# Quantitative Detection of Financial Fraud Based on Deep Learning with Combination of E-Commerce Big Data

Authors: Jian Liu; Xin Gu; Chao Shang
Journal: Complexity
 (2020)

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## Abstract

At present, there are more and more frauds in the financial field. The detection and prevention of financial frauds are of great significance for regulating and maintaining a reasonable financial order. Deep learning algorithms are widely used because of their high recognition rate, good robustness, and strong implementation. Therefore, in the context of e-commerce big data, this paper proposes a quantitative detection algorithm for financial fraud based on deep learning. First, the encoders are used to extract the features of the behaviour. At the same time, in order to reduce the computational complexity, the feature extraction is restricted to the space-time volume of the dense trajectory. Second, the neural network model is used to transform features into behavioural visual word representations, and feature fusion is performed using weighted correlation methods to improve feature classification capabilities. Finally, sparse reconstruction errors are used to judge and detect financial fraud. This method builds a deep neural network model with multiple hidden layers, learns the characteristic expression of the data, and fully depicts the rich internal information of the data, thereby improving the accuracy of financial fraud detection. Experimental results show that this method can effectively learn the essential characteristics of the data, and significantly improve the detection rate of fraud detection algorithms.


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## Body

## 1. Introduction

With the development of the economy, there are more and more frauds in the financial field. The detection and prevention of financial fraud are of great significance for regulating and maintaining a reasonable financial order [1, 2]. Due to abnormal or unfair transactional nature, the transaction behaviours involved in fraud are different from the general customer and account operation behaviours and exhibit various abnormal characteristics, including abnormal transaction behaviours, abnormal transaction objects, abnormal transaction data, and abnormal capital trends. Anomaly detection refers to describing the user’s behavioural characteristics to distinguish between abnormal and abnormal behavioural characteristics that violate normal behaviour [3]. It can be used to monitor the transaction behaviour of multiple customers, employees, and financial transaction parties. It is very helpful for discovering the internal connection of things hidden in the data. It can effectively track and detect frauds [4].In the study of financial fraud, the neural network algorithm has been widely used due to its high recognition rate, good robustness, and strong implementation [5, 6]. Hu et al. [7] used radial basis function neural network to detect credit card fraud. Fisch et al. [8] proposed a data mining system that uses historical transaction data to build a neural network model to detect fraud. Merchant et al. [9] proposed a neural network model based on merchant credit and ROC analysis. Kolalikhormuji et al. [10] proposed a credit card fraud detection system for cascade neural network recognition. That is, the gating network is used to aggregate the confidence values of the three parallel artificial neural network classifiers, and the weight of the gating network is trained by the imperialist competition algorithm to obtain the optimal. Experiments show that this algorithm can obtain very high recognition rate and reliability. Liu et al. [11] used an evolutionary approach to construct a neural network model to identify fraud. Hu et al. [12] combined Bayesian and neural networks to build a detection model. They found that the simple Bayesian network takes less time to train in building the classifier, and the accuracy is higher. Nevertheless, the effect on the new data is not good, so they joined the neural network algorithm, and the effect has been improved very well. Mosbach et al. [13] used a Bayesian algorithm to construct an experimental system of bank antifraud model, to identify whether a credit card user has committed fraud. Credit card transaction records are also time-specific, and their records have corresponding relevance. Therefore, you can use association rules to find out customer transaction rules and then use the decision tree for anomaly detection. Ordyan et al. [14] used decision trees to analyse the differences between normal and abnormal transactions and then used the differences to identify fraud. Menon et al. [15] introduced a new theory of cost-sensitive machine learning into the decision tree and he found that this decision tree algorithm not only has traditional performance such as accuracy, recall rate is higher than existing algorithms but also has a good expressiveness to the newly defined cost sensitivity in the field of credit card fraud. Roldán-García et al. [16] proposed a multicore support vector machine and introduced user configuration information instead of pure transaction information. Mhatre et al. [17] used Hidden Markov Model to detect fraud. Jana et al. [18] used a new idea of fuzzy logic to detect fraud detection. The method first calculates the initial credit of each transaction through the first-order Sugeno fuzzy model. If the transaction is found to be suspicious, the back credit is calculated using the previous doubt score and applied by Bayesian fuzzy inference. Lin et al. [19] constructed a fraud detection system by combining neural networks and association analysis. Cao et al. [20] introduced a new algorithm based on the root-searching fast hierarchical clustering algorithm in the research on the detection algorithm of merchant category codes and carried out classification experiments on the entire merchant category codes, and achieved good results. Ryan et al. [4] used deep belief networks to extract behavioural features and support vector machines (SVM) to detect fraudulent behaviours. Liu et al. [21] used the spatial-temporal convolutional neural network to extract fraudulent behaviour features for abnormal behaviour detection and localization. Peng et al. [22] used image saliency information and multiscale optical flow histograms as low-level features, and then the deep learning network PCAnet is used to extract more effective features from these underlying features for abnormal behaviour detection.Through the analysis of the above literature, most of the existing abnormal behaviour detection uses artificial features, but artificial features have high computational complexity, and it is difficult to select and design an effective behaviour feature in complex scenarios. Therefore, this paper proposes a quantitative fraud detection algorithm based on deep learning of e-commerce big data. By establishing a model for e-commerce big data feature learning, mining the financial fraud behaviour characteristics of e-commerce big data, and inputting the features into the abnormal behaviour detection model, it can effectively, quickly, and accurately identify financial fraud behaviour, quantify fraud risk levels, and do well in advance relevant prevention work to avoid unnecessary losses caused by financial fraud.


