# Effect of Improved Association Algorithm on Mining and Recognition of Audit Data

Authors: Putianyi Qiu
Journal: Journal of Electrical and Computer Engineering
 (2022)

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## Abstract

Audit evidence is the proof material on which the auditors issue audit opinions and make relevant audit conclusions, and audit evidence in the era of big data presents new characteristics in terms of adequacy, relevance, and reliability. This paper combines the improved association algorithm to construct the audit data mining system to improve the data processing effect of the audit process. Moreover, this paper proposes a new dynamic threshold method, gives the calculation method of some important parameters in the algorithm, and presents the improved cell-based association algorithm flow. In addition, this paper discusses how the outlier algorithm is applied to the acquisition of audit evidence and the application scenarios in the audit system. The experimental research results show that the audit data mining system based on the improved association algorithm proposed in this paper has a good effect in the audit of accounting and financial data.


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## Body

## 1. Introduction

With the advent of the era of big data, massive and diverse data pushes the difficulty of audit work to a higher level. How to combine big data with audit and gradually transform traditional audit functions is the focus of this paper.Big data technology makes up for the insufficiency of sampling audit, can analyze and process all data, and change the way of processing structured data. Moreover, it is no longer the inductive analysis of the abstracted information, but the direct analysis of the original data. However, this also creates a new problem, that is, a large part of the super-large-capacity data is meaningless or even erroneous, which results in the property of low value density of big data. For example, valuable footage in hours of surveillance footage may only be two or three seconds, but those few seconds are the crux of the problem. At the same time, valuable big data is like oil and gold, which are rare in quantity but have extremely high commercial value after being mined.Sufficiency puts forward higher requirements for the quantity of audit evidence, but in the traditional audit process, some audit evidences are difficult to obtain, sufficiency cannot be satisfied, and the correctness of audit results cannot be guaranteed. In the era of big data, with the development of information technology, it has become easy to obtain audit evidence, and the problem of difficulty in obtaining sufficient evidence has been solved.The relevance of audit evidence in the era of big data is higher, which is embodied in the following three aspects. First, audit evidence can be obtained in time, which reduces the time cost and improves the lag of manual information acquisition [1]. The second is to improve the audit confirmation ability, and use big data technology to weave an interlocking audit evidence network to check and review the internal and external non-financial information of the enterprise, which can quickly and accurately find problematic links. This method overcomes the defects of untimely acquisition of manual information, low accuracy and weak objectivity, and the audit evidence obtained by this method has a higher confirmation value [2]. Third, the audit data has the function of prediction, and the data mining technology can predict the future information by analyzing the relevant data and establishing the corresponding model. For example, the regression analysis method is one of the most widely used methods. The prediction function not only enables auditors to formulate audit plans in advance and improve audit efficiency, but more importantly, it can turn post-event audits into pre-event audits, and pay attention to the key points, difficulties, and easy omissions of the audit in advance [3].Objectivity means that the audit evidence cannot be mixed with personal subjective assumptions. For example, verbal evidence may be highly subjective, and it needs to be filtered and screened reasonably. Traditional forensics methods mainly rely on the information provided by enterprises, in order to pursue their own interests, enterprises may provide false information. However, in the era of big data, auditors can obtain third-party information through various data collection devices, which have higher objectivity. Finally, authenticity and integrity mean that audit evidence must be true and complete. Audit evidence in the era of big data is readily available, but its authenticity cannot be fully guaranteed, and data may be wrong or intentionally tampered with when entering the information system. It can be imagined how difficult it is to identify misinformation in the mass of information. Therefore, the true integrity of audit evidence in the era of big data has declined to a certain extent.This paper discusses how the outlier algorithm is applied to the acquisition of audit evidence and the application scenarios in the audit system, improves the data processing effect of the audit process, and improves the reliability of the audit process.The main contribution of this paper: the association rules and outlier algorithms are introduced into the audit and supervision information system to obtain audit evidence. When using the association rule algorithm, the algorithm is further improved to improve the time efficiency and space efficiency of the algorithm. When using the outlier algorithm, the cell-based outlier algorithm is optimized, and the dynamic threshold method is used to improve the accuracy of the edge outlier detection.The organizational structure of this paper is as follows: the introduction part points out the necessity and feasibility of applying data mining technology to the research on the acquisition of audit evidence; the second part summarizes the relevant research, explores the starring research content of the existing research, and introduces the content of this paper. In the third part, the algorithm is improved. Aiming at the disadvantage that the cell-based outlier detection algorithm is not friendly to edge “point” detection, the improvement of the algorithm is proposed. Then, after preprocessing the audit data, the improved unit-based outlier detection algorithm is used in the study of audit evidence acquisition based on outlier algorithm, and the system structure of this paper is constructed, and the algorithm and model are carried out through experimental research. Finally, the research content of this paper is summarized.


