aachen, Germany
11email<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
# Credit Card Fraud Detection Using Asexual Reproduction Optimization

Anahita Farhang Ghahfarokhi 11 Taha Mansouri 22 Mohammad Reza Sadeghi Moghadam
11 Nila Bahrambeik 11 Ramin Yavari 33 Mohammadreza Fani Sani 44

###### Abstract

As the number of credit card users has increased, detecting fraud in this
domain has become a vital issue. Previous literature has applied various
supervised and unsupervised machine learning methods to find an effective
fraud detection system. However, some of these methods require an enormous
amount of time to achieve reasonable accuracy. In this paper, an Asexual
Reproduction Optimization (ARO) approach was employed, which is a supervised
method to detect credit card frauds. ARO refers to a kind of production in
which one parent produces some offspring. By applying this method and sampling
just from the majority class, the classification’s effectiveness is increased.
A comparison to Artificial Immune Systems (AIS), which is one of the best
methods implemented on current datasets, has shown that the proposed method is
able to remarkably reduce the required training time and at the same time
increase the recall that is important in fraud detection problems. The
obtained results show that ARO achieves the best cost in a short time, and
consequently, it can be considered as a real-time fraud detection system.

###### Keywords:

Machine Learning $\cdot$ Asexual Reproduction Optimization$\cdot$ Credit Card
Fraud Detection $\cdot$ Fraud Detection $\cdot$ Artificial Immune Systems.

##  1 Introduction

Credit card fraud inflicts plenty of costs on banks and card issuers and
threatens their reputation [1]. A huge amount of money disappears annually
from legitimate accounts by fraudulent transactions [2]. In fact, E-business
has become one of the most important global markets which demands strong fraud
detection systems [3, 4]. In 2017, Online Fraud Report of Cyber Source
distinguishes average annual fraud loss among different order
channels111http://www.cybersource.com. 0.9% of the annual e-commerce revenues
is lost due to payment frauds through Web store channel in North America. This
value is 0.8% for Mobile channels and 0.3% for phone/mail order channel.
Different definitions of fraud have been presented by different organizations.
Based on The World Bank Group’s definition of fraud, the fraudulent practice
covers solicitation, offering or taking bribes, or the manipulation of loans
in the form of misrepresentation [5]. According to the division of the
Association of Certified Fraud Examiners, there are two types of fraud, i.e.,
internal frauds and external frauds. Internal fraud occurs when an employee
deliberately misuses an organization’s properties [6]. External frauds include
a more comprehensive variety in comparison with internal frauds. Dishonest
vendors who take bribes are a desirable example to mention. Untruthful
customers might alter account information to mislead payments. Besides, third
parties may use intellectual properties [7].

The credit card fraud techniques have changed over time, from physically
stealing the cards to online frauds [4]. Credit card frauds are categorized
into two categories, i.e., application frauds and behavioral frauds. An
application defrauder is a person who gets a new credit card from issuing
companies by utilizing the wrong information. A behavioral defrauder is a
person who has attained the information of a legitimate card fraudulently and
makes purchases when the cardholder is not present [8]. As the number of
frauds increases, the fighting techniques against fraud become more
significant [9]. Protection techniques against fraud include prevention and
detection systems. The first layer to protect the system against fraud is
prevention. Fraud prevention stops the fraud from occurring at the initial
level. Fraud detection is the next protection step. It identifies fraudulent
activities when they penetrate the system [10]. People use credit card-based
online payments more and more these days, forcing the banks to deploy fraud
detection systems [11]. Expert-driven, data-driven, and the combination of
both are the three kinds of fraud detection systems. Expert-driven systems are
based on fraud scenarios. If the data-stream matches the scenario from the FDS
viewpoint, the fraud has happened. Data-driven methods learn the fraud
patterns and find them in data streams [12].

Credit card fraud happens when a transaction on someone’s credit card is done
by another person [13]. If the fraud becomes a prevalent issue in a
competitive environment without any preventive systems, it will threaten
businesses and organizations seriously [6]. On the other hand, the number of
credit card transactions is increasing rapidly, which results in the growth of
fraudulent activities [14] It is pretty expensive to analyze the transaction
is done by the client or not [15]. The fraud detection system is aimed to stop
it as soon as possible. Whether the fraud detection system is manual or
automatic, it has to be effective. The system should identify a high
percentage of fraudulent transactions while keeping the false alarm rate low.
Otherwise, the users will become apathetic to alarms [16]. To reduce the cost
of detection, many machine learning techniques have been implemented.
Supervised methods are more common than unsupervised techniques [8].

Nowadays, different data mining techniques have been developed [17, 18, 19,
20, 21, 22] and by acknowledging the development of data mining methods,
efficient ways have been found to detect fraud [23]. However, many of these
methods need a time-consuming training phase. This limitation decreases the
applicability of these methods. To address this problem, we propose to use
Asexual Reproduction Optimization (ARO). In this paper, we implemented and
applied this method on a publicly available dataset. The experimental results
show that using the proposed method enables us to achieve reasonable accuracy
faster, compared to one of the state-of-the-art fraud detection methods, i.e.,
Artificial Immune Systems (AIS).

The remaining part of the paper has been organized as follows. Section 2
provides a literature review on credit card fraud detection methods.
Following, Section 3 describes the ARO and AIS models. Afterwards,
experimental results are presented in Section 4 and analyzed in Section 5.
Finally, Section 6 concludes the paper and provides some new directions to
continue this research.

