Abstract: In this paper, an innovative fraud detection model built upon existing data mining and fraud detection methods has been proposed. Here a bagging model has been applied and has been compared with other methods such as Logistic Regression, Naïve Bayes and Decision tree (DD). We use these methods as basic classifiers and make a bagging model according to them. A variety of measures are used for measuring and evaluating the efficiency and performance of each classifier and then all of them with the proposed model. This study is based on a real world dataset which has been divided into 4 smaller datasets with different fraudulent transaction rates. The proposed bagging model has shown higher performance compared to other mentioned models regarding almost all measures. The introduced model is using a virtual binary dataset which has been derived from the real life dataset.
Keywords: Fraud detection, Bagging, Naïve Bayes, Logistic Regression, Decision Tree.
1. Introduction
Rapid growth of E-commerce and the use of credit cards and online purchasing has caused an explosion in credit card fraud (Raj and Portia, 2011). The 14th annual online fraud report by CyberSource shows that although the revenue loss percentage has been decreased in online payment during the last four years in developed countries, but due to the very large volume of E-commerce transactions, the amount of revenue loss is still very large and cannot be underestimated (CyberSource Report, 2014). This report also indicates that applying fraud detection systems has a great effect on decreasing frauds. One important point that should not be ignored is that the report is for developed countries where E-commerce started many years ago and now spends its maturity age, but in developing countries like Iran which recently started E-commerce the situation is worse and hence using fraud detection systems especially in electronic banking is an important necessity.
In recent years and with the improvement in fraud detection and prevention techniques, fraudsters have improved their methods correspondingly and they apply very smart methods for doing fraud (West and Bhattacharya, 2016). On the other hand, the behaviour of fraudsters varies from one culture to another and this adds more complexity to the process of fraud detection so applying just one model for all types of fraud is not practically possible. Hence, the methods for detecting fraud always require revision.
The performance of fraud detection methods can be estimated based on different measures and the importance of these measures depends on the fraud detection system and the type of the business.
Three famous data mining methods are used in this study for detecting fraud in card transactions and different performance measures are used for comparing them.
The cost (money value) is always the most important measure for evaluating the performance of a method in commerce and especially in E-commerce. Hence, a bagging method which is based on simple methods is introduced that has the best result in almost all measures including cost.
The rest of the paper is organized as follows. Section 2 describes the work related to card fraud detection. Section 3 describes the card frauds. Section 4 describes the data mining techniques which have been used as a basis in this paper. Section 5 describes meta classifiers. The proposed bagging model has been described in section 6. Section 7 describes the dataset. The performance measures used for evaluation are described in section 8. Results are put forth in section 9, and section 10 describes the conclusion and future works.
2. Literature Review
Predictive models have been greatly used in practice. Some of them are mentioned in (Kou et al., 2004). Regarding the reputation of data mining techniques and application in recent years, however, there have been relatively few reported studies of data mining for card fraud detection and also there is no dominant method accepted as a basis in this field (West and Bhattacharya, 2016). Prevalent methods in credit card fraud detection are artificial immune systems (Wong et al., 2012) (Soltani Halvaiee and Akbari, 2014), fuzzy logics (Sánchez et al., 2009) (Jans et al., 2011), self-organising map (Quah and Sriganesh, 2008) (Olszewski, 2014), decision trees (Bai et al., 2008) (Whitrow et al., 2009) (Sahin et al., 2013), support vector machines (Kim et al., 2003) and hybrid methods (Duman and Ozcelik, 2011).
Case based reasoning is another fraud detection technique (Wheeler and Aitken, 2000) and recently Markov models have been used enormously (Raj and Portia, 2011), (Srivastava et al., 2008). The evaluation of some other techniques such as support vector machine, random forest and logistic regression has been discussed in (Whitrow et al., 2009).
3. Card Frauds
Card frauds can be divided into two main categories: Card present frauds (CP) and card not present (CNP) frauds (Krivko, 2010). Counterfeit cards, stolen cards, lost cards and receiving cards from banks with the presentation of another person’s information all fall in CP frauds. The most occurring of CNP frauds are online transactions with the help of a computer device or a cell phone. This type of fraud has assigned the most amount of card frauds in recent years (“cybersource 2015 annual report,” 2015). In these cases, obtaining the personal information of others leads fraudsters to getting access to accounts. There are several methods for obtaining others personal information, some of which are mentioned in (Bolton and Hand, 2002).