## 2. Financial Fraud

Fraud is a subject of widespread concern in the current society. The definition of financial fraud is diverse [23]. One argument is that financial fraud is the act of using loopholes in the rules of financial products to obtain illicit benefits. It can also be said that any unjust act in the financial market that seeks to gain its own interests and causes losses to others or organizations is financial fraud.Faced with thousands of financial products and their derivatives in the financial market, the means of financial fraud are diversified. According to the financial products involved, there are loan fraud, deposit fraud, bill fraud, bankcard fraud, securities fraud, and insurance fraud. From the source of fraud, it can be divided into external fraud and internal fraud. According to fraud, it can be divided into the following three types:(1)
Using the banking transaction system to carry out illegal intrusion or illegal operations, to seek illegitimate benefits. Bankcard fraud, identity theft, and a large number of internal violations of the bank are all of this type. Typical is business process fraud; that is, fraudulent acts that use loopholes in business processes to gain profits, as shown in Figure1.(2)
Providing false promises or false credit guarantee information for fraud. Most investment and financing fraud fall into this category. Fraudsters often use high-profit investments as bait to obtain a means of financial fraud input by investors.(3)
Concealing important information and fraudulently creating information asymmetry. In the securities market, a large amount of insider trading, deliberately hiding its risks during the promotion of derivative products, and using various means to manipulate the securities market with a view to arbitrage are all types of fraud.Figure 1
Fraud in financial business processes.Regardless of the specific form of expression, there are two types of fraud commonly used by financial fraudsters: one is “make something out of nothing, it’s fake,” and the other is “the next one is good, the fish is mixed.” The details are shown in Figure2.Figure 2
The main ways of financial fraud.


## 3. Quantitative Detection Algorithm for Financial Fraud Based on Deep Learning

### 3.1. Stacked Denoising Encoder (SDAE)

The denoising encoder DAE is a three-layer neural network used to reconstruct the original dataxi from the noise data x˜i. DAE contains two parts, namely encoder and decoder. DAE learning is learning two mapping functions feW,b and feW′,b′. The variable W and the variable b, respectively, represent the weight matrix and deviation vector of the encoder part. The variable W′ and the variable b′, respectively, correspond to the parameters of the decoder. For noise data xi, the hidden layer output of the encoder is y:(1)y=fex˜¯i=sWx˜i+b=11+e−Wx˜i+b.The purpose of the decoder is to reconstruct the original dataxi from the noise data x˜i:(2)zi=fdy=sW′y+b′.Given a set of training samplesX=xii=1N, learn the parameters of DAE by solving the following optimization problem:(3)minW,W′,b,b′∑i=1Nxi−zi22+λWF2+W′F2+β∑j=1KKLμμ′.Among them, the first term represents the reconstruction error, the second term is the weight penalty term, and the third term is the sparsity constraint. Variableλ and variable β are equilibrium parameters. The variable μ is a sparsity parameter, which represents the coefficient level of the hidden layer node. The variable K is the number of nodes in the hidden layer. The variable μ^j is the activation value of the average threshold of the jth node of the hidden layer for all training samples. If the average activation value is greater than 0.5, the formula μ^j=1 is established. Otherwise, the formula μ^j=0 is established. The third sparsity constraint is as follows:(4)KLμμ′=−μlogμ^j+1−μlog1−μ^j.Using gradient descent method to solve equation (3), the DAE parameters can be determined.Multiple DAEs are stacked layer by layer to form SDAE, where the output of the lower layer DAE is used as the input of the upper layer DAE. For SDAE training, the DAE in each layer is trained from the lower layer to the higher layer. The trained SDAE can be used to learn an effective feature representation from the input data.


### 3.2. In-Depth Features of Financial Fraud

We use two SDAEs to extract behavioural features in the 3D volume cantered on the trajectory. The size of the 3D volume isN×N×L. Among them, the value of the length L of the trajectory is 15, and the variable N takes 32. In order to embed structural information, first, divide the cube into a space-time grid of nσ×nσ×nτ, where variable nσ takes the value 2, and nτ takes the value 3. Then use SDAE to extract depth features in these grids. Finally, the features of all mesh are combined to obtain the depth features corresponding to the trajectory.Figure3 shows the structure of SDAE for extracting behaviour depth features. SDAE includes two parts: encoder and decoder. The number of input layer nodes of the encoder is equal to the number of dimensions of the input data. Then, half by layer reduces the number of nodes in each layer until the “bottleneck” hidden layer. The structure of the decoder is symmetrical to the encoder. The output of the “bottleneck” hidden layer is the depth feature.Figure 3
Structure of stacked denoising encoder.


### 3.3. Word Packet Representation of Behaviour Characteristics

For a trajectory, a 1440-dimensional feature vector can be obtained. As the number of targets is different, the number of points of interest and the corresponding number of trajectories are different, and the dimension of behavioural characteristics is different. Therefore, the word packet method is used to express the behaviour characteristics as visual words, to unify the dimensionality of the behaviour.First, extract the depth features/depth of the trajectory. Then, cluster all trajectory depth features/depths to obtainNv class centres. Each category corresponds to a visual word. For the test behaviour samples, according to the nearest neighbour principle, each of its trajectories is classified into each category. Therefore, the frequency of occurrence of each visual word in the sample can be obtained, and these frequencies constitute the visual word representation of the sample.After many experiments, the number of appearance visual words and sports visual words were 370 and 430, respectively. Therefore, 370-dimensional and 430-dimensional visual word vectors represent the appearance depth feature and the motion depth feature, respectively.