## 2. Related Work

Literature [4] proposes the term CAATTs (Computer-Assisted Audit Tools and Techniques). Literature [5] believes that computer-aided auditing techniques refer to the use of any technology in the process of helping to complete the audit. The CNAO with Computer-aided auditing technology is defined as “audit institutions and auditors use computers as an auxiliary audit tool to audit the finances, financial revenues and expenditures of the audited units and their computer application systems. Help auditors collect audit evidence, improve audit efficiency, and reduce auditing.” The specific process is to use audit software to collect electronic data according to the needs of audit tasks, and then preprocess these electronic data and complete data analysis to obtain audit evidence. Audit software mainly includes general data analysis software and professional audit software. The software generally has data collection and analysis functions. Through data collection, the electronic data of the audited unit is imported into the database of the audit software, and audit clues are found by data sampling, statistical generalization, data query, abnormal detection, etc., and finally submitted for audit. The department collects evidence to form audit conclusions [6]. Compared with manual audit, computer-aided audit can effectively expand audit scope and improve audit efficiency. However, it also has certain limitations. For example, it is effective for explicit violations; for more complex and concealed activities, electronic data analysis is relatively inefficient or even ineffective; there is no way to deal with the information islands existing in the audit, and there is a lack of consideration for the association of independent data; electronic data collection is time-consuming and labor-intensive, and it is impossible to conduct cross-regional and cross-industry audits [7].Literature [8] believes that big data will become a powerful supplement to traditional audit evidence collection methods because of its adequacy, reliability, and relevance. Literature [9] analyzes the ability of big data and current continuous audit data analysis in data consistency (consistency), integrity (integrity), aggregation (aggregation), identification (identification), confidentiality (confidentiality), and other aspects of the gap. Literature [10] believes that modern audit management needs to integrate big data and complex business analysis methods. Literature [11] discusses the challenges of big data to computer auditing, and looks forward to how to use big data to promote the development of computer auditing. Literature [12] discusses the audit thinking in the context of big data suggestions on the development of the audit model, audit technology methods, audit personnel training, and management model. Literature [13] analyzes the impact of the big data environment on the data audit model and the feasibility of improvement, and analyzes the logical process, network architecture, and application architecture from the perspective of the perfect design, and application index design of the data audit model are carried out from an equal perspective.Literature [14] proposed the big data audit work model of “centralized analysis, discovery of doubts, decentralized verification, and systematic research,” as well as “the vertical relationship between the central government and the provinces and cities, the horizontal relationship between the first- and second-level budget units, the financial data, the data association of enterprises, the association of finance with other multi-department and multi-industry data, the association of financial data with business data, and macroeconomic data” five analysis requirements, and have been used many times in enterprise audit, financial audit, resource and environmental audit, Cloud computing, intelligent mining, social networking, natural language understanding, visualization, word cloud analysis and geographic information technology and other big data analysis technologies. The US Audit Office has adopted a variety of new technologies for unstructured data analysis and web data mining. In a specific audit practice, potential fraud was detected by correlating the list of people who died in society with the list of people receiving federal subsidies [15].


