# The Impact of Intelligent Accounting Information Management on Corporate Governance Information Transparency

Authors: Baiyu He
Journal: Security and Communication Networks
 (2022)

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## Abstract

In order to improve the transparency of corporate governance information, this paper combines intelligent accounting information technology to analyze the information transparency in the process of corporate governance, analyzes the fast adaptive neighbor clustering algorithm, and realizes the joint spectral embedding of data by creating block diagonal anchor graphs. Moreover, this paper re-selects anchor points from the spectral embedding data and constructs a new block diagonal anchor graph. In addition, using the principle of adaptive nearest neighbor clustering, this paper performs structured graph learning on the block diagonal anchor graph matrix. After derivation, the Laplace eigenvalue decomposition problem of the whole graph in adaptive nearest neighbor clustering can be transformed into a block matrix singular value decomposition problem. The regression analysis shows that there is a linear correlation between the advanced degree of intelligent accounting information management technology and the transparency of corporate governance information.


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## Body

## 1. Introduction

Among corporate information transparency, accounting information transparency is a very important and particularly critical component. Moreover, improving the transparency of corporate accounting information can significantly improve the quality of corporate information and greatly reduce the behavior of “adverse selection” in in-app purchases. In addition, accounting information plays an irreplaceable and important role in the finance of enterprises, especially listed companies, as well as business operators. The public judges the financial situation of the enterprise through the accounting information of the enterprise. For a long time, financial information fraud has occurred frequently, so improving the transparency of corporate accounting information is still an urgent problem to be solved. The study of this topic has far-reaching and important significance for maintaining the normal market economic order and protecting the rights and interests of investors.In the process of economic development, the role of capital is very important. Not only in the external capital market, but also in the internal market, capital plays a very important role in the allocation of internal resources. In the process of research on ICM by foreign scholars, the research focus is mainly set on the existence, efficiency, enterprise organization structure, and the relationship between equity results and so on. China’s research on ICM is relatively in its infancy. However, although the research on ICM in China started relatively late, the development speed is very fast.Most scholars believe that ICM plays an important role in alleviating corporate financing constraints. At the same time, in the process of researching ICM, scholars have also paid full attention to issues such as rent-seeking, agency behavior, and management incentives. Many scholars have also deeply studied the problem of ICM resource allocation efficiency and have achieved some research results in the research process [1]. On the one hand, the research of ICM has very ideal theoretical value, and on the other hand, it has practical significance to promote the improvement and improvement of ICM of group enterprises. Therefore, in the research process of this paper, the research perspective is locked on the problem of internal capital market efficiency allocation. The research on accounting information transparency has long attracted the attention of many scholars at home and abroad. At this stage, domestic and foreign scholars have made a lot of definitions, but they have not yet reached a consensus and have not formed a conclusion [2]. Usually, people think that the transparency of accounting information and the quality of accounting information are closely related. The higher the transparency of the former, the lower the information cost investors need in the investment process. A relatively high information cost is required. Therefore, in the process of reducing or reducing adverse selection behavior in the capital market, improving the transparency of accounting information can be said to be an effective way [3]. The management of accounting information is an integral part of the corporate governance structure. For the improvement of the quality of accounting information, the management of accounting information is an indispensable guarantee. The corporate governance mechanism can be reflected through the corporate governance language of accounting and can promote the corporate governance function to maximize its function [4]. There is a great degree of correlation between corporate governance and transparency of accounting information, and the effectiveness of the former can ensure the authenticity and integrity of the latter. Corporate governance will cause differences in the quality of accounting information, and on this basis, the transparency of accounting information will be reflected [5].Accounting information transparency, as an important component in the study of corporate transparency, has become another hot issue in academia in recent years. However, neither foreign nor domestic companies have reached a consensus on the meaning of accounting information transparency [6]. The study defines transparency as “Public disclosure of reliable and timely information helps information users to accurately evaluate a bank’s financial status and performance, business activities, risk distribution and risk management practices” [7]. The discussion concluded that: “To achieve transparency, timely, accurate, relevant and adequate qualitative and quantitative disclosures must be provided, and these disclosures must be based on sound measurement principles”. The quality characteristics of transparent information include comprehensiveness, relevance, timeliness, reliability, comparability, and significance [8]. Pu defines the concept of “opaqueness” as “the lack of clear, accurate, formal, easy-to-understand and generally recognized conventions in the fields of commercial economy, fiscal finance, government regulation, etc.”