### 3.4. Feature Fusion Based on Weighted Correlation

In order to improve the classification ability of features, feature fusion method based on weighted correlation is used to combine appearance depth features and motion depth features to form 800-dimensional feature vectors. For the convenience of presentation, the appearance depth feature and the motion depth feature are denoted byy1 and y2, respectively, and then the fused feature y is as follows:(5)y=w1y1,w2y2,where wi is the weighting coefficient, and w12+w22=1. We determine the weighting coefficient based on intraclass consistency and interclass separability.Intraclass consistency: it is generally desired that samples in the same category are as close as possible in the feature space. Nevertheless, usually, the sample features in the same category will have a larger variance. Therefore, there is no need to require all samples in the same category to be close to each other. One trade-off is to ensure that the samples within the same neighbour in the same class are as close as possible. Letyi=w1yi1,w2yi2 and yj=w1yj1,w2yj2 represent ith and jth samples, respectively, then the intraclass consistency is defined as follows:(6)Sc=∑i=1N∑j∈Nk+Fiyi,yjyiyj=∑i=1N∑j∈N1/kFi∑k=12wk2yikyjk∑k=12wk2yik2∑k=12wk2yjk2.In the formula, the variableNk+Fi represents the index set of K nearest neighbour samples of sample Fi that belong to the same class as Fi.Separability between classes: it is required that the features have good distinguishability; that is, two samples of different classes are as far away as possible in the feature space. However, there are many such sample pairs. In order to reduce the amount of calculation, only the sample pairs near the interface of the feature space are considered. Therefore, the separability between classes is defined as follows:(7)Sb=∑i=1N∑j∈Nk−Fiyi,yjyiyj=∑i=1N∑j∈N1/kFi∑k=12wk2yikyjk∑k=12wk2yik2∑k=12wk2yjk2.In the formula, the variableNk−Fi represents the index set of K nearest neighbour samples of sample Fi that are different from Fi. The fused features should have good intraclass consistency and interclass separability. Therefore, the weighting coefficient is determined by solving the following optimization problem:(8)maxSc−Sb+λsw,s.t.wk>0,w=1.In the formula, the variableλss is the control parameter. Use a gradient descent method to solve equation (8), namely:(9)wkt+1=wkt+η∂L∂wk|wk=wkt.In the formula, the variablet is the number of iterations, the variable η is the iteration step, and the formula L=Sc−Sb+λsw is the objective function.(10)∂L∂wk=∑i=1N∑j∈Nk+xi∂hijw∂wk−∑j∈Nk−xi∂hijw∂wk+2λswk.


### 3.5. Fraud Detection Based on Sparse Reconstruction

After obtaining the characteristics of the behaviour, sparse reconstruction is used to detect fraud. The basic idea is that any behaviour can be represented by a sparse linear combination of normal training samples. For normal behaviour, the sparse reconstruction error is small, while the abnormal behaviour sparse reconstruction error is relatively large. Therefore, we can detect fraud based on reconstruction errors.There are classC normal behaviours, and the above feature vector represents each behaviour. The variable D=D1,D2,D3,...,DC represents a sparse dictionary, where Di is a subdictionary composed of K behaviours of type i, which can be expressed as follows:(11)y=Da.The variablea=a1,a2,a3,...,aCT is a sparse coding vector.Given a dictionaryD, the test sample y can be expressed by formula (11). Among them, the sparse code a can be obtained by solving the following formula:(12)a∗=minay−Da2+λa.Once the optimal sparse codinga∗ is obtained, the sparse reconstruction cost can be calculated:(13)Sy,a∗,D=y−Da2+λa∗.For normal behaviour, the cost of sparse reconstruction is smaller, while the abnormal behaviour is more expensive. So if(14)Sy,a∗,D>ε.Theny is fraud. In the formula, ε is a present threshold.As shown in Figure4, the fraud detection method includes two stages. The first is the training phase of the model, as shown in Figure 4(a). Model training includes feature learning model and classification model training. Among them, the data preprocessing standardizes and normalizes the input data and completes the conversion of data types. The feature learning model training takes preprocessed unlabelled data as input to train the feature learning model. The trained feature learning model can be directly used to learn the features of the data and transform the representation of the sample in the original space into a new feature space. The training and testing of classification models should use labelled training sets and test sets for supervised training and testing.Figure 4
Detection process of financial fraud based on feature learning. (a) Model training stage. (b) Anomaly detection stage.
(a)(b)The second stage is the detection stage of financial fraud, shown in Figure4(b). In this stage, the input data is first preprocessed, then the feature learning model obtained in the first stage of training is applied to learn the features of the data to be classified, and finally, the learned data features are used as input to the classification model to classify the data.