Fraud detection researches are facing many challenges which are real obstacles in this field. Some of them are mentioned in (Dal Pozzolo et al., 2014) and (Phua et al., 2012). The dearth of public literature on card fraud detection makes the exchange of ideas difficult and holds back potential innovation in fraud detection. On one hand, academicians have difficulty in obtaining card transaction datasets, thereby impeding research, while on the other hand, not much of the detection techniques get discussed in public lest fraudsters gain knowledge and evade detection (Whitrow et al., 2009).
The attributes of financial transaction such as card transactions are a combination of numerical and categorical attributes. An attribute like “Amount” for example is numeral while the others such as card holder’s name, code, and the date of doing the transaction all fall in the categorical sector. Some of the categorical attributes have many choices, and in some cases exceed from hundreds or thousands. This makes the analysing process of the dataset more complex and time consuming. In such cases using the machine learning and data mining applications is inevitable.
In this study some new numeric attributes have been derived from the main dataset. An effective model has been proposed for making a new dataset based on the main dataset in which all attributes are binary.
4. Data mining techniques
Classifiers are supervised data mining methods. In this paper three classification methods namely Naïve Bayes (NB), logistic regression (LR) and C5 are used. According to (Entezari-Maleki et al., 2009) C4.5 (C5 is an improved version of C4.5) is better than NB and LR based on the measure of AUC , and NB and LR have the same performance. Here we compare these three classifiers according to other measures as mentioned in section 8.
4.1 Naïve Bayes(NB)
The NB classifier algorithm is based on the Bayes rule of conditional probability and is particularly suitable for situations in which the size of inputs is very high (Lewis, 1998).
This theory makes it possible to gain secondary probabilities according to primary probabilities (Lewis, 1998).
Pr[Y│X]=(Pr[X│Y] Pr[Y])/Pr[X] (1)
Here Pr[Y] denotes the probability of an event Y, and Pr[Y|X] denotes the probability of Y conditional on another event X. The evidence X can be seen as a particular combination of attribute values, X=(X1,…,Xp).
4.2 Logical Regression (LR)
LR is a data mining technique which originates in statistics. It has been derived from linear regression and is used in situations in which the output variable has only two states just like fraud detection, fraud or not fraud. LR is useful for situations in which some want to predict the presence or absence of a characteristic or outcome based on values of a set of predictor variables (Shen et al., 2007). The model of the Logistic Regression is:
log(p/(1-p))=β_0+β_1 X_1+β_2 X_2+⋯+β_n X_n (2)
where p denotes the probability of the response variable Y being 1. X1, X2…Xn are the explanatory variables and ß0, ß1 … ßn are the regression coefficients to be determined by the regression model, usually estimated using a maximum likelihood estimation.
LR can be used ideally in binary classification problems in which the occurrence of class1 implies the non-occurrence of class 2 and vice versa. Therefore, Logistic Regression can be applied to fraud detection problems, which are very typical two-class problems.
4.3 C5 Decision tree
There are several important reasons for using decision trees in classification problems. Their predictive ability often outperforms even more sophisticated algorithms and they are easy to interpret and implement. In some domains it is not only necessary to get an accurate prediction, but also to get some reasoning behind that prediction. For example, if a customer applies for a loan and his request is denied he would appreciate to know why. If this bank uses decision trees to predict customers with a high risk to default, they can tell the customer exactly why he hasn’t been approved. With other classifiers this is not easy and for some even impossible. Another reason for the popularity of decision trees is that classifying a new observation according to a tree is simple and does not involve any complex or time-consuming calculations. High accuracy rate, simplicity, and high efficiency are other advantages of the decision tree algorithm. It can handle nonnumeric data in addition to numeric data and is very suitable for individual credit evaluation of commercial banks (PANG and GONG, 2009, p. 5).
The C5 decision tree is based on an ID3 algorithm and both of them have been developed by Quinlan.
5. Meta Classifiers
Meta-classifiers are algorithms which strive to improve the performance of a predictive model using any given classifier as base classifier. The nice thing about these meta-classifiers is that they basically work with any classifier, although some classifiers are more suited in conjunction with specific meta-classifiers than the others (Westreich et al., 2010). Improving performance, of course, depends on how you measure performance. The measures for evaluating a data mining method can be divided into two main categories: reducing the error rate which is computed by dividing the number of incorrectly classified instances and the other is reducing the amount of cost which is due to the wrong classified samples and extra costs which the fraud detection system imposes to the business (Westreich et al., 2010).