. According to this statement, the information transparency of listed companies can be understood as “clear, accurate, formal, easy to understand and generally recognized” [9]. Reference [10] defines the degree to which the reported accounting earnings cannot provide information about the real economic earnings of the enterprise as earnings opacity. Literature [11] believes that “The information quality characteristics of financial reports can be divided into two categories: one is the quality of financial statement content; the other is the quality of financial statement presentation and disclosure in other financial reports”. Literature [12] believes that accounting information transparency is a comprehensive and comprehensive concept that includes accounting information quality standards, information disclosure and supervision, and the formulation and implementation of accounting standards. Reference [13] defines the transparency of accounting information as the degree to which an enterprise's accounting earnings reflect the real economic earnings, or the degree to which investors can see through the enterprise’s behavior through the enterprise’s accounting information. Highly transparent accounting information should have a higher information content. It can reduce the information cost of investors.The research of literature [14] shows that the stock price of the company will increase with the increase of the transparency of accounting information, that is, investors are more aware of the company with higher information disclosure standards and higher transparency, and are willing to buy its stock, so that its stock price is relatively high. The literature [15] believes that the problem of information asymmetry and agency conflict between external investors and enterprise management can be alleviated by providing authentic financial reports and improving information disclosure. Literature [16] studies the relationship between accounting transparency and cost of capital, and the results show that the cost of capital will decrease with the increase of accounting transparency. It is believed that the more stable the level of information disclosure, the more conducive to improving the liquidity of corporate stocks. Reference [17] selected the research results to show that the degree of information disclosure of enterprises is positively correlated with company value and business performance. In the literature [18], the research on voluntary disclosure of information by enterprises believes that the internal and external governance mechanisms of enterprises have obvious complementary effects. Literature [19] studies the relationship between the level of corporate information disclosure and the cost of refinancing, and the results show that the improvement of the level of disclosure can help reduce the cost of corporate refinancing. Reference [20] confirms the results from the perspective of the financial ratios and the degree of disclosure of earnings information of enterprises. The results show that enterprises with higher debt ratios tend to disclose early earnings forecasts, while companies with high return on assets are more inclined to conduct forward-looking earnings information. Literature [21] studies the impact of listed companies’ accounting information disclosure on the forecasts of securities analysts. The empirical results show that the transparency of accounting information is positively correlated with the accuracy of securities analysts' forecasts. Literature [22] adopts an empirical method to confirm that there is a positive correlation between the transparency of accounting information of listed companies and the size of the board of directors, and there is no significant correlation with the proportion of external directors.At present, researchers’ understanding of accounting information transparency has gradually become more consistent, focusing on the key points of financial information transparency, from only focusing on the quality of partial accounting information to focusing on the protection of investors’ interests, and at the content level, it also extends to the disclosure of the superior company. All information is concerned because investors can understand the essence of the enterprise through the appearance of enterprise accounting information. However, there is still no unified standard to measure accounting information transparency in academia. The research on accounting information transparency will lead to different results with different measurement methods. However, the research on accounting information transparency is very important because real and effective accounting information is the cornerstone of building an advanced capital market. However, the more information disclosed by listed companies is not the better, and the timeliness and effectiveness of the disclosed information should also be considered. Throughout the domestic and foreign scholars’ research on accounting transparency, their measurement of accounting information transparency can be roughly attributed to two methods: one is to directly use the disclosure evaluation of authoritative organizations as a variable to measure information transparency and build your own transparency index to measure.This paper combines intelligent accounting information technology to analyze the information transparency in the process of corporate governance to improve the efficiency of information management in the process of corporate governance, effectively improve the management efficiency of modern companies, and improve the operational efficiency of corporate financial management.