##  2 Credit Card Fraud Detection Methods

Table 1: Approaches for credit card fraud detection.

Machine learning algorithm | Method | references
---|---|---
Supervised classifying | k-Nearest Neighbors (KNN) |  [24], [25], [1], [26], [27], [28], [29], [30], [31]
Bayesian Networks (BN) |  [32], [33], [34],[15],[15], [35], [36], [37], [38]
Decision Trees (DT) |  [39], [25], [34], [15], [40], [41], [26], [42] [43] [44] [45]; [46], [47], [48], [49], [50], [31]
Artificial Immune Systems (AIS) |  [51], [34], [15], [1], [52], [53]
Naïve Bayes (NB) |  [54], [55], [56], [24], [25], [33], [15], [34], [26], [57], [58], [44], [38], [30], [30], [28], [59], [49], [29], [47], [31]
Support Vector Machines (SVM) |  [4], [23], [60], [61], [62], [63], [39], [25], [26], [64], [44], [45], [46], [65], [29], [66], [67], [68], [31]
Logistic Regression |  [24], [4], [23], [25] [44] [30], [28], [67], [59], [45]; [69]
Random Forest |  [56], [4], [23], [39], [25], [12], [26] [57], [44], [70], [69], [50], [71], [72], [49], [59], [73], [66];[74]; [75]
Genetic Algorithm (GA) |  [76], [77], [78], [79], [80], [81], [82]
Neural Networks (NN) |  [83], [84], [85], [86], [2], [25], [87], [11], [88], [34], [15], [89], [90], [91], [92], [30], [93], [94], [67], [95], [96], [97], [98], [99],
|  [12], [100], [101], [26], [35], [102], [78], [103], [44], [104], [45],
[70], [105], [69], [106], [107], [108], [68]
Scatter Search | [76]
APATE | [69]
Fisher Discriminant | [109]
Unsupervised clustering | Self-Organizing Maps |  [110], [111], [112]
Fuzzy |  [84], [113], [114], [115]
Principal Component Analysis | [116]
Hidden Markov Model (HMM) |  [117], [118], [119], [120]; [121], [122], [75]
Simple K-Means | [116]

Fraud detection merges anomaly-based detection and misuse-based detection by
applying data mining techniques. Anomaly-based detection consists of
supervised, unsupervised, and semi-supervised algorithms [123]. Supervised
algorithms require all existing transactions, which are labeled as fraudulent
and non-fraudulent transactions. These algorithms assign a score to a new
transaction, which determines the transaction’s label [8, 6]. Unsupervised
methods work with unlabeled test dataset and try to find the unusual
transactions. These algorithms represent a baseline distribution for the
normal behavior. Transactions with a great distance from it are considered
unusual ones [8, 124]. Semi-supervised methods contain both labeled and
unlabeled instances. Semi-supervised learning aims to design the algorithms,
which can use these combined instances [124]. In general, the concept of
anomaly/outlier is problem-dependent and it is challenging to capture all
aspects of behavior in one single metric [125]. In Table 1, we presented some
of the data mining based approaches which are used for credit card fraud
detection, carried out in the literature [123, 126, 127, 128].

In [83], the authors presented a neural network-based system with a user-
friendly interface for fraud detection, implemented on synthetic datasets
[83]. In credit card fraud detection, datasets have skewed distributions. Chen
et al. employed Binary Support Vector System (BSVS), which could handle this
problem better than oversampling techniques. For support vector selection, the
genetic algorithm is used. Based on these vectors, they proposed BSVS [60].
Gadi et al. employed BN, NB, AIS, and DT techniques on the Brazilian bank
dataset that we used in this paper. They showed that generally applying cost-
sensitive and robust optimization leads to better results [34]. Because of
optimizing the parameters, AIS is the best technique [15]. Sánchez et al.
applied the association rules in the credit card fraud detection system. The
system determined patterns for legitimate transactions. The transactions that
do not match with the patterns are recognized as fraudulent [114]. Instead of
looking individually at data, authors in [68] consider them sequentially. They
applied SVM and Long Short-Term Memory Recurrent Neural Network (LSTM) for
modeling time series in fraud detection records. LSTM was a more suitable
classifier [68]. Rani et al. suggested a method using HMM which could conserve
user’s data effectively and bring back the information with ease [121]. Modi
et al. examined a single-layer feed-forward neural network for fraud
detection. The fraud categorization was divided into four groups of low to
high risk. If a transaction is recognized as a fraudulent one, it will belong
to one of these groups [102].

Using negative selection in addition to clonal selection, Halvaiee and Akbari
improved AIS. They suggested a new method AIS-based Fraud Detection Model
(AFDM) for calculating the samples’ fitness. Furthermore, in their proposed
model, they used cloud computing for training, which reduced the processing
time [1]. Zareapoor and Shamsolmoali examined bagged ensemble decision tree on
a real dataset and compared it with SVM, KNN, and NB. It achieved the highest
detection rate. The time was reduced significantly, and the ensemble technique
could solve the imbalanced dataset problem [31]. Carneiro et al. aim the
development and implementation of a fraud detection system at an e-tail
merchant. They showed that choosing the right variables in the dataset is a
key factor. Random forests, logistic regression, and support vector machines
were tested. A random forest can be an appropriate practical model [23]. Fiore
et al. used Generative Adversarial Networks (GAN) to detect credit card fraud.
GAN is a multiple-layer neural network consisted of a generator and a
discriminator. They employed GAN for solving imbalanced dataset problem. GAN
generates an augmented dataset that has more fraudulent transactions than the
initial dataset [11]. Behera and Panigrahi proposed a two-stage system. The
first stage tries to match the patterns. It consists of a fuzzy module which
computes a score. Given this score, one can envisage three categories:
legitimate, fraudulent, and suspicious. The next stage concludes a neural
network, which determines whether the suspicious one belongs to a fraudulent
or legitimate group [84].