Bagging, AdaBoost and Stacking are the most popular meta-classifiers (Bauer and Kohavi, 1999). In this study, a Bagging meta-classifier is used.
Bagging: The word bagging stands for Bootstrap Aggregating. Bootstrap means taking equally sized samples from a dataset with replacement. In this case the subsets may contain repeated samples several times (Dudoit and Fridlyand, 2003).
The basic idea behind the Bagging model is to aggregate different models derived by the same classifier using different bootstrap samples. All models in Bagging are taking part in an ensemble vote with equal weight. In order to classify a new instance of all created models which are usually quite different, one should vote for a class. The class with the most votes will be chosen as the predicted class (Dudoit and Fridlyand, 2003).
6. The proposed Bagging model
Here a multi-level method is presented. Each level has several models (the models that have been mentioned previously) with equal voting value. The accuracy degree of this model is higher and its cost is lower in comparison with simple models. This model can be made in 5 steps (Figure 1):
Using the training dataset, corresponding models of simple algorithms (LR, NB and C5) will be created.
Created models will be evaluated with the training dataset. The result for all samples is a column of 0 or 1 and this column will be added to the training dataset. Here we used 3 models, so three new binary columns will be added to the training dataset.
Except the three new binary columns all other training dataset columns will be removed. Hence we will have a training dataset with three new binary columns plus the object column.
Steps 2 and 3 will be repeated but this time for the test dataset. Hence a new test dataset with 4 binary columns will be obtained.
Based on the new test and training datasets, new models will be created and the results will be evaluated.
Figure 1- Proposed Bagging Model
7. Dataset
The real life dataset in this study contains the POS transactions of an Iranian bank. There are 102423 transactions from 4472 customers in a period of 23 months. In the pre-processing phase, 4221 transactions have been removed. The transactions belong to 3576 separate accounts and the total number of devices that these transactions were done on were 5061 which were distributed in 411 different city points. The total number of fraudulent transactions in this dataset is 786 transactions (0.8% of all transactions).
The transactions mostly belong to B2C commerce and the average amounts are about 700000 (22 US dollar).
Primary attributes are those attributes that are available in the real dataset (like amount, time, id etc.) and all of them except the “amount” are non-numerical.
Incompatibility and high dimensionality always make it impossible to apply all transactions of the dataset in fraud detection systems (Whitrow et al., 2009). For solving this problem, an integrated transaction strategy can be used. In this strategy, the current behaviours of customers will be integrated in new attributes (Whitrow et al., 2009). In this study, a similar method is used and based on primary attributes in the dataset, some new attributes are exported. The new derived attributes are integrations of historical backgrounds of recent transactions and some of these derived attributes are like the number of purchases, average amount of purchases, maximum and minimum amount of purchases in special periods like days, weeks or months, and etc.
In this study, three classifier methods, the C5 decision tree, Naïve Bayes and Logistic Regression are evaluated and compared with a meta-learning algorithm. The meta-learning algorithm that is used here works based on a virtual dataset which is derived from the real dataset. Due to the low rate of fraudulent transactions in comparison with legal transactions (0.8%) which is typical in such applications, data from the two classes are sampled at different rates to obtain training data with a reasonable proportion of fraud to non-fraud cases. Hence, according to (Liu et al., 2009), random under-sampling of the majority class has been found to be generally better than other sampling approaches for our purpose.
We examine the performance of the different algorithms on four training datasets having 15%, 10%, 5% and 1% fraudulent transactions. These are labelled, DS-15, DS-10, DS-5, and DS-1 in the results. Performance is observed on a separate test dataset having 0.1% fraudulent transactions.
Clementine, which is a popular suite of machine learning, is used for analysing the data. For our comparative evaluation, parameters for the techniques were set from what has been found generally useful in the literature and as determined from the preliminary tests on our data. No further fine tuning of parameters was conducted. While fine tuning of parameters to specific datasets can be beneficial, consideration of generally accepted settings is more typical in practice. The need for significant effort and time for parameter fine tuning can often be a deterrent to practical use, and can also lead to issues of overfitting to specific data (Goodwin et al., 2003).