## 2. Intelligent Accounting Information Processing

In the fast clustering of accounting information, the discretization of fast embedded data plays an important role in the discovery of cluster structure. The traditional method is to use the k-means method to discretize the spectral embedded data, and there is still room for further improvement in the clustering accuracy. In this chapter, using the FCAG algorithm to describe the similarity between data points, an improved fuzzy clustering algorithm based on the FCAG algorithm is proposed and applied to the fast embedded data discretization of accounting information to improve the clustering accuracy.


### 2.1. FCAG Algorithm

The fuzzy weight of the objective function of FCM is set to 1, the objective function can be written as(1)minyi=1,Y≥0,mj∑i=1n∑j=1cyijxi−mj22.Among them,yij represents the fuzzy membership degree between the data point xi and the cluster center mj.When the input data are replaced with the fast spectral threshold input dataU, problem (1) can be expressed as(2)minyi=1,Y≥0,mj∑i=1n∑j=1cyijui−mj22.It can be seen from formula (2) that the size of fuzzy membership depends on the distance between the spectral embedded data and its cluster center. In order to improve the accuracy of the fuzzy membership matrix, inspired by the literature, a similarity measure in the needle graph space can be added to formula (2).wil is an element of the ith row and l-column of the needle graph matrix W. The larger the value of the element, the closer the data points ui and uj are. Because the fuzzy membership vector yi describes the distance relationship between the data point ui and all cluster centers, when the data points ui and uj are adjacent to each other, their fuzzy membership vectors are also close. Therefore, formula (2) can be rewritten as(3)minyi=1,Y≥0,mj∑i=1n∑j=1cyijui−mj22+λ2∑i=1n∑l=1nwilyi−yl22.Among them,λ is the regularization parameter. The regular term adds the similarity measure in the needle graph space, which can make the fuzzy membership matrix more accurately describe the relationship between the data and the cluster centers.In spectral clustering, the Laplace matrix has the following properties:(4)TrYTLY=12∑i=1n∑l=1nwilyi−yl22,s.t.YTY=I.By fusing formulas (3) and (4), the objective function can be rewritten as(5)minyi=1,Y≥0,YTY=l,mj∑i=1n∑j=1cyijui−mj22+λTrYTL˜Y.The update of fuzzy membership in objective function (5) has profound physical meaning. It is not only affected by the distance between the fast spectral embedding data and the cluster center but also constrained by the similarity between the cluster data in the graph domain. The new objective function can combine the advantages of FCM and spectral clustering to obtain a better fuzzy membership matrix.The objective function (5) preserves the probability constraints of fuzzy membership and does not require additional information in the process of constructing similarity graphs.The objective function (5) is solved by alternate iteration method. Since the objective function has two variables (cluster center M and fuzzy membership matrix Y), this is a nonconvex problem. Therefore, when solving the objective function, one of the variables needs to be fixed to update the other variable.(1)