## 3. Our Improved Association Algorithm

This paper introduces the cell-based outlier detection algorithm. However, there is a problem with this algorithm, that is, the thresholdM is fixed. However, it is not appropriate to use the same threshold M for boundary cells and non-boundary cells.For non-boundary cellC, the number of cells in the first layer is 32−1=8, and the number of cells in the second layer is 72−32=40, that is, the proportion of cells in the first layer is 8/8+40=1/6, and the proportion of cells in the second layer is 40/8+40=5/6. However, for boundary cells, the situation is different. When cell C is at the border, it has fewer cells in layer 1 and layer 2 than in the non-border case. This will cause the total number of objects in layer 1 cells and layer 2 cells to be less than the threshold M. In this case, if the same M is used for the non-boundary case and the boundary case, the data objects in the boundary case are easily misjudged as outliers.To solve this problem, this paper proposes a dynamic threshold method. The core idea is to use different thresholdsM according to the different positions of cell C. We assume the interval value when cell C is non-boundary is M0, and count the number of cells in layer 1 of cell C as C1 and the number of cells in layer 2 as C2. Then, based on the number and proportion of cells in layers 1 and 2 in the non-boundary situation, M0 is scaled down as the value Mc in this situation, and the specific formula is as follows [16]:(1)Mc=c18×16+c240×56×M0.When it is a non-boundary case,Mc=M0. This method can effectively solve the problem of misjudging outliers in boundary situations. Since there are many boundary situations, only two examples are given below.In the case of Figure1(a), cell C is located at the top corner of the boundary, and the number of cells in the first layer is 3 and the number of cells in the second layer is 12. According to formula (1), we can get [17]:(2)Mc=38×16+1240×56×M0=516M0.Figure 1
Boundary case. (a) One of the boundary cases. (b) Boundary case 2.
(a)(b)In the case of Figure1(b), cell C is located at the non-vertical corner of the boundary and not close to the edge, and the number of cells in the first layer is 8 and the number of cells in the second layer is 26. According to formula (1), we can get:(3)Mc=88×16+2640×56×M0=1724M0.The above discussion is for 2D datasets, but the extension to cube datasets is still valid. The following extends formula (1) to multi-dimensional, and we assume that the dimension of the dataset is w, we have [18]:(4)Mc=c13w−1×3w−17w−1+c27w−3w×7w−3w7w−1×M0=c1+c27w−1∗M0.After improving the dynamic threshold of the original algorithm, compared with the original algorithm, there is only one more calculation ofMc, and the calculation of Mc is also very simple. It is only necessary to count the number of cells in the 1 st and 2 nd layers of the target cell, and use formula (4) to calculate. Therefore, the time complexity of the improved algorithm does not increase, but it effectively solves the problem of misjudgment and standpoint in boundary cases.Regarding the calculation of the distance, this topic adopts the Euclidean distance for calculation. For the two objectsxi1,xi2,…,xiw and xj1,xj2,…,xjw, the distance dij can be calculated by the following formula:(5)dij=∑k=1wxik−xjk2.Among them,w is the dimension of the dataset, and i, j represent the i-th object and the j-th object.In the cell-based outlier detection algorithm, the “area” of the data space is the product of the “side lengths” of each dimension.We assume that there aren points in the w-dimensional data space, which are C1X11,X12,…,X1w,C2X21,X22,…,X2w,…,CnXnl,Xn2,…,Xnw respectively. For the “side length” of the i-th dimension, it is necessary to find the maximum value Xi−max and the minimum value Ximin of the i-th dimension in these n points, and calculate the difference by Di=Ximax−Ximin, which is the side length of the i-th dimension. Thus, the “area” of the data space can be obtained as [19]:(6)S=∏i=1wDi=∏i=1wXimax−Ximin.For the determination of the distance thresholdr, the common practice of distance-based outlier detection methods is to calculate the distance between all objects in the dataset, and then take the average of all distances as the distance threshold r. It can be seen that the computational complexity of this method is very large.Therefore, the determination of ther value here does not adopt this traditional method, but adopts a new calculation method. Taking a two-dimensional plane as an example, an ideal two-dimensional plane graph with no vertical points at all should be a graph with all points evenly distributed. If this two-dimensional plan is divided into many small squares of the same size, then each point should occupy a small square. If there are some points that are close to each other, there must be two or more points in a square, and there must be no points in some squares. At this point, the points in the 2D plan form clusters and outliers. Figure 2(a) shows a uniform distribution with no outliers, while Figure 2(b) shows clusters and outliers.Figure 2
Clustering situation. (a) The case of uniform distribution. (b) The case where there are outliers and clusters.