De Sá et al. implemented a customized Bayesian Network Classifier (BNC) on the
dataset of a Brazilian payment service. They used a Hyper-Heuristic
Evolutionary Algorithm for generating BNC. The proposed method increased
economic efficiency remarkably [32]. Gómez et al. used an end-to-end neural
network for credit card fraud detection. They focused on solving imbalanced
dataset and cost evaluation problems and obtained valuable results[90]. Lucas
et al. modelled a sequence of credit card transactions from three different
perspectives. Each of these sequences with HMM and the likelihood associated
with HMM is used as additional features in the Random Forest classifier for
fraud detection [75]. Gianini et al. used a game theory-based approach for
detecting credit card fraud by managing a pool of rules [129].

Monirzadeh et al. increased the efficiency of the neural network by using the
genetic algorithm. Their research showed that the most effective criterion is
the information related to the transaction. Age, gender, and such factors do
not affect the detection [78]. In any fraud detection system, the chief
problem is always to increase the accuracy of approving a legal transaction,
whether in the shortest possible time or at the lowest cost for financial
institutions [15]. Therefore, the principal purpose of all the models
presented for this issue is to reduce the detection time, increase the
accuracy, reduce the costs, and present a model that can improve these factors
with better performance. According to the description, the algorithms’
performance has been compared through the three aspects of fraud detection
speed, accuracy, and cost presented in Table 2 [14].

As shown in Table 2, most of the algorithms have some disadvantages in the
mentioned indicators, and among them, AIS performs the best. This confirms the
results presented in [34], where different techniques are compared with each
other and AIS is the best technique based on their costs [15]. For this
reason, it is chosen for comparison with the ARO algorithm. We employed ARO,
which is a supervised method for credit card fraud detection. ARO is an
asexual reproduction optimization algorithm. Like Particle Swarm Optimization
(PSO), Genetic Algorithms (GA), and Ant Colony Optimization (ACO), ARO is also
an Evolutionary Single-Objective Optimization technique [130]. ARO has some
advantages that make it completely different from other algorithms. First, it
is an individually based technique which reaches the global optimal point,
astonishingly faster than other algorithms. Thus, unlike population-based
algorithms that require a large number of computational resources to convert,
ARO consumes much fewer resources and converges faster. The second case is
about mathematical convergence. It has good exploration and exploitation
rates. Third, ARO does not require parameter settings, so it is unlikely to
have trouble in setting parameters, which is a common meta-cognitive problem
of Genetic Algorithms (GA), Annealing Simulation (SA), Taboo Search (TS), and
Particle Swarm Optimization (PSO). Besides, ARO does not use any selective
mechanism such as a roulette wheel. Inappropriate adoption of selection
mechanisms may lead to problems such as premature convergence due to excessive
selection pressure. Fourth, ARO is a free model algorithm that can be applied
to various types of optimization [131, 132]. For all of the above reasons, ARO
can be selected for comparison with the AIS in fraud detection problems. ARO
has not been used in fraud detection up to this point. In this paper, a
comparison is made between ARO and AIS. We run ARO on the same dataset on
which the AIS has been implemented [34, 1].

Table 2: Comparison of algorithms.

Algorithm | NN | BN | SVM | KNN | DT | fuzzy | AIS | GA | HMM
---|---|---|---|---|---|---|---|---|---
Fraud detection speed | Fast | Very fast | Low | Good | Fast | Very low | Very fast | Good | Fast
Accuracy | Medium | High | Medium | Medium | Medium | Very high | Good | Medium | Low
Cost | Expensive | Expensive | Expensive | Expensive | Expensive | High expensive | Inexpensive | Inexpensive | High expensive

##  3 Using ARO for Fraud Detection

In this section, we explain ARO in more details and how we implement that to
detect fraud. Moreover, the AIS algorithm that has the highest performance is
briefly explained [1]. As the ARO method is a supervised method, we need to
separate the data into train and validation parts. Therefore, like any other
supervised method, we use the train part of data for the training and the
validation part for the testing phase.

####  3.0.1 ARO algorithm

ARO is taken from asexual reproduction. Asexual reproduction refers to a kind
of production in which one parent produces offspring identical to herself
[133]. In populations like bacteria, asexual reproduction is prevalent [134].
There are several kinds of asexual reproduction like budding [135], asexual
spore production [136], and binary fission [137]. ARO is inspired by the
budding method. In the budding method, the parent produces a smaller copy of
itself called a bud. The bud separates itself from the parent to become an
independent one [130].

Here, we explain how we use ARO for detecting frauds. According to the label
of transactions in the training data, two separate matrices were created for
fraud and legal transactions. For each feature in the legal matrix, the
maximum and the minimum values are determined and placed in the maximum and
the minimum legal matrices, and a parent is created randomly between the
values of the maximum and the minimum matrices. Note that the value of each
bit in this parent is a random value between its corresponding bit in the
maximum and the minimum legal matrices. The value of the parent fitting was
calculated using the fitting function given in Equation 2 and named “parent-
fitting”.