FixY to update MWhenY is fixed, formula (5) can be rewritten as(6)minM∑i=1n∑j=1cyijui−mj22.For each cluster centermj, there are(7)minmj∑i=1nyijui−mj22j=1,2,…,c.When formula (7) is differentiated with respect to mj and set equal to 0, the closed-form solution of mj is(8)mj=∑i=1nyijui∑i=1nyijj=1,2,…,c.(2)
FixM to update YWhenM is fixed, formula (5) can be rewritten as(9)minyi=1,Y≥0,YTY=I∑i=1n∑j=1cyijui−mj22+λTrYTL˜Y.Whendijm=ui−mj22, formula (9) is rewritten as(10)minyil=1,Y≥0,YTY=I∑i=1n∑j=1cyijdijm+λTrYTL˜Y.By constructing matrixDm,dijm∈Dm, formula (10) can be written in matrix form:(11)minyil=1,Y≥0,YTY=ITrYTDm+λTrYTL˜Y.Considering probability constraints, inequality constraints and orthogonal constraints, the Lagrangian function of optimization problem (11) is(12)LY,γ,α,β=TrYTDm+λTrYTL˜Y+γ2YTY−IF2+TrαYT+β2YC−EF2.Among them,γ is the penalty parameter to ensure the orthogonality of the fuzzy membership matrix Y, α is the Lagrange multiplier, and β is the regular term parameter to ensure that the row sum of the fuzzy membership matrix is 1. The matrix elements of matrix C∈ℝc×n,E∈ℝn×n are all 1 s. Taking the derivative of Y by formula (12) and setting its derivative to 0, we can get:(13)Dm+2λL˜Y+γYYTY+α+βYCCT=γY+βECT.When formula (9) is used to construct the bipartite graph matrix Z˜ of fast spectral embedded data, then the anchor graph matrix is(14)W˜=Z˜Λ˜−1Z˜T.Thus, the Laplace matrix is(15)L˜=I−W˜=I−Z˜Λ˜−1Z˜T.SubstitutingL˜ in formula (15) into formula (13), we get:(16)Dm+2λY+γYYTY+α+βYCCT=γY+2λZ˜Λ˜−1Z˜TY+βECT.According to the Karush-Kuhn-Tuckre (KKT) condition, there isα°Y=0, which represents the Hadamard product. Using the multiplicative update rule, the optimization method of formula (16) is(17)yijt+1=yijtγYt+2λZ˜Λ˜−1Z˜TYt+βECTijDm+2λYt+γYtYTtYt+βYtCCTij.M and Y are iteratively updated until the objective function (5) converges.(3)
The clustering category of the data can be easily obtained according to the following formula:(18)li=argmaxj∈1,2,…,cyij1Ty.j.We assume that the input data isX∈ℝn×d, where n and d represent the data volume and data dimension, respectively. In the fast spectral embedding stage, its time complexity is Onn1dt+nn1d+nn1k+n12k. In the fuzzy discretization stage of fast spectral embedded data, its time complexity is Onn1ct1+nn1c+nc2+n2ct2. Among them, n1 and k represent the number of data points and the number of neighbors, respectively, and t,t1 and t2 represent the needle points selected from the original data by the k-means method. The k-means method selects needle points from the fast spectral embedding data and iterates the fuzzy clustering process, and c is the number of clustering categories. Although the time complexity of FCAG is lower than that of spectral clustering On2c+n2d, it still has a quadratic relationship with the amount of data.