## 3.1. Stacked Denoising Encoder (SDAE)

The denoising encoder DAE is a three-layer neural network used to reconstruct the original dataxi from the noise data x˜i. DAE contains two parts, namely encoder and decoder. DAE learning is learning two mapping functions feW,b and feW′,b′. The variable W and the variable b, respectively, represent the weight matrix and deviation vector of the encoder part. The variable W′ and the variable b′, respectively, correspond to the parameters of the decoder. For noise data xi, the hidden layer output of the encoder is y:(1)y=fex˜¯i=sWx˜i+b=11+e−Wx˜i+b.The purpose of the decoder is to reconstruct the original dataxi from the noise data x˜i:(2)zi=fdy=sW′y+b′.Given a set of training samplesX=xii=1N, learn the parameters of DAE by solving the following optimization problem:(3)minW,W′,b,b′∑i=1Nxi−zi22+λWF2+W′F2+β∑j=1KKLμμ′.Among them, the first term represents the reconstruction error, the second term is the weight penalty term, and the third term is the sparsity constraint. Variableλ and variable β are equilibrium parameters. The variable μ is a sparsity parameter, which represents the coefficient level of the hidden layer node. The variable K is the number of nodes in the hidden layer. The variable μ^j is the activation value of the average threshold of the jth node of the hidden layer for all training samples. If the average activation value is greater than 0.5, the formula μ^j=1 is established. Otherwise, the formula μ^j=0 is established. The third sparsity constraint is as follows:(4)KLμμ′=−μlogμ^j+1−μlog1−μ^j.Using gradient descent method to solve equation (3), the DAE parameters can be determined.Multiple DAEs are stacked layer by layer to form SDAE, where the output of the lower layer DAE is used as the input of the upper layer DAE. For SDAE training, the DAE in each layer is trained from the lower layer to the higher layer. The trained SDAE can be used to learn an effective feature representation from the input data.


## 3.2. In-Depth Features of Financial Fraud

We use two SDAEs to extract behavioural features in the 3D volume cantered on the trajectory. The size of the 3D volume isN×N×L. Among them, the value of the length L of the trajectory is 15, and the variable N takes 32. In order to embed structural information, first, divide the cube into a space-time grid of nσ×nσ×nτ, where variable nσ takes the value 2, and nτ takes the value 3. Then use SDAE to extract depth features in these grids. Finally, the features of all mesh are combined to obtain the depth features corresponding to the trajectory.Figure3 shows the structure of SDAE for extracting behaviour depth features. SDAE includes two parts: encoder and decoder. The number of input layer nodes of the encoder is equal to the number of dimensions of the input data. Then, half by layer reduces the number of nodes in each layer until the “bottleneck” hidden layer. The structure of the decoder is symmetrical to the encoder. The output of the “bottleneck” hidden layer is the depth feature.Figure 3
Structure of stacked denoising encoder.


## 3.3. Word Packet Representation of Behaviour Characteristics

For a trajectory, a 1440-dimensional feature vector can be obtained. As the number of targets is different, the number of points of interest and the corresponding number of trajectories are different, and the dimension of behavioural characteristics is different. Therefore, the word packet method is used to express the behaviour characteristics as visual words, to unify the dimensionality of the behaviour.First, extract the depth features/depth of the trajectory. Then, cluster all trajectory depth features/depths to obtainNv class centres. Each category corresponds to a visual word. For the test behaviour samples, according to the nearest neighbour principle, each of its trajectories is classified into each category. Therefore, the frequency of occurrence of each visual word in the sample can be obtained, and these frequencies constitute the visual word representation of the sample.After many experiments, the number of appearance visual words and sports visual words were 370 and 430, respectively. Therefore, 370-dimensional and 430-dimensional visual word vectors represent the appearance depth feature and the motion depth feature, respectively.


## 3.4. Feature Fusion Based on Weighted Correlation

In order to improve the classification ability of features, feature fusion method based on weighted correlation is used to combine appearance depth features and motion depth features to form 800-dimensional feature vectors. For the convenience of presentation, the appearance depth feature and the motion depth feature are denoted byy1 and y2, respectively, and then the fused feature y is as follows:(5)y=w1y1,w2y2,where wi is the weighting coefficient, and w12+w22=1. We determine the weighting coefficient based on intraclass consistency and interclass separability.Intraclass consistency: it is generally desired that samples in the same category are as close as possible in the feature space. Nevertheless, usually, the sample features in the same category will have a larger variance. Therefore, there is no need to require all samples in the same category to be close to each other. One trade-off is to ensure that the samples within the same neighbour in the same class are as close as possible. Letyi=w1yi1,w2yi2 and yj=w1yj1,w2yj2 represent ith and jth samples, respectively, then the intraclass consistency is defined as follows:(6)Sc=∑i=1N∑j∈Nk+Fiyi,yjyiyj=∑i=1N∑j∈N1/kFi∑k=12wk2yikyjk∑k=12wk2yik2∑k=12wk2yjk2.In the formula, the variableNk+Fi represents the index set of K nearest neighbour samples of sample Fi that belong to the same class as Fi.Separability between classes: it is required that the features have good distinguishability; that is, two samples of different classes are as far away as possible in the feature space. However, there are many such sample pairs. In order to reduce the amount of calculation, only the sample pairs near the interface of the feature space are considered. Therefore, the separability between classes is defined as follows:(7)Sb=∑i=1N∑j∈Nk−Fiyi,yjyiyj=∑i=1N∑j∈N1/kFi∑k=12wk2yikyjk∑k=12wk2yik2∑k=12wk2yjk2.In the formula, the variableNk−Fi represents the index set of K nearest neighbour samples of sample Fi that are different from Fi. The fused features should have good intraclass consistency and interclass separability. Therefore, the weighting coefficient is determined by solving the following optimization problem:(8)maxSc−Sb+λsw,s.t.wk>0,w=1.In the formula, the variableλss is the control parameter. Use a gradient descent method to solve equation (8), namely:(9)wkt+1=wkt+η∂L∂wk|wk=wkt.In the formula, the variablet is the number of iterations, the variable η is the iteration step, and the formula L=Sc−Sb+λsw is the objective function.(10)∂L∂wk=∑i=1N∑j∈Nk+xi∂hijw∂wk−∑j∈Nk−xi∂hijw∂wk+2λswk.