$distance_{record-normal-
transtions}=\frac{\sum_{i=1}^{M}\sum_{j=1}^{N}(\frac{|r_{i}-nt_{ji}|}{max_{i}-min_{i}})}{kN}$
(1)

Where $M$ is the number of features in our dataset.

The cut point in a dataset is the best fitness achieved in that dataset.

$distance_{record-normal-
transtions}=\frac{\sum_{i=1}^{M}\sum_{j=1}^{N}(\frac{|r_{i}-nt_{ji}|}{max_{i}-min_{i}})}{kN}$
(2)

Afterwards, we repeat the following process until the parent fit is smaller
than the cut point of the data set.

  * •

Select the starting bit (S) as a random number within the range of the number
of features. Select the end (E) between the starting bit and the last number
of features. Calculate the probability of mutation through Equation 3:

$P=\frac{1}{1+Ln(E-S+1)}$ (3)

  * •

Put the bud equal to the parent.

  * •

For the bits between the starting and ending bit selected randomly as above,
if the probability P calculated in Equation 3 is greater than or equal to an
arbitrary random number between zero and one in MATLAB, the value of the bit
will be mutated. In this way, the bud will be mutated.

  * •

The value of the mutated bud in Equation 4 is calculated (using the fitting
function) and named as ”bud fit”.

$distance_{record{-}final{-}transtions}{=}distance_{record{-}fraud{-}transtions}{-}distance_{record{-}normal{-}transtions}$

(4)

  * •

If the bud is fitted, it is more than the parent, and the bud replaces the
parent. Fitting the bud replaces the parent fitting. The bud is added to the
identifier matrix, and one unit is added to the count of the matrix rows of
the identifier.

  * •

In each fitting calculation, separate bud fits are calculated for the
fraudulent matrix and the legal matrix. Fit the bud for the fraudulent matrix
added to fraudulent matrix Equation 5. One is added to the counter of the
fraudulent fitting matrix. The fitting of the bud for the legal matrix is
added to the legal matrix Equation 2, and one is added to the count of the
legal matrix rows. The loop termination condition reaches to a value more than
or equal to the parent fit compared to the cut point.

$distance_{record-fraud-
transtions}=\frac{\sum_{i=1}^{M}\sum_{j=1}^{F}(\frac{|r_{i}-ft_{ji}|}{max_{i}-min_{i}})}{kF}$
(5)

Figure 1: Flowchart of ARO.

The schematic view of ARO algorithm is presented in Figure 1. In ARO
algorithm, an individual is shown by a vector of variables
$X{=}(x_{1},x_{2},…,x_{n})$, $X{\in}\mathcal{R}_{n}$. Each variable is
considered as a chromosome. A binary string represents a chromosome consisted
of genes. The length of the string is $L{=}l_{1}+l_{2}+1$. It is supposed that
every generated answer exists in the environment, and because of limited
resources, only the best solution can remain alive. The algorithm starts with
a random individual in the answer scope. This parent reproduces the offspring
named bud. Just the parent or the offspring can survive. In this competition,
the one which outperforms in fitness function remains alive. If the offspring
has suitable performance, it will be the next parent, and the current parent
becomes obsolete. Otherwise, the offspring perishes, and the present parent
survives. The algorithm recurs until the stop condition occurs.

In the reproduction stage, a substring with $\lambda$bits is picked out in all
chromosomes, which is named larva. $\lambda$ is a random number between 1 and
L. In the exploration phase, the substring is mutated, in each gene in the
substring, 1 is swamped by 0 and 0 by 1. In the exploitation phase, the parent
and larva merge as shown in Figure 3. Process of bud reproduction. If $P$
which is calculated from $P{=}\frac{1}{1+{L_{n}(\lambda)}}$ is higher than
$0.5$, the bud gene is picked out from the larva, otherwise the bud gene will
be picked out from the parent chromosome.

Figure 2: A model for a chromosome in ARO.  Figure 3: Process of bud
reproduction.

Equation 6 relates the exploitation and exploration. If $\lambda$ is a big
number, less exploitation is needed and vice versa. In fact, exploration and
exploitation are inversely related.

$P{=}\frac{1}{1+L_{n}(\lambda)}$ (6)

The fitness of both bud and parent is calculated to choose the best one for
the algorithm’s next run after reproduction [131, 130]. Note that we do this
procedure for all records and all features. Each record has a fraud or normal
label. There are the following hints to mention:

  1. 1.

According to Figure 2, a chromosome has three parts. Here, just the integer
part is considered because we do not have the sign or decimal part.

  2. 2.

Genes are not binary and they contain integer numbers.

  3. 3.

Only the normal (or legal) records are sampled because the dataset is skewed
toward normal transactions. The number of normal transactions is significantly
more than the fraudulent transactions. Thus, normal records society is
suitable for sampling versus the fraudulent society.

  4. 4.

For generating the first parent, one should determine the range for each bit
(gene). Then, for each gene in the first parent chromosome, a random number
between the maximum and the minimum of that gene is chosen.

  5. 5.

The fitness function will be used, which is described in the next section.

  6. 6.

First, a larva should be generated when reproducing a bud. For generating a
larva, a random length should be created. Each gene in this length assumes a
random number between the maximum and the minimum of that gene. This length
would be a larva. The next step for reproducing a bud is choosing the gene
between larva and parent, like in Figure 3 (the process of bud reproduction).
In this step, for choosing each gene between larva and parent, a random number
is generated. If the random number is less than $p$, which is obtained from
(1), the gene is selected from the larva, otherwise the gene is selected from
a parent.