### 2.2. FANSEC Clustering Algorithm

In this paper, the construction method of anchor graph is introduced, which uses the second-order state transition probability of data points and anchor points to describe the relationship between data points and data points in the graph domain. Inspired by the joint clustering composition method, an adjacency graph matrix is constructed by the first-order state transition probabilities of data points and anchor points. In the composition of the joint clustering, the similarity graph structure is in the form of a block matrix, and the values of the input data represent the connections between data points and features. Joint clustering can achieve the effect of clustering data points and features of data points at the same time. Similarly, the first-order state transition probability from the data point to the anchor point (or the anchor point to the data point) represented by the bipartite graphZ is used as the connection relationship to form the graph at the subdiagonal position of the graph, which is described by the formula as follows:(19)W=0ZZT0.Since this composition method is generated based on data points and needle points and is a block diagonal matrix, for the convenience of description, this kind of graph structure is called block diagonal needle diagram. From the knowledge of spectral clustering, the objective function of the normalized cut graph can be expressed as(20)minFWTFW=ITrFWTLWFW.Among them,LW=I−DW−1/2WDW−1/2 is the normalized Laplacian matrix of the block diagonal pin graph. The matrices FW and DW are represented in the following form:(21)FW=UU¯,DW=DW100DW2.Formula (20) can be transformed into the solution:(22)maxUTU+U¯TU¯=ITrUTDW1−1/2ZDW2−1/2U¯.In order to solve U andU¯, a lemma is introduced.Lemma 1.
IfM∈ℝn×m,G∈ℝn×c,H∈ℝn×m is assumed, the solution of the optimization problem is G=2/2V1,H=2/2V2.(23)maxGTG+HTH=ITrGTMH.
Among them,V1 and V2 are the left and right singular value vectors corresponding to the largest c singular values after M singular value decomposition.
The proof of Lemma 1 can be found in the literature. According to Lemma 1, U and U¯ are, respectively, the left and right singular value vectors corresponding to the largest c singular values after the decomposition of matrix DA1−1/2ZDA2−1/2 multiplied by 2/2. According to the definition, the physical meaning of U is the spectral embedded data of the data points that have not been discretized, and the physical meaning of U¯ is the spectral embedded data of the pin points that have not been discretized. So far, we have obtained the joint spectral embedding results of data points and pinpoints. Spectral embedding data can be directly discretized using methods such as k-means to obtain final results. However, the clustering results based on k-means discretization methods are usually unstable and suboptimal. In order to obtain better clustering results, this chapter adopts the method of data spectral embedding combined with other clustering algorithms for data clustering.
We assume thatU^ is a pinpoint selected from the spectral embedding data U using the k-means method. The data U and the needle points U^ form a new data set U˜=U,U^T,U˜∈ℝn+n1×c, where n1 is the number of needle points. Referring to the definition of the block diagonal matrix, the composition of the data set U˜ is S, and its element values satisfy:(24)sij≥0,u˜i∈U,u˜j∈U^oru˜i∈U^,u˜j∈U,sij≡0,otherwise.
Formula (24) is written in the form of a block diagonal matrix:(25)S=0PPT0,S∈ℝn+n1×n+n1.
According to the traditional adaptive nearest neighbor rule, a large value ofsij corresponds to a small distance u˜i−u˜j22, which can be described as the following problem:(26)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2s.t.0≤sij≤1,si1=1.
Among them,si represents the ith row vector of matrix S. The second term in formula (26) is the regular term, and γ is the regularization parameter. In the clustering process, the ideal composition S is that the number of its connected domains is equal to the number of cluster categories. However, in most cases, only graph structures with a connected domain of 1 can be obtained by solving formula (26).
If the similarity matrixS˜ is assumed to have c connected domains, then its normalized Laplacian matrix L˜S˜=I−DS˜−1/2S˜DS˜−1/2 has the following properties:Theorem 1.