## 3.5. Fraud Detection Based on Sparse Reconstruction

After obtaining the characteristics of the behaviour, sparse reconstruction is used to detect fraud. The basic idea is that any behaviour can be represented by a sparse linear combination of normal training samples. For normal behaviour, the sparse reconstruction error is small, while the abnormal behaviour sparse reconstruction error is relatively large. Therefore, we can detect fraud based on reconstruction errors.There are classC normal behaviours, and the above feature vector represents each behaviour. The variable D=D1,D2,D3,...,DC represents a sparse dictionary, where Di is a subdictionary composed of K behaviours of type i, which can be expressed as follows:(11)y=Da.The variablea=a1,a2,a3,...,aCT is a sparse coding vector.Given a dictionaryD, the test sample y can be expressed by formula (11). Among them, the sparse code a can be obtained by solving the following formula:(12)a∗=minay−Da2+λa.Once the optimal sparse codinga∗ is obtained, the sparse reconstruction cost can be calculated:(13)Sy,a∗,D=y−Da2+λa∗.For normal behaviour, the cost of sparse reconstruction is smaller, while the abnormal behaviour is more expensive. So if(14)Sy,a∗,D>ε.Theny is fraud. In the formula, ε is a present threshold.As shown in Figure4, the fraud detection method includes two stages. The first is the training phase of the model, as shown in Figure 4(a). Model training includes feature learning model and classification model training. Among them, the data preprocessing standardizes and normalizes the input data and completes the conversion of data types. The feature learning model training takes preprocessed unlabelled data as input to train the feature learning model. The trained feature learning model can be directly used to learn the features of the data and transform the representation of the sample in the original space into a new feature space. The training and testing of classification models should use labelled training sets and test sets for supervised training and testing.Figure 4
Detection process of financial fraud based on feature learning. (a) Model training stage. (b) Anomaly detection stage.
(a)(b)The second stage is the detection stage of financial fraud, shown in Figure4(b). In this stage, the input data is first preprocessed, then the feature learning model obtained in the first stage of training is applied to learn the features of the data to be classified, and finally, the learned data features are used as input to the classification model to classify the data.


## 4. Results and Discussion

### 4.1. Model Evaluation Index

In the fraud detection algorithm, it is very important to find a good classifier evaluation index. On the one hand, a good evaluation index fully indicates the classifier’s ability to solve problems and can show the effect on users more comprehensively. On the other hand, the selected classifier evaluation index is also conducive to developers to optimize the classifier model. The main evaluation criteria of this article are accuracy rate, recall rate, and FM. Table1 is a confusion matrix, which introduces common concepts such as TP, FP, FN, TN. Where “0” means normal behaviour, and “1” means fraudulent behaviour. “Y” indicates that the number of detection stages is classified as normal behaviour, and “N” indicates that the number of detection stages is classified as fraud.Table 1
Confusion matrix applied to the detection model.
Experiment classification label01Predict fraud categoryYTP: Correct and affirmative.FP: The error is positive.A sample of normal behaviour predicted to be normal behaviour.A sample of normal behaviour predicted to be fraudulent.NFN: False negative.TN: Correctly denied.A sample of fraudulent behaviour predicted as normal behaviour.A sample of fraudulent behaviour predicted to be fraudulent.Based on the above four classifications, the following two concepts can be further extended to evaluate the performance of the classifier:(15)Precision=TPTP+FP,(16)Recall=TPTP+FN.Precision reflects accuracy. Recall reflects the recall rate. In general, the accuracy rate is to determine how accurate the detected classification is, and the recall rate indicates how many items with the correct classification are detected. Accuracy and recall indicators are sometimes opposite. The measure of model performance that combines accuracy and recall into a single value is theF metric. The F measure uses the harmonic mean to integrate the accuracy and recall rates. The specific formula is shown in the following formula:(17)F=q2+1Precision∗Recallq2Precision+Recall.When the parameterq=1 is established, it is the most common FM. The formula is as follows:(18)FM=2Precision∗RecallPrecision+Recall.Because theF metric turns the model’s performance index into a single value, it provides a convenient way to compare the model to good or bad. However, this requires assuming that the accuracy and recall rates have the same weight. A better practice is to combine F measures with other measures.In order to weigh the quality of the model, this paper also adds the ROC curve and AUC index to measure the overall credibility of the classifier. ROC represents the relationship between TPR and FPR in the classification confusion matrix. Therefore, the abscissa of the ROC curve represents the probability of a negative instance being regarded as a positive instance, and the ordinate represents the probability of a positive instance being regarded as a positive instance. In the ROC graph, TPR increases with the increase of FPR, and the faster the increase is, the more prominent the curve is, and the better the classification performance of the response model is. The value of AUC is the size of the area under the ROC curve. The larger the AUC is, the better the classifier performance is.In summary, this paper uses four indicators: accuracy rate, recall rate, FM, and ROC chart to measure the quality of the experimental results of this paper.