Parameter setting causes plenty of problems in methods such as PSO and GA. ARO
does not need parameter setting. ARO is an individual-based technique which
saves time, unlike population-based techniques that waste time. ARO can be
used in different kinds of optimization issues despite many algorithms, which
can only be used in one sort of optimization problems. Adjustment with a
diverse genetic environment is one of the problems faced in ARO. However, it
can be solved by special reproduction operators [130].

Fitness function In case one decides to evaluate fitness for a specific
record, at first, the distance between the record and all fraud transactions
is calculated by Equation 4, and then the distance between the record and all
normal transactions is calculated by Equation 1. The difference between these
two numbers, as shown in Equation 3, would be the fitness. Due to only
sampling the normal records, the higher is the fitness number, the better it
is because it shows that the record is closer to the normal transactions than
the fraud ones. Thus, it can be a suitable normal sample. In Equations 4 and
1, each record is considered to have $k$ fields. Here, $k$ is 17. The value of
the $i$’th field of the record is $r$, the value of the $i$’th field of the
j’th normal transaction is $nt_{ji}$, and the value of the i’th field of the
j’th fraud transaction is $ft_{ji}$. The maximum and the minimum of i’th field
in all records of dataset are represented by $max_{i}$ and $min_{i}$. The
number of all normal transactions in the considered dataset is $N$, and the
number of all fraudulent transactions is $F$.

####  3.0.2 AIS algorithm

AIS is inspired by the immune system of the human body. It creates the
detectors called lymphocytes for identifying non-self-cells like viruses.
Negative selection and clonal selection are two stages of the AIS. Through
negative selection, lymphocytes are created by a random combination of protein
patterns. Lymphocytes should not detect self-cells. Thus, the immune system
eliminates the lymphocytes that react to self-cells. In fact, all of the
lymphocytes generated randomly that react to self-cells are eliminated
immediately after creation, and other lymphocytes survive. This procedure is
named negative selection. After negative selection, a short life starts for
the remaining lymphocytes. They meet any non-self-cells. If any lymphocyte
reacts to a non-self-cell, it can survive to protect the body against those
non-self-cells. This procedure is named clonal selection. The lymphocyte which
detects a non-self-cell is cloned by mutation. The colony cells, which are
closer to the non-self-cell, are chosen to survive. These colony cells are
considered as memory cells and will react to non-self-cells like viruses [1].

Both non-self-/self-cells are considered as vectors. At first, the training-
set should be normalized. Initializing the parameters is the next step. Then,
$N_{pop}$ of normal records is selected randomly as primary detectors (Just
the normal records like ARO were sampled). The affinity of these records is
calculated using the distance function. $N_{c}$ of the records with higher
affinity is selected. A colony is expanded from them. It means the records
with more affinity will be replicated more. The colony is mutated. $N_{m}$ of
the best-mutated population is chosen to replicate $N_{m}$ of the worst memory
cells. This algorithm continues until the stop condition occurs [1]. Here, the
loop repeats are considered 150 times. $N_{pop}$, $N_{c}$, and $N_{m}$ are 25,
7, and 5, which have been driven from Gadi et al. and Halvaiee [15, 1].

Algorithm 1 AIS 1:Determine $N_{pop}$ $\%$ the number of all detectors
2:Determine $N_{c}$ $\%$ the number of detectors best match with non - self
cell  3:Determine $N_{m}$ $\%$ the number of best mutated detectors  4:while
stop conditions do not occur do 5: Choose $N_{pop}$ of population randomly,
call it $first{-}pop$ 6: Choose $N_{c}$ of best $first{-}pop$ based on their
fitness, call it $best{-}first{-}pop$ 7: Expand a colony from
$best{-}first{-}pop$, call it $colony{-}pop$ 8: Mutate $colony{-}pop$, call it
$mutated{-}pop$ 9: Choose $N_{m}$ of best $mutates{-}pop$ based on their
fitness, call it $best{-}mutated{-}pop$;  10: Replace $N_{m}$ of worst
detectors in memory cell by $best-mutated-pop$ 11:end while

##  4 Experiments

In this section, first, the experimental dataset is described. Afterward, we
explain some details of the experimental-setting, and next, we will present
the results based on the metrics discussed above.

###  4.1 Dataset

In our experiments, we used a Brazilian bank’s dataset, according to which
3.74% of all transactions are fraudulent. Nine splits are generated from all
transactions in the dataset. Each split has two parts. The first part, which
contains 70% of transactions, is for the training phase. The second part,
which contains 30% of transactions, is for the testing phase. The number of
fraudulent and legitimate transactions in each split is shown in Table 4 [34].
We used MATLAB 2016 software for AIS and ARO implementation. Thus, we changed
the format of datasets to CSV. We trained the fraud detection system by two
methods, i.e., ARO and AIS, as explained in the previous sections.

###  4.2 Experimental Settings

After training the model, in the second step, we ran our model on the
validation data with labeled transactions as fraud or normal. Then, in the
next step, a comparison is made between the predicted labels and real labels
by calculating four parameters:

  * •

$False\leavevmode\nobreak\ positive$ $(FP)$: The number of normal transactions
that mistakenly predicted as frauds by our method.

  * •

$False\leavevmode\nobreak\ negative$ $(FN)$: The number of fraud transactions
that mistakenly predicted as normal by our method.

  * •

$True\leavevmode\nobreak\ positive$ $(TP)$: The number of fraud transactions
that correctly detected by our method.