The number of zero eigenvalues of the Laplace matrix L˜S˜ is equal to the number of connected domains of the similarity matrix S˜.According to Theorem1, the number of nonzero eigenvalues of a matrix L˜S˜ is equal to the rank of the matrix. In order to obtain S˜ with c connected domains, we add a rank constraint to formula (26).(27)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2s.t.0≤sij≤1,si1=1,rankL˜S=n+n1−c.However, the optimization problem (27) with added rank constraints is still difficult to solve. We assume that σkL˜S represents the k-th smallest eigenvalue of L˜S. Since L˜S is a positive semi-definite matrix, σkL˜S≥0. Problem (27) can be transformed into:(28)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2+λ∑k=1cσkL˜Ss.t.0≤sij≤1,si1=1.When the parameterλ is large enough, formulas (28) and (27) are equal.According to KyFan’s theorem, we have:(29)∑k=1cσkL˜S=minF∈ℝn+1||,FTF=ITrFTL˜sF.Then, problem (28) can be rewritten as(30)minS,F∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2+λTrFTL˜SFs.t.0≤sij≤1,si1=1,F∈ℝn+n1×c,FTF=I.Compared with equation (27) and (30) is obviously easier to solve. Observing problem (30), we can see that there are two variables S and F that need to be optimized, which can be solved by alternately updating the two variables.(1)
FixS to update FWhenS is fixed, formula (30) can be rewritten as(31)minF∈ℝn+m×,FTTrFTL˜SF.Among them,L˜S=I−DS−1/2SDS−1/2 is the normalized Laplacian matrix and F and DS represent the form of the block matrix:(32)F=F¯F˜,D=DS100DS2.SubstitutingL˜S=I−DS−1/2SDS−1/2 and (32) into (31), we get:(33)maxF¯TF¯+F¯TF˜=ITrF¯TDS1−1/2PDS2−1/2F˜.According to Lemma1, the F matrix can be updated by singular value decomposition of matrix DS1−1/2SDS2−1/2.(2)
FixF to update SWhenF is fixed, formula (30) can be rewritten as(34)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2+λTrFTL˜SFs.t.0≤sij≤1,si1=1.Considering that the Laplace matrixL˜S has the following properties:(35)TrFTL˜SF=12∑i=1n+n1∑j=1n+n1fidi−fjdj22sij.Substituting (35) into (34), we get:(36)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sijs.t.0≤sij≤1,si1=1.Among them, the parameterα=λ/2.Considering the definition of similarity graph matrixS in (25), formula (36) can be rewritten as(37)mins∑i=1n∑j=n+1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sij+∑i=n+1n+n1∑j=1nu˜i−u˜j22+γsij+αfidi−fjdj22sijs.t.0≤sij≤1,si1=1.Since(38)∑i=1n∑j=n+1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sij=∑i=n+1n+n1∑j=1nu˜i−u˜j22+γsij+αfidi−fjdj22sij.Formula (37) can be rewritten as(39)minS∑i=1n∑j=n+1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sijs.t.0≤sij≤1,si1=1.The updates of each row si in formula (39) are independent of each other, so we can optimize each row separately. Problem (39) is equivalent to optimization:(40)minsi∑j=n+1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sijs.t.0≤sij≤1,si1=1.liju=u˜i−u˜j22,lijf=fi/di−fj/dj22,lij=liju+αlijf, then formula (40) can be rewritten as(41)minsisi+12γli22,s.t.0≤sij≤1,si1=1.It can be proved that the optimal update method ofsij is(42)sij=−lij2γi+η+.Among them,γ,γi, and η are Lagrange multipliers, and their solution methods are(43)γi=k2li,k+1−12∑j=1klij,γ=1n∑i=1nγi,η=1k+12kγi∑j=1klij.Among them,k is the number of neighbors. So far, we have obtained the closed-form solution of the S-optimized update in equation (34).(3)
Iteratively update F and S until the objective function (29) converges.We assume that the input data areX∈ℝn×d, where n and d represent the data volume and data dimension, respectively. The time complexity of the clustering method proposed in this chapter mainly includes two parts. n1,t,k, and t1 represent the number of pinpoints, the number of k-means clustering iterations, the number of neighbors, and the number of optimization iterations, respectively. The time complexity mainly includes two aspects, data joint spectral embedding and fast adaptive nearest neighbor clustering based on block diagonal needle graph.(1)
Data joint spectral embedding(a)
The time complexity required to selectn1 needle points from the data points using the k-means method is Onn1dt;(b)
The time complexity required to obtain the bipartite graph matrixZ between the data point and the pin point is Onn1d;(c)
The time complexity of the singular value decomposition ofDA1−1/2ZDA2−1/2 is Onn1k+n12k.(2)
Fast adaptive neighbor clustering based on block diagonal matrix graph(a)
The time complexity required to select n1 pinpoints from the fast spectral embedding data U using the k-means method is Onn1ct; a.(b)
The time complexity required to initialize the matrix S is Onn1c;(c)
The time complexity required for the iterative update process is On13+n12n+nn1kt1.