8. Performance measures
We use several measures of classification performance commonly noted in the literature, some of which are mentioned in (Bhattacharyya et al., 2011). Accuracy alone is inadequate as a performance indicator where there is significant class imbalance in the data. Since a default prediction of all cases into the majority class (non-fraud) will show a high performance value, here 99.2%, sensitivity and specificity measure the accuracy on the positive (fraud) and negative (non-fraud) cases. A trade off between these true positives and true negatives is typically sought. The F-measure gives the harmonic mean of precision and recall and G-mean gives the geometric mean of fraud and non-fraud accuracies (Bhattacharyya et al., 2011). The various performance measures are defined with respect to the confusion matrix below, where positive corresponds to Fraud cases and negative corresponds to non-fraud cases.
Table 1- Confusion Matrix
Predicted as non-fraud Predicted as fraud
False Negative(FN) True Positive(TP) Fraud
True Negative(TN) False Positive(FP) Non-fraud
The various measures are calculated as follows:
Accuracy= (TP+TN) / (TP+FP+TN+FN) (3)
Sensitivity=TP/ (TP+FN) (4)
Specificity =TN/ (FP+TN) (5)
Precision= TP/ (TP+FP) (6)
F-measure=2×(Precision ×Sensitivity)/(Precision+Sensitivity) (7)
G-mean= √((Sensitivity Specificity)) (8)
Those transactions that are more prone to fraud are investigated more than others, and this will impose more cost to the business. Correct detection of fraud cases prevents the loss of fraudulent activities. The cost of losses is always more than the cost of investigation of a fraud prone transaction. This means that the cost of FP and cost of FN are not equal. Hence, measures like AUC which treat FN and FP equally (Dal Pozzolo et al., 2014) are not useful for problems like fraud detection.
The importance of cost measure in fraud detection is so high that it can easily overshadow other measures. Cost can be regarded as the time, power and resources needed for processing a transaction. In fraud detection and in this study when we say cost, we mean the money value lost because of false recognition. False recognitions are either “False Positive” or “False Negative” and their costs are not equal. In almost all businesses it is obvious that the cost of FN is greater than the cost of FP. Regardless of the overall cost of using a fraud detection system, we can say that the cost of TP and TN are equal to zero. The cost of FP is equal to the review cost plus credit costs. The cost of FN is equal to the expected loss because of the fraud plus a credit cost. These costs are different for different businesses and also different cultures and should be estimated using historical data of that business and also expert’s recommendation.
The cost of fraud can be estimated as below:
Cost of fraud is equal to immediate direct loss due to fraud plus the cost of fraud prevention and detection plus the cost of lost business (when replacing card) plus opportunity cost of fraud prevention/detection plus deterrent effect on spread of e-commerce.
In this study, the cost measure is computed with respect to the cost matrix below.
Table 2- Cost Matrix
Not Fraud Fraud Cost Matrix
Credit loss = 23 0 Alarm Fraud
0 Loss cost=70 Alarm non-fraud
Here we consider the cost of fraud as the immediate direct loss due to fraud and set the other parameters equal to zero and since the average amount of all transactions in our sample dataset is about 700000, we set this equal to 70.
The credit loss has been estimated according to the following formula:
Credit loss= CCP * (CPR + CFN) (9)
Where CCP is the customer churn probability, CPR is the average of customer profit and CFN is the cost of finding a new customer. In this paper, CCP is set to 0.05. CPR is equal to all of the money that a customer spent in this business multiplied by 0.2 (the average profit of the money a customer spent in retail business is 20 percent of all that he/she spent), and CFN is set to zero. For our case, the result of this formula is equal to 23 which is the cost of the FN.
The value of these parameters can be estimated using the nature of the business data and also using expert’s opinion.
9. Results
This section presents results from our experiments comparing the performance of Naïve Bayes(NB), Logistic Regression(LR) and C5 decision tree with each other and finally with respect to the Bagging model which is proposed in this study.
The results of the mentioned models and the respected Bagging models for the DS-1 dataset are presented in table 3. The difference in Accuracy measure for NB, LR and C5 is low while the difference of Sensitivity measure for these three models is notable. Among them C5 has the best results.