  * •

$True\leavevmode\nobreak\ negative$ $(TN)$: The number of normal transactions
that correctly detected by our method.

Using the above parameters, we are able to compute some common metrics to
evaluate the performance. We used four metrics in our testing phase:

  * •

$Sensitivity$ $(\frac{TP}{TP+FN})$: It is the ability to recognize a
fraudulent transaction as a fraudulent one.

  * •

$Precision$ $\frac{TP}{TP+FP}$: It is the accuracy on cases predicted as
fraud.

  * •

$Specificity$ $\frac{TN}{FP+TN}$: It is the ability to recognize a legitimate
transaction as a legitimate one.

  * •

$Accuracy$ $\frac{TP+TN}{TP+FP+TN+FN}$: It presents the proportion of correct
predictions.

In addition, we measured training and testing time, which are critical issues
in fraud detection. We used Equation 7 for cost calculating on this dataset.
Gadi et al. used this formula because the dataset has 100% of fraudulent
records and only 10% of legitimate records [15].

$Cost=100\times{FN}+10\times{FP}+TP$ (7)

In the next step, we compared the performance of the two algorithms. The whole
process of the fraud detection system is described in Figure 4.

Figure 4: Fraud detection system.

As mentioned before, each dataset has a specific cut point. By trial and error
method, we found the cut points presented in Table 3. In each training
dataset, there are about 28,000 records with 17 features. Finally, test (or
validation) datasets are used in the testing phase. For testing the samples
obtained by ARO or AIS method, these steps are followed:

Table 3: Cut points in the datasets. dataset | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
---|---|---|---|---|---|---|---|---|---
Cut point | 0.1754 | 0.1841 | 0.1739 | 0.1762 | 0.175 | 0.1777 | 0.176 | 0.1916 | 0.1749

  1. 1.

The distance of the record from all normal samples is measured.

  2. 2.

The distance is divided by the number of normal samples. One can call it final
distance.

  3. 3.

If the final distance is below the best cut-off value, one can categorize the
distance as normal, otherwise it would be fraudulent.

The performance is measured by the metrics discussed above. For the AIS
method, we have provided the results presented in [1], also the results of our
implemented version of this algorithm to have a more fair comparison. All the
codes are available in https://gitlab.com/Anahita-Farhang/ARO-AIS.

Table 4: Number of fraudulent and legitimate transactions in datasets.

Split type | Transaction type | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
---|---|---|---|---|---|---|---|---|---|---
train | Legitimate | 27,904 | 28,012 | 28,061 | 28,145 | 28,045 | 27,973 | 28,113 | 27,884 | 28,188
Fraudulent | 1,084 | 1,092 | 1,088 | 1,075 | 1,081 | 1,116 | 1,099 | 1,106 | 1,100
test | Legitimate | 12,184 | 12,076 | 12,027 | 11,943 | 12,043 | 12,115 | 11,975 | 12,204 | 11,960
Fraudulent | 475 | 467 | 471 | 484 | 478 | 443 | 460 | 453 | 459

###  4.3 Experimental results

This subsection presents the computational results of running AIS and ARO
algorithms111All the experiments were performed in a PC with an Intel® Core™
i5-3210M CPU @ 2.5GHz with 4GB RAM in Windows 8(x64).. In sensitivity,
precision, specificity, and accuracy, ARO achieved a higher average than AIS,
as shown in Table 5. For training time, test time, and cost, ARO shows better
performance. Results are shown in Table 6. As shown in Figure 5, ROC curve of
testing results with ARO and AIS algorithm for all datasets, by implementing
ARO, AUC, which is a suitable criterion for imbalanced datasets, is increased
by 13% more than the AIS method. It shows that for each cut-off value, ARO
outperforms AIS.

Table 5:  The results of implementing ARO and AIS on datasets. Metric | Sensitivity | Precision | Specificity | Accuracy
---|---|---|---|---
Method | ARO | AIS | ARO | AIS | ARO | AIS | ARO | AIS
DS 1 | 0.86 | 0.68 | 0.42 | 0.33 | 0.95 | 0.95 | 0.95 | 0.94
DS 2 | 0.88 | 0.8 | 0.46 | 0.22 | 0.96 | 0.89 | 0.96 | 0.89
DS 3 | 0.79 | 0.61 | 0.34 | 0.22 | 0.94 | 0.92 | 0.93 | 0.9
DS 4 | 0.65 | 0.63 | 0.23 | 0.16 | 0.91 | 0.87 | 0.9 | 0.86
DS 5 | 0.88 | 0.78 | 0.58 | 0.23 | 0.97 | 0.9 | 0.97 | 0.89
DS 6 | 0.86 | 0.58 | 0.38 | 0.24 | 0.95 | 0.94 | 0.95 | 0.92
DS 7 | 0.74 | 0.6 | 0.32 | 0.34 | 0.94 | 0.96 | 0.93 | 0.94
DS 8 | 0.72 | 0.51 | 0.23 | 0.2 | 0.91 | 0.93 | 0.91 | 0.91
DS 9 | 0.95 | 0.63 | 0.54 | 0.33 | 0.97 | 0.95 | 0.97 | 0.94
Average | 0.81 | 0.65 | 0.39 | 0.25 | 0.95 | 0.92 | 0.94 | 0.91
Table 6:  The results of implementing ARO and AIS on datasets. Metric | Train time (s) | Test time (s) | Cost | AUC
---|---|---|---|---
Method | ARO | AIS | ARO | AIS | ARO | AIS | ARO | AIS
DS 1 | 8.08 | 24.25 | 1.87 | 1.85 | 12,570 | 22,072 | 0.91 | 0.81
DS 2 | 8.46 | 24.90 | 1.32 | 1.19 | 10,781 | 23,213 | 0.92 | 0.84
DS 3 | 7.33 | 24.65 | 2.22 | 1.75 | 17,473 | 28,966 | 0.87 | 0.76
DS 4 | 4.68 | 24.44 | 1.23 | 1.52 | 27,923 | 33,864 | 0.78 | 0.75
DS 5 | 4.63 | 24.66 | 1.13 | 1.62 | 9,132 | 23,115 | 0.93 | 0.84
DS 6 | 7.78 | 24.57 | 1.34 | 1.75 | 12,889 | 26,925 | 0.9 | 0.76
DS 7 | 3.8 | 24.25 | 1.27 | 1.68 | 19,522 | 24,224 | 0.84 | 0.78
DS 8 | 7.06 | 24.32 | 1.79 | 1.72 | 23,944 | 31,599 | 0.81 | 0.72
DS 9 | 4.43 | 25.30 | 1.54 | 1.80 | 6,407 | 23,071 | 0.96 | 0.79
Average | 6.25 | 24.59 | 1.52 | 1.65 | 15,627 | 26,339 | 0.88 | 0.78
Figure 5: ROC curve of testing results with ARO and AIS algorithm for all
datasets.