## 2.1. FCAG Algorithm

The fuzzy weight of the objective function of FCM is set to 1, the objective function can be written as(1)minyi=1,Y≥0,mj∑i=1n∑j=1cyijxi−mj22.Among them,yij represents the fuzzy membership degree between the data point xi and the cluster center mj.When the input data are replaced with the fast spectral threshold input dataU, problem (1) can be expressed as(2)minyi=1,Y≥0,mj∑i=1n∑j=1cyijui−mj22.It can be seen from formula (2) that the size of fuzzy membership depends on the distance between the spectral embedded data and its cluster center. In order to improve the accuracy of the fuzzy membership matrix, inspired by the literature, a similarity measure in the needle graph space can be added to formula (2).wil is an element of the ith row and l-column of the needle graph matrix W. The larger the value of the element, the closer the data points ui and uj are. Because the fuzzy membership vector yi describes the distance relationship between the data point ui and all cluster centers, when the data points ui and uj are adjacent to each other, their fuzzy membership vectors are also close. Therefore, formula (2) can be rewritten as(3)minyi=1,Y≥0,mj∑i=1n∑j=1cyijui−mj22+λ2∑i=1n∑l=1nwilyi−yl22.Among them,λ is the regularization parameter. The regular term adds the similarity measure in the needle graph space, which can make the fuzzy membership matrix more accurately describe the relationship between the data and the cluster centers.In spectral clustering, the Laplace matrix has the following properties:(4)TrYTLY=12∑i=1n∑l=1nwilyi−yl22,s.t.YTY=I.By fusing formulas (3) and (4), the objective function can be rewritten as(5)minyi=1,Y≥0,YTY=l,mj∑i=1n∑j=1cyijui−mj22+λTrYTL˜Y.The update of fuzzy membership in objective function (5) has profound physical meaning. It is not only affected by the distance between the fast spectral embedding data and the cluster center but also constrained by the similarity between the cluster data in the graph domain. The new objective function can combine the advantages of FCM and spectral clustering to obtain a better fuzzy membership matrix.The objective function (5) preserves the probability constraints of fuzzy membership and does not require additional information in the process of constructing similarity graphs.The objective function (5) is solved by alternate iteration method. Since the objective function has two variables (cluster center M and fuzzy membership matrix Y), this is a nonconvex problem. Therefore, when solving the objective function, one of the variables needs to be fixed to update the other variable.(1)
FixY to update MWhenY is fixed, formula (5) can be rewritten as(6)minM∑i=1n∑j=1cyijui−mj22.For each cluster centermj, there are(7)minmj∑i=1nyijui−mj22j=1,2,…,c.When formula (7) is differentiated with respect to mj and set equal to 0, the closed-form solution of mj is(8)mj=∑i=1nyijui∑i=1nyijj=1,2,…,c.(2)
FixM to update YWhenM is fixed, formula (5) can be rewritten as(9)minyi=1,Y≥0,YTY=I∑i=1n∑j=1cyijui−mj22+λTrYTL˜Y.Whendijm=ui−mj22, formula (9) is rewritten as(10)minyil=1,Y≥0,YTY=I∑i=1n∑j=1cyijdijm+λTrYTL˜Y.By constructing matrixDm,dijm∈Dm, formula (10) can be written in matrix form:(11)minyil=1,Y≥0,YTY=ITrYTDm+λTrYTL˜Y.Considering probability constraints, inequality constraints and orthogonal constraints, the Lagrangian function of optimization problem (11) is(12)LY,γ,α,β=TrYTDm+λTrYTL˜Y+γ2YTY−IF2+TrαYT+β2YC−EF2.Among them,γ is the penalty parameter to ensure the orthogonality of the fuzzy membership matrix Y, α is the Lagrange multiplier, and β is the regular term parameter to ensure that the row sum of the fuzzy membership matrix is 1. The matrix elements of matrix C∈ℝc×n,E∈ℝn×n are all 1 s. Taking the derivative of Y by formula (12) and setting its derivative to 0, we can get:(13)Dm+2λL˜Y+γYYTY+α+βYCCT=γY+βECT.When formula (9) is used to construct the bipartite graph matrix Z˜ of fast spectral embedded data, then the anchor graph matrix is(14)W˜=Z˜Λ˜−1Z˜T.Thus, the Laplace matrix is(15)L˜=I−W˜=I−Z˜Λ˜−1Z˜T.SubstitutingL˜ in formula (15) into formula (13), we get:(16)Dm+2λY+γYYTY+α+βYCCT=γY+2λZ˜Λ˜−1Z˜TY+βECT.According to the Karush-Kuhn-Tuckre (KKT) condition, there isα°Y=0, which represents the Hadamard product. Using the multiplicative update rule, the optimization method of formula (16) is(17)yijt+1=yijtγYt+2λZ˜Λ˜−1Z˜TYt+βECTijDm+2λYt+γYtYTtYt+βYtCCTij.M and Y are iteratively updated until the objective function (5) converges.(3)
The clustering category of the data can be easily obtained according to the following formula:(18)li=argmaxj∈1,2,…,cyij1Ty.j.We assume that the input data isX∈ℝn×d, where n and d represent the data volume and data dimension, respectively. In the fast spectral embedding stage, its time complexity is Onn1dt+nn1d+nn1k+n12k. In the fuzzy discretization stage of fast spectral embedded data, its time complexity is Onn1ct1+nn1c+nc2+n2ct2. Among them, n1 and k represent the number of data points and the number of neighbors, respectively, and t,t1 and t2 represent the needle points selected from the original data by the k-means method. The k-means method selects needle points from the fast spectral embedding data and iterates the fuzzy clustering process, and c is the number of clustering categories. Although the time complexity of FCAG is lower than that of spectral clustering On2c+n2d, it still has a quadratic relationship with the amount of data.