### 4.2. Detection Performance Analysis of the Algorithm

In this paper, based on each sample group in the training set and prediction set, the actual fraud rate and the predicted fraud rate in each group are calculated to evaluate the prediction ability of the model. The actual fraud rate and predicted fraud rate values and the line chart of each group are shown in Tables2 and 3 and Figure 5, respectively.Table 2
Comparison of actual fraud rate and predicted fraud rate in the training set.
Sample numberNumber of samplesContains the number of fraudsActual fraud ratePredicted fraud rate130012239.665%39.495%23005015.258%15.021%33003510.178%9.885%4300329.156%8.882%5300267.125%6.647%6300205.085%5.472%7300205.731%5.658%8300163.731%3.115%9300143.058%3.102%10300122.389%2.178%Table 3
Comparison of actual fraud rate and predicted fraud rate in the test set.
Sample numberNumber of samplesContains the number of fraudsActual fraud ratePredicted fraud rate130011637.632%35.946%23004714.246%14.268%33004513.596%12.587%43003510.175%10.158%5300308.457%8.328%6300205.082%4.389%7300236.125%5.821%8300143.059%2.985%9300122.379%3.109%10300101.695%1.479%Figure 5
Grouped predictions for training and test sets. (a) Training. (b) Testing.
(a)(b)Through the analysis of the above chart data, we can find that the algorithm proposed in this paper has a good predictive ability regardless of the balanced distribution of data or the extreme distribution of imbalance.In order to verify the effectiveness of the proposed method, the algorithm in this paper is compared with the following four methods:(1)
Lin et al. [19] constructed a fraud detection system by combining neural networks and association analysis.(2)
Ryan et al. [4] used deep belief networks to extract behavioural features and SVMs to detect fraudulent abnormal behaviours.(3)
Liu et al. [21] used spatial-temporal convolutional neural networks to extract fraudulent behaviour features for abnormal behaviour detection and location.(4)
Peng et al. [22] used image saliency information and multiscale optical flow histogram as low-level features. Then, the deep learning network PCANet is used to extract more effective features from these underlying features for abnormal behaviour detection.In the experiment, we first extracted the dense trajectory. Secondly, randomly select 5 million trajectories to train SDA and used the K-means clustering method to get 370 appearance visual words and 430 motion visual words. Then, we randomly selected 800 normal behaviour learning feature fusion parameters to obtain the parametersw1=0.3,w2=0.7. Finally, we learned sparse dictionaries with 800 normal behaviours. All abnormal fraud behaviour samples and the remaining 200 normal samples are used as test samples. The test results are shown in Table 4.Table 4
Test results of different algorithms.
AlgorithmPrecisionRecallFMAUCLiterature [19]82.853%72.581%70.831%91.021%Literature [4]93.581%89.367%88.213%96.123%Literature [21]91.952%85.987%75.902%95.368%Literature [22]93.598%90.002%89.291%96.225%This paper97.582%93.691%90.781%99.687%From Table4, we draw a clustered bar chart of the table, as shown in Figure 6. Through a comprehensive comparison, we find that the algorithm proposed in this paper has not only a high accuracy rate but also a high recall rate. While other algorithms have different degrees of defects, these are not suitable for practical engineering applications.Figure 6
Cluster graph of test results of different algorithms.Figure7 shows the ROC curves of several detection methods. The results show that the algorithm proposed in this paper has better detection accuracy than the other four methods for the detection of financial fraud. Literature [19] adopts the combination of neural network and association analysis for abnormal behaviour detection, resulting in a lower abnormal detection rate than other algorithms. Literature [4] uses deep confidence networks to extract behavioural features and uses SVM to detect fraudulent behaviours. However, SVM takes a long time to find the optimal parameters. Literatures [21, 22] use space-time convolutional neural networks and PCANet networks to extract behavioural features, which can describe behaviours well, so their detection rate exceeds 90%. However, the detection rate of these two algorithms is lower than the algorithm proposed in this paper, because these two algorithms require a large number of samples for training deep learning networks, and the behaviour database samples are relatively small. At the same time, in order to balance the computational cost, these two algorithms extract behaviours that usually indicate a downsampling strategy, which leads to loss of information. Due to the rich motion information near the dense trajectory, the method proposed in this paper uses the powerful learning ability of the stacked denoising encoder to extract effective behavioural features. At the same time, the deep network does not directly extract the entire behaviour features, but only extracts the characteristics of the sampling points in the behaviour area. Moreover, the number of these sampling points is sufficient to train the deep network, so a large number of samples are not required to train the deep network, which solves the shortage and impact of training samples on deep learning, so the fraud detection rate of the algorithm proposed in this paper is higher than several other methods.Figure 7
ROC curves of different algorithms.


### 4.3. Time Performance Analysis of the Algorithm

In order to verify the superiority of the fraud detection model of the algorithm proposed in this paper, this paper mainly conducts two experiments. The first experiment is to compare the time efficiency of the algorithm in this paper and the other four comparison algorithms. The second experiment is to analyse the acceleration ratio of the cluster, that is, to compare the time efficiency of different classifier detection with different numbers of nodes.In this experiment, we selected different amounts of data. Among them, the system selects four nodes for parallel computing. The experimental results are shown in Figure8. It can be seen from Figure 8 that when the amount of data is small, the algorithm proposed in this paper has the highest time efficiency. This is because the algorithm proposed in this paper uses the deep network not to directly extract the entire behaviour features, but only extracts the features of the sampling points in the behaviour area, and the number of these sampling points is sufficient to train the deep network. Therefore, a large number of samples are not required to train the deep network. With the increase of data volume, other algorithms will show greater fluctuations in time.Figure 8
Time performance comparison of different algorithms.We continue to increase the number of nodes to detect the time efficiency of different numbers of nodes to complete fraud detection tasks. For the number of nodes, select 2 nodes, 4 nodes, 6 nodes, 8 nodes, 10 nodes, 12 nodes, 14 nodes, 16 nodes, 18 nodes, and 20 nodes for statistics. The experimental results are shown in Figure9. From Figure 9, we can find that the running time of the algorithm proposed in this paper decreases with the increase of the number of nodes, but there is no big change in the comparison algorithm. It can be seen that the increase of nodes can improve the classification efficiency of the financial fraud detection algorithm proposed in this paper. This shows that when we are faced with a larger and larger amount of data, we can simply increase the number of machines to improve the execution efficiency of fraud detection algorithms.Figure 9
Performance comparison of different algorithms at different node numbers.