Finally, two non-parametric statistical tests (i.e, wilcoxon and Kruskal-
Wallis) were conducted to ensure the statistical significance in terms of
accuracy for the ARO model. The Wilcoxon test results are illustrated in Table
8 that the ARO model almost reaches the significance level compared to AIS.
The Kruskal-Wallis test was used to show the equality of results in all nine
sections of the dataset. Results are presented in Table 9.

##  5 Discussion

We trained the system with ARO and AIS methods. As mentioned in Section 2,
given that ARO is a single-solution evolutionary algorithm, it responds faster
than the AIS that generates a community of data [131, 130, 132]. Therefore,
the good speed with no parameter setting and good convergence rate have made
ARO a good candidate versus AIS, and in our experiment, this claim was
confirmed in four indicators. In classification problems, there are some
common metrics to evaluate the performance: sensitivity (recall), precision,
specificity, and accuracy. These four metrics have been measured in our
testing phase. AUC was measured, which is the area under the ROC curve. ROC
curve plots sensitivity versus false-positive rate. In fact, the cut-off value
in the test phase is located at the top left corner in ROC curve. It is the
point where sensitivity and specificity are equal. Gadi et al. found that if
they use a cost function shown in Equation 7 in which they adopted an average
cost of 1 dollar for every verification and an average loss of 100 dollars for
every undetected fraud, they will obtain more applicable results. They used
this formula because the dataset has 100% of fraudulent records and only 10%
of legitimate records [15, 1, 138, 139]. This was considered to be more
similar to the practice used for a fraud score compared to a ROC curve that
compares multiple references simultaneously [15].

One of the main problems of AIS is the extreme need for a hyper-parameter
setting, which is not present in ARO. ARO is a bio-inspired algorithm, and we
aimed to test this algorithm against one of the algorithms that works best in
detecting fraud on a Brazilian bank’s dataset. Compared to other studies on
this dataset, the detecting speed and the computational cost were important.
We trained each dataset by each algorithm thirty times and registered the
results of the best cost. As shown in Tables 5 and 6, ARO has better
performance than AIS in all the metrics. The ARO method’s best performance
appears on the ninth dataset with the sensitivity of 0.95 and the cost of
6,407, which is better than the AIS method (sensitivity=0.63 & cost=23071).
The ARO method’s worst performance appears on the fourth dataset with the
sensitivity of 0.65 and the cost of 27,923, which is still better than the AIS
method (sensitivity=0.63 & cost=33864). The average sensitivity for ARO is
0.81 with the average precision 0.39. For the AIS technique, the average
sensitivity and precision are 0.65 and 0.25. Training time, which is a vital
issue in fraud detection, has been remarkably reduced. The average training
time for ARO is 6.25s, so ARO fraud detection system can be considered as a
real-time one. ARO improved sensitivity up to 25%, and precision up to 56%,
decreased cost up to 41%, and training time up to 75%. The first fraud
detection on our dataset was implemented by Gadi et al. He proved that by
optimizing the parameters, AIS is the best method in comparison with BN, NB,
and DT [15]. One of the best fraud detection systems on this dataset was
performed in [1]. They employed AFDM which is a kind of improved AIS method.
They achieved 17,389 for cost and 79 seconds for training time. By
implementing ARO, we achieved 15,627 for cost and 6.25 for training time which
are considerably better than the previous results. The obtained results and
the results of the previous researches are shown in Table 7.

Table 7: History of the previous and obtained results. Method | AIS | AFDM | AIS | ARO
---|---|---|---|---
Cost | 23,303 | 17,389 | 26,339 | 15,627
Reference | [15] | [1] | Proposed AIS | Proposed ARO

In the last part, we have used two non-parametric statistical tests. We have
applied Wilcoxon to show the significant difference between AIS and ARO
algorithms. This test ranks all differences and applies a negative sign to all
the ranks where the difference between the two observations is negative. The
hypothesis $H0$ in this test is the equality of the two algorithms and, as
shown in Table 8, in accuracy, sensitivity, precision, train time, and cost,
because of the p-values which are less than alpha ($\alpha=0.05$), this
hypothesis was rejected that means two algorithms are not equal. Also, in the
Wilcoxon test, negative rank for train time, test time, cost, and positive
rank for other indices showed that ARO performs better than AIS in all
indices.