(a)(b)We assume that the side length of the small square in the figure isr0. Then, it can be found from Figure 2 that if a point has no adjacent points in the radius neighborhood of r0, then it is impossible for the point to be in a certain cluster. Based on this, we use r0 as our distance threshold r. By formula (6), we can obtain the area S of the two-dimensional plane graph, and denote the number of points in the plane graph as n, then we have:(7)r=r0=sn.Similarly, it can be extended to multi-dimensional space. We assume that the dimension isw, and the number of data objects in the data space is n. According to formula (6), the “area” S of the multi-dimensional space is obtained, then there are:(8)r=r0=snw.In the cell-based outlier detection algorithm, the data space is divided into multi-dimensional grids, and the calculation method of grid division is given below.The side length of each small hypercube divided isr0/2w, where r0 is the distance threshold, w is the dimension, and t=r0/2w.We assume that there aren points in the w-dimensional data space, which are C1X11,X12,…,X1w,C2X21,X22,…,X2w,…,CnXnl,Xn2,…,Xnw respectively.For thei-th dimension, it is necessary to find out the maximum value Ximax and the minimum value Ximin of the i-th dimension among the n points, and then the number of divisions of the i-th dimension can be obtained as:(9)SUMi=Xi−max−Xi−mint.It is worth noting that the result ofSUMi is rounded down. When SUMi is calculated for each dimension of the w dimension, the cell division of the entire data space is completed.Next, we need to assign a total ofn points C1,C2,……,Cn to a divided cell. Now, this paper considers the j-th point CjXj1,Xj2,…,Xjw, and the cells assigned to this point in the i-th dimension are divided into:(10)NUMi=minXji−Ximint+1,SUMi.It is worth noting that the result ofNUMi is also rounded down, and NUMi indicates that the point falls on the NUMi-th division in the i-th dimension (counting from the first division). When NUMi is calculated for each dimension of the w dimension, the point Cj is assigned to the divided cell space.M0 represents the threshold of the number of objects in a circle with the target object as the center and the distance threshold r as the radius. However, the length of the diagonal of the divided small hypercube is r/2. Therefore, we can determine M0 as follows:The algorithm counts the total number of objects in the first-level unit of each unit, and the maximum value is recorded asMmax, which is as follows by default in the audit system:(11)M0=0.4∗Mmax.Among them,M0 is rounded, and the threshold coefficient 0.4 is given artificially, and auditors can also give a threshold coefficient by themselves during actual operation.WhenM0 is determined, the dynamic threshold Mc can be calculated according to this paper.The improved cell-based outlier detection Algorithm1 flow is described as follows:Algorithm 1: Cell-based outlier detection algorithm flow.
(1)
The algorithm inputs all data objects, and calculates its distance thresholdr according to formula (8).(2)
The algorithm divides the cells according to formula (9), records the number of objects in each cell as count, and assigns the initial value count = 0.(3)
The algorithm assigns each object to the corresponding cell according to formula (10), and makes the count++ of the corresponding cell.(4)
The algorithm determines the thresholdM0 of the number of points in the neighborhood according to formula (11).(5)
The algorithm repeats steps (6)–(18) for each cellCx,y.(6)
The algorithm calculates the dynamic thresholdMc according to formula (4).(7)
IfCx,y corresponds to count≥Mc+1, then all objects in Cx,y are not isolated points, and the algorithm goes to step (5).(8)
Elseif:count+count1≥Mc+1, then all objects in Cx,y are not outliers, and the algorithm goes to step (5), where count1 represents the number of first-level units of Cx,y.(9)
Elseif:count+count1+count2<Mc+1, then all objects in Cx,y are isolated points, mark all objects in Cx,y as Red, and the algorithm goes to step (5), where count2 represents the number of the second layer unit of Cx,y.(10)
Else: The algorithm repeats steps (11) –(17) for each objectP in Cx,y.(11)
We assume that the number of objects in ther neighborhood of object P is countp, and initialize it by countp=count+count1−1.(12)
The algorithm repeats steps (13) –(15) for each objectQ of the second level unit of Cx,y.(13)
The algorithm calculates the distancedistP,Q between P and Q.(14)
If:distP,Q≤r, then countp++.(15)
The algorithm goes to step (12).(16)
If:countp<Mc, then the object P is an isolated point, which is marked as Red.(17)
The algorithm goes to step (10).(18)
The algorithm goes to step (5).(19)
The algorithm removes all objects marked as Red as all outliers.In order to test the actual effect of the improved algorithm, a comparative experiment is carried out on the outlier detection algorithm based on the unit before and after the improvement.The specific experimental method is to use MATLAB 7.11.0 software to randomly generate coordinate points on a two-dimensional plane. The outlier detection algorithm based on the unit before the improvement and the outlier detection algorithm based on the unit after the improvement are, respectively, used to detect the outliers, and the detection results are compared and analyzed.The experiment is shown in Figure3. The size of the two-dimensional plane is 30∗30, and the number of coordinate points is 300. According to formula (8), the distance threshold r=30=30/300=1.73 can be obtained, and the number of points threshold M0=0.4∗8=3 can be obtained according to formula (11). Then, this paper, respectively, writes programs to use the algorithm before and after the improvement to detect outliers, and the parameters r and M0 take the same value.Figure 3
Randomly generated two-dimensional plane point set.The isolated points detected by the algorithm before the improvement are shown in Figure4, and the isolated points detected by the improved algorithm are shown in Figure 5. Among them, the red marked points represent the detected outliers.Figure 4
Outliers detected by the algorithm before the improvement.Figure 5
Outliers detected by the improved algorithm.By comparing Figures4 and 5, it can be found that the outliers detected in the non-boundary situation are completely consistent before and after the algorithm is improved. However, the detection results in the boundary case are quite different. After analyzing the detected outliers, it is found that the algorithm before the improvement misjudged many non-outliers on the boundary as outliers. However, the improved algorithm effectively avoids this situation because of the dynamic threshold method.The experimental results show that our improvement of the algorithm is reasonable, and the dynamic threshold method effectively solves the problem that the original algorithm easily misjudges the boundary points as outliers.