## 4.1. Model Evaluation Index

In the fraud detection algorithm, it is very important to find a good classifier evaluation index. On the one hand, a good evaluation index fully indicates the classifier’s ability to solve problems and can show the effect on users more comprehensively. On the other hand, the selected classifier evaluation index is also conducive to developers to optimize the classifier model. The main evaluation criteria of this article are accuracy rate, recall rate, and FM. Table1 is a confusion matrix, which introduces common concepts such as TP, FP, FN, TN. Where “0” means normal behaviour, and “1” means fraudulent behaviour. “Y” indicates that the number of detection stages is classified as normal behaviour, and “N” indicates that the number of detection stages is classified as fraud.Table 1
Confusion matrix applied to the detection model.
Experiment classification label01Predict fraud categoryYTP: Correct and affirmative.FP: The error is positive.A sample of normal behaviour predicted to be normal behaviour.A sample of normal behaviour predicted to be fraudulent.NFN: False negative.TN: Correctly denied.A sample of fraudulent behaviour predicted as normal behaviour.A sample of fraudulent behaviour predicted to be fraudulent.Based on the above four classifications, the following two concepts can be further extended to evaluate the performance of the classifier:(15)Precision=TPTP+FP,(16)Recall=TPTP+FN.Precision reflects accuracy. Recall reflects the recall rate. In general, the accuracy rate is to determine how accurate the detected classification is, and the recall rate indicates how many items with the correct classification are detected. Accuracy and recall indicators are sometimes opposite. The measure of model performance that combines accuracy and recall into a single value is theF metric. The F measure uses the harmonic mean to integrate the accuracy and recall rates. The specific formula is shown in the following formula:(17)F=q2+1Precision∗Recallq2Precision+Recall.When the parameterq=1 is established, it is the most common FM. The formula is as follows:(18)FM=2Precision∗RecallPrecision+Recall.Because theF metric turns the model’s performance index into a single value, it provides a convenient way to compare the model to good or bad. However, this requires assuming that the accuracy and recall rates have the same weight. A better practice is to combine F measures with other measures.In order to weigh the quality of the model, this paper also adds the ROC curve and AUC index to measure the overall credibility of the classifier. ROC represents the relationship between TPR and FPR in the classification confusion matrix. Therefore, the abscissa of the ROC curve represents the probability of a negative instance being regarded as a positive instance, and the ordinate represents the probability of a positive instance being regarded as a positive instance. In the ROC graph, TPR increases with the increase of FPR, and the faster the increase is, the more prominent the curve is, and the better the classification performance of the response model is. The value of AUC is the size of the area under the ROC curve. The larger the AUC is, the better the classifier performance is.In summary, this paper uses four indicators: accuracy rate, recall rate, FM, and ROC chart to measure the quality of the experimental results of this paper.