Table 8:  Results of Wilcoxon signed-rank test with $\alpha{=}0.05$.

Compared model | Sensitivity | Precision | Specificity | Accuracy | Train time (s) | Test time (s) | Cost | AUC
---|---|---|---|---|---|---|---|---
Asymp. Sig. | 0.008 | 0.011 | 0.118 | 0.020 | 0.008 | 0.314 | 0.008 | 0.008

We have done Kruskal-wallis test because our dataset was divided into nine
sections and it is important to check whether all the samples are originated
from the same distribution. We performed this test to check whether there is a
significant difference between the nine samples in each index. The results are
shown in Table 9. The hypothesis $H0$ in this test is the equality between all
the nine samples. Due to the p-values which are greater than alpha
($\alpha=0.05$), and also because of the values of chi-square that are 8,
which is less than 15.5073 ($\chi^{2}_{0.05}=15.5073$ with $df=8$), the $H0$
hypothesis cannot be rejected which means in all indexes, our nine sections
are the same.

Table 9: Results of Kruskal-Wallis test.

Compared model | Sensitivity | Precision | Specificity | Accuracy | Train time (s) | Test time (s) | Cost | AUC
---|---|---|---|---|---|---|---|---
Chi-square | 8.000 | 8.000 | 8.000 | 8.000 | 8.000 | 8.000 | 8.000 | 8.000
df | 8 | 8 | 8 | 8 | 8 | 8 | 8 | 8
Asymp. Sig. | 0.433 | 0.433 | 0.433 | 0.433 | 0.433 | 0.433 | 0.433 | 0.433

As it was discussed, we have achieved promising results by using ARO
algorithm. However, there is room for improvement. For example, an algorithm
can be employed to choose the optimized cut-point values in Section 4.2.
Moreover, to increase the performance of the algorithm, we suggest using cloud
computing, i.e. implementing ARO algorithm on a cloud-based file system (e.g,
Hadoop) which makes data parallelization possible. Furthermore, new methods in
the deep learning area show progress in terms of time in comparison with
metaheuristic algorithms. Therefore, employing deep learning methods may
reduce the training time and have positive impacts on the final results.

##  6 Conclusion

Fraud is a critical concern for financial services (e.g., commercial banks,
investment banks, insurance companies, etc.) and individuals. Different types
of fraud cost millions of dollars every year. Among different types of fraud,
credit card fraud is the most common one and several solutions have been
proposed to detect fraudulent transactions. In this paper, we have implemented
the ARO (Asexual Reproduction Optimization) in credit card fraud detection.
This effective approach has achieved better results than the best techniques
implemented on our dataset so far. We have compared the results with those of
the AIS, which was one of the best methods ever implemented on the benchmark
dataset.

The chief focus of the fraud detection studies is finding the algorithms that
can detect legal transactions from the fraudulent ones with high detection
accuracy in the shortest time and at a low cost. ARO meets all these demands.
ARO is an Evolutionary Single-Objective Optimization algorithm with lots of
advantages that make it suitable for implementing in fraud detection problems.
First of all, being an individually based technique, it converges faster to
the global optimal point. Secondly, it has good exploration and exploitation
rates. Thirdly, it has no parameter settings, which is a common issue in meta-
cognitive problems such as Genetic Algorithms (GA), Annealing Simulation (SA),
Taboo Search (TS), and Particle Swarm Optimization (PSO). Results show that
ARO has increased the AUC, sensitivity, precision, specificity, and accuracy
by 13%, 25%, 56%, 3%, and 3%, in comparison with AIS, respectively. We have
achieved a high precision value indicating that if ARO detects a record as a
fraud, with a high probability, it is a fraud one. Supporting a real-time
fraud detection system is another vital issue. ARO outperforms AIS not only in
the mentioned criteria, but also decreases the training time by 75% in
comparison with the AIS, which is significant. Furthermore, two non-parametric
statistical tests (i.e., Wilcoxon and Kruskal-Wallis) were conducted to ensure
the statistical significance in terms of accuracy for the ARO model. The
Wilcoxon test results show that the ARO model almost reaches the significance
level compared to AIS. The Kruskal-Wallis test was used to show the equality
of results in all nine sections of the dataset. The results of applying these
two statistical tests ensure the statistical significance in our study.

##  7 Future Work

Our framework has addressed the problems such as high costs and training time
in credit card fraud detection. Although, there is still room for further
improvement. To increase the performance of the proposed method, it is
possible to test the proposed model in a cloud environment, i.e., Hadoop.
Moreover, ARO can be compared to PSO and QPSO, which have fewer parameter
settings than AIS.

In addition, the writers believe ARO has the potential to obtain much better
results. One improvement can be done by weighting the fields that compose a
transaction. In fact, there are plenty of fields in a transaction and some
fields are more important than other fields. Therefore, we can increase or
decrease the effect of the field on the final results through weighting fields
in the distance function. Furthermore, the distance function can be different
for each property in the dataset. As we discussed, each transaction has
several fields with different meanings. Then the concept of distance is not
the same for all the fields. As an example, suppose the person goes shopping
once per month. So the distance of 30 is usual and it equals zero for the time
concept. However, the distance of 30 for the amount column is important and it
is not equal to zero. Therefore, considering application-based distance
functions for each field is an interesting point to address in future work.

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