Table 3- Comparative table of mentioned measures on DS-1
G-Mean F-Measure Precision Specificity Sensitivity acc
0.7029 0.4129 0.3522 0.9908 0.4987 0.9860 LR
0.4394 0.2605 0.3976 0.9966 0.1937 0.9874 NB
0.7960 0.7758 1 1 0.6337 0.9895 C5
0.8913 0.7906 0.7846 0.9970 0.7968 0.9943 Bagging-LR
0.8953 0.8791 0.9728 0.9996 0.8019 0.9965 Bagging-NB
0.7960 0.7758 1 1 0.6337 0.9963 Bagging-C5
After applying the proposed Bagging model on each of the three models, all measures have improved (Table 3). In this case, the Accuracy of Bagging-NB is more than the others. Except for Specificity and Precision, the equation below is true:
Bagging-NB > Bagging-C5>Bagging-LR
For Precision and Specificity, the following equation is true:
Bagging-C5 > Bagging-BN > Bagging-LR
In the following, the performance of the mentioned models according to different measures on datasets with different fraud rates is presented (refer to tables 4,5 and 6).
Table 4- Performance of Logistic Regression across different fraud rates
DS-1 DS-5 DS-10 DS-15 LR
0.9860 0.9898 0.8416 0.0096 accuracy
0.4987 0.1896 0.4103 0.9766 sensitivity
0.9908 0.8459 0.8459 0 specificity
0.3522 0.4620 0.0258 0.0096 precision
0.4129 0.2688 0.0486 0.0190 F-measure
0.7029 0.4004 0.5892 0 G-Mean
Table 5- Performance of Naive Bayes across different fraud rates
DS-1 DS-5 DS-10 DS-15 NB
0.9874 0.9519 0.7999 0.7416 accuracy
0.1937 0.3048 0.5287 0.6190 sensitivity
0.9966 0.8034 0.8034 0.7433 specificity
0.3976 0.0888 0.0329 0.0310 precision
0.2605 0.1376 0.0620 0.0590 F-measure
0.4394 0.4948 0.6517 0.6783 G-Mean
One of the most important measures in fraud detection systems is Cost measure. In most cases, Cost is a measure for accepting or rejecting a fraud detection system, especially in retail commerce and E-commerce. The overall cost involves the cost of using the fraud detection system and the cost of wrong prediction of the system.
The cost of false negative (FN) and false positive (FP) is presented in Table 2.
Since the model on DS-1 had the best performance across different measures, we computed the cost measure for DS-1 and the results were compared with the results of the proposed Bagging model.
Table 6- Performance of C5 across different fraud rates
DS-1 DS-5 DS-10 DS-15 C5
0.9895 0.9584 0.9967 0.0096 accuracy
0.6337 0.7409 0.6935 0.9766 sensitivity
1 0.9997 0.9997 0 specificity
1 0.1581 0.9673 0.0096 precision
0.7758 0.2607 0.8078 0.0190 F-measure
0.7960 0.8606 0.8326 0 G-Mean
The results of comparing the costs are presented in Table 7. On the right part of the table the cost of applying C5, NB and LR is shown and here the C5 model has the best result, but as we see in the right part of the table, the cost of applying Bagging models is shown. The overall costs in comparison with simple models are far less, and the B-NB (Bagging Naïve Bayes) has the best result with 4501, while the worst result in Bagging models belongs to B-C5 with 9870. For C5, the Bagging model and the simple model have the same results.
Table 7- Comparing Cost measure for models
LR NB C5 B-LR B-NB B-C5 Model
21629 22179 9870 6160 4501 9870 Cost
Figure 2- Comparative diagram of costs
Figure 3- Performance of mentioned models across different fraud rates
10. Conclusion
This paper examined the performance of three famous data mining techniques Naïve Bayes, Logistic Regression, C5 decision tree and their respective Bagging models for fraud detection in card transactions. The real dataset belongs to transactions of an Iranian bank. Due to the highly imbalanced data which is typical in such applications, an under sampling method was used for obtaining datasets with a reasonable proportion of fraud to non–fraud cases. Hence, 4 different datasets with different rates of fraud transactions were obtained and the performance measures were computed for them separately.
The results showed that the models are not the same according to different measures and on different datasets with different fraud rates. Although it seemed that the unbalanced nature of fraud datasets caused incorrect results, here DS-1 had better results in comparison to other datasets. The C5 model had better results in comparison with other simple models like LR and NB. After applying the Bagging model on them, all results improved and Bagging-C5 still had better results according to transactional measures.
As mentioned before, Cost measure is very important in retail E-commerce. Bagging models have much lower cost among the Bagging models, and the result of Bagging-NB is better than others and imposes lower cost to the business (Figure 3- Performance of mentioned models across different fraud rates).
Since the performance of meta learning models in fraud detection is so high, it is expected that more research be carried out on improving their performance in the future.
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