## 4.2. Detection Performance Analysis of the Algorithm

In this paper, based on each sample group in the training set and prediction set, the actual fraud rate and the predicted fraud rate in each group are calculated to evaluate the prediction ability of the model. The actual fraud rate and predicted fraud rate values and the line chart of each group are shown in Tables2 and 3 and Figure 5, respectively.Table 2
Comparison of actual fraud rate and predicted fraud rate in the training set.
Sample numberNumber of samplesContains the number of fraudsActual fraud ratePredicted fraud rate130012239.665%39.495%23005015.258%15.021%33003510.178%9.885%4300329.156%8.882%5300267.125%6.647%6300205.085%5.472%7300205.731%5.658%8300163.731%3.115%9300143.058%3.102%10300122.389%2.178%Table 3
Comparison of actual fraud rate and predicted fraud rate in the test set.
Sample numberNumber of samplesContains the number of fraudsActual fraud ratePredicted fraud rate130011637.632%35.946%23004714.246%14.268%33004513.596%12.587%43003510.175%10.158%5300308.457%8.328%6300205.082%4.389%7300236.125%5.821%8300143.059%2.985%9300122.379%3.109%10300101.695%1.479%Figure 5
Grouped predictions for training and test sets. (a) Training. (b) Testing.
(a)(b)Through the analysis of the above chart data, we can find that the algorithm proposed in this paper has a good predictive ability regardless of the balanced distribution of data or the extreme distribution of imbalance.In order to verify the effectiveness of the proposed method, the algorithm in this paper is compared with the following four methods:(1)
Lin et al. [19] constructed a fraud detection system by combining neural networks and association analysis.(2)
Ryan et al. [4] used deep belief networks to extract behavioural features and SVMs to detect fraudulent abnormal behaviours.(3)
Liu et al. [21] used spatial-temporal convolutional neural networks to extract fraudulent behaviour features for abnormal behaviour detection and location.(4)
Peng et al. [22] used image saliency information and multiscale optical flow histogram as low-level features. Then, the deep learning network PCANet is used to extract more effective features from these underlying features for abnormal behaviour detection.In the experiment, we first extracted the dense trajectory. Secondly, randomly select 5 million trajectories to train SDA and used the K-means clustering method to get 370 appearance visual words and 430 motion visual words. Then, we randomly selected 800 normal behaviour learning feature fusion parameters to obtain the parametersw1=0.3,w2=0.7. Finally, we learned sparse dictionaries with 800 normal behaviours. All abnormal fraud behaviour samples and the remaining 200 normal samples are used as test samples. The test results are shown in Table 4.Table 4
Test results of different algorithms.
AlgorithmPrecisionRecallFMAUCLiterature [19]82.853%72.581%70.831%91.021%Literature [4]93.581%89.367%88.213%96.123%Literature [21]91.952%85.987%75.902%95.368%Literature [22]93.598%90.002%89.291%96.225%This paper97.582%93.691%90.781%99.687%From Table4, we draw a clustered bar chart of the table, as shown in Figure 6. Through a comprehensive comparison, we find that the algorithm proposed in this paper has not only a high accuracy rate but also a high recall rate. While other algorithms have different degrees of defects, these are not suitable for practical engineering applications.Figure 6
Cluster graph of test results of different algorithms.Figure7 shows the ROC curves of several detection methods. The results show that the algorithm proposed in this paper has better detection accuracy than the other four methods for the detection of financial fraud. Literature [19] adopts the combination of neural network and association analysis for abnormal behaviour detection, resulting in a lower abnormal detection rate than other algorithms. Literature [4] uses deep confidence networks to extract behavioural features and uses SVM to detect fraudulent behaviours. However, SVM takes a long time to find the optimal parameters. Literatures [21, 22] use space-time convolutional neural networks and PCANet networks to extract behavioural features, which can describe behaviours well, so their detection rate exceeds 90%. However, the detection rate of these two algorithms is lower than the algorithm proposed in this paper, because these two algorithms require a large number of samples for training deep learning networks, and the behaviour database samples are relatively small. At the same time, in order to balance the computational cost, these two algorithms extract behaviours that usually indicate a downsampling strategy, which leads to loss of information. Due to the rich motion information near the dense trajectory, the method proposed in this paper uses the powerful learning ability of the stacked denoising encoder to extract effective behavioural features. At the same time, the deep network does not directly extract the entire behaviour features, but only extracts the characteristics of the sampling points in the behaviour area. Moreover, the number of these sampling points is sufficient to train the deep network, so a large number of samples are not required to train the deep network, which solves the shortage and impact of training samples on deep learning, so the fraud detection rate of the algorithm proposed in this paper is higher than several other methods.Figure 7
ROC curves of different algorithms.


## 4.3. Time Performance Analysis of the Algorithm

In order to verify the superiority of the fraud detection model of the algorithm proposed in this paper, this paper mainly conducts two experiments. The first experiment is to compare the time efficiency of the algorithm in this paper and the other four comparison algorithms. The second experiment is to analyse the acceleration ratio of the cluster, that is, to compare the time efficiency of different classifier detection with different numbers of nodes.In this experiment, we selected different amounts of data. Among them, the system selects four nodes for parallel computing. The experimental results are shown in Figure8. It can be seen from Figure 8 that when the amount of data is small, the algorithm proposed in this paper has the highest time efficiency. This is because the algorithm proposed in this paper uses the deep network not to directly extract the entire behaviour features, but only extracts the features of the sampling points in the behaviour area, and the number of these sampling points is sufficient to train the deep network. Therefore, a large number of samples are not required to train the deep network. With the increase of data volume, other algorithms will show greater fluctuations in time.Figure 8
Time performance comparison of different algorithms.We continue to increase the number of nodes to detect the time efficiency of different numbers of nodes to complete fraud detection tasks. For the number of nodes, select 2 nodes, 4 nodes, 6 nodes, 8 nodes, 10 nodes, 12 nodes, 14 nodes, 16 nodes, 18 nodes, and 20 nodes for statistics. The experimental results are shown in Figure9. From Figure 9, we can find that the running time of the algorithm proposed in this paper decreases with the increase of the number of nodes, but there is no big change in the comparison algorithm. It can be seen that the increase of nodes can improve the classification efficiency of the financial fraud detection algorithm proposed in this paper. This shows that when we are faced with a larger and larger amount of data, we can simply increase the number of machines to improve the execution efficiency of fraud detection algorithms.Figure 9
Performance comparison of different algorithms at different node numbers.


## 5. Conclusion

Fraud is very common in the field of financial services. Large database management systems are basic system software widely used by financial institutions. The use of data mining in large database systems is an advanced technical means for detecting financial fraud. It is an effective method to detect financial fraud by mining and analysing the data in a large amount of processing business data and finding the corresponding rules, rules and conclusions, and then combining manual analysis. In this paper, the encoder is first used to extract the appearance and motion features of the behaviour, and in order to reduce the computational complexity, the feature extraction is constrained to the space-time volume of the dense trajectory. Secondly, the deep learning model is used to transform the features into behavioural visual word representations, and the feature fusion is performed using the weighted correlation method to improve the classification ability of the features. Finally, the sparse reconstruction error is used to judge the abnormality of fraud. The results show that the algorithm proposed in this paper can effectively learn the essential characteristics of the data and has a higher detection rate and lower computational complexity. Although this article has achieved good experimental results, the results are still in the experimental stage. Our next research plan is to apply the algorithm to the actual environment. By obtaining data in the actual environment, we can further optimize our algorithm.



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*Source: 6685888-2020-12-24.xml*