## 4. Performance Analysis

Big data auditing is a new auditing method with the development of big data technology. Its contents include electronic data auditing in big data environment (how to use big data technology to audit electronic data and how to audit electronic data in big data environment) and auditing of information systems in big data environment. Among them, the electronic data auditing in the big data environment is a research hotspot, and the overall block diagram of the big data auditing technology based on the improved association algorithm is shown in Figure6.Figure 6
Overall block diagram of big data audit technology based on improved association algorithm.Under big data auditing, it is necessary to coordinate the relationship between data collection and analysis and traditional auditing processes. At the same time, it is necessary to optimize the audit workflow to adapt to the big data audit environment, so as to standardize the audit business behavior, improve the audit control level, and realize the improvement of the audit efficiency. The big data internal control audit process framework is shown in Figure7.Figure 7
Big data internal control audit process framework.After obtaining the above improved association algorithm and big data internal control audit process framework system, the effect of the system is verified, the audit data mining effect and audit effect are counted, and the results shown in Tables1 and 2 are obtained.Table 1
Audit data mining effect.
NumberAudit miningNumberAudit miningNumberAudit mining188.582385.994491.16290.262484.854585.61391.482591.004686.60490.352684.474791.63584.102791.844889.08685.032888.774988.16787.672990.255087.07885.303087.865189.86987.713186.465290.761087.213287.155387.431187.473387.585486.421290.463488.065590.891390.913591.585690.491489.033684.365788.541591.843788.915890.761689.793888.585989.491784.173985.536090.741886.154084.166186.691990.074190.646286.562089.554286.946389.192190.774388.276486.352289.80Table 2
Auditing effect of financial data.
NumberAudit effectNumberAudit effectNumberAudit effect186.392388.034479.73278.692479.214582.17387.202582.474688.53485.512688.124783.83583.132784.654879.65679.392887.664979.67780.422989.805088.28887.663083.945187.91979.853183.085284.261088.383285.745384.641179.553379.265477.791280.883489.765578.541382.563577.165685.471484.613686.285785.981584.103784.325879.121681.513888.625978.501778.633978.086081.551883.804085.806178.181981.084177.926284.532081.934280.736381.392181.504387.616487.342289.41It can be seen from the above research that the audit data mining system based on the improved association algorithm proposed in this paper has a good effect in the audit of accounting and financial data.


## 5. Conclusion

Big data also has a profound impact on the reliability of audit evidence, and the reliability of audit evidence needs to be considered from three aspects: verifiability, objectivity, and integrity. Audit evidence can be cross-verified with each other to see if it actually exists. The traditional verification method of audit evidence is relatively simple, and it is often through the traceability of business processes to check whether the data matches, and then to find forged or wrong audit evidence. However, with the support of big data technology, the singleness of audit evidence has evolved into diversity, and auditors can obtain more audit evidence from channels outside the financial account and outside the enterprise, which enhances its verifiability. This paper combines the improved association algorithm to construct the audit data mining system to improve the data processing effect of the audit process. The research shows that the audit data mining system based on the improved association algorithm proposed in this paper has a good effect in accounting and financial data auditing.At present, this paper only applies the association algorithm and the outlier algorithm to the limited scenarios of the system. In the future, more scenarios that can use the above two algorithms can be explored and implemented in the system. The current amount of data is not “very” huge, so in the system, a single machine is used to implement the association rule algorithm and the outlier algorithm. In the future, it is necessary to consider how to implement the algorithm in this paper when the amount of data is very large.



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