## 2.2. FANSEC Clustering Algorithm

In this paper, the construction method of anchor graph is introduced, which uses the second-order state transition probability of data points and anchor points to describe the relationship between data points and data points in the graph domain. Inspired by the joint clustering composition method, an adjacency graph matrix is constructed by the first-order state transition probabilities of data points and anchor points. In the composition of the joint clustering, the similarity graph structure is in the form of a block matrix, and the values of the input data represent the connections between data points and features. Joint clustering can achieve the effect of clustering data points and features of data points at the same time. Similarly, the first-order state transition probability from the data point to the anchor point (or the anchor point to the data point) represented by the bipartite graphZ is used as the connection relationship to form the graph at the subdiagonal position of the graph, which is described by the formula as follows:(19)W=0ZZT0.Since this composition method is generated based on data points and needle points and is a block diagonal matrix, for the convenience of description, this kind of graph structure is called block diagonal needle diagram. From the knowledge of spectral clustering, the objective function of the normalized cut graph can be expressed as(20)minFWTFW=ITrFWTLWFW.Among them,LW=I−DW−1/2WDW−1/2 is the normalized Laplacian matrix of the block diagonal pin graph. The matrices FW and DW are represented in the following form:(21)FW=UU¯,DW=DW100DW2.Formula (20) can be transformed into the solution:(22)maxUTU+U¯TU¯=ITrUTDW1−1/2ZDW2−1/2U¯.In order to solve U andU¯, a lemma is introduced.Lemma 1.
IfM∈ℝn×m,G∈ℝn×c,H∈ℝn×m is assumed, the solution of the optimization problem is G=2/2V1,H=2/2V2.(23)maxGTG+HTH=ITrGTMH.
Among them,V1 and V2 are the left and right singular value vectors corresponding to the largest c singular values after M singular value decomposition.
The proof of Lemma 1 can be found in the literature. According to Lemma 1, U and U¯ are, respectively, the left and right singular value vectors corresponding to the largest c singular values after the decomposition of matrix DA1−1/2ZDA2−1/2 multiplied by 2/2. According to the definition, the physical meaning of U is the spectral embedded data of the data points that have not been discretized, and the physical meaning of U¯ is the spectral embedded data of the pin points that have not been discretized. So far, we have obtained the joint spectral embedding results of data points and pinpoints. Spectral embedding data can be directly discretized using methods such as k-means to obtain final results. However, the clustering results based on k-means discretization methods are usually unstable and suboptimal. In order to obtain better clustering results, this chapter adopts the method of data spectral embedding combined with other clustering algorithms for data clustering.
We assume thatU^ is a pinpoint selected from the spectral embedding data U using the k-means method. The data U and the needle points U^ form a new data set U˜=U,U^T,U˜∈ℝn+n1×c, where n1 is the number of needle points. Referring to the definition of the block diagonal matrix, the composition of the data set U˜ is S, and its element values satisfy:(24)sij≥0,u˜i∈U,u˜j∈U^oru˜i∈U^,u˜j∈U,sij≡0,otherwise.
Formula (24) is written in the form of a block diagonal matrix:(25)S=0PPT0,S∈ℝn+n1×n+n1.
According to the traditional adaptive nearest neighbor rule, a large value ofsij corresponds to a small distance u˜i−u˜j22, which can be described as the following problem:(26)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2s.t.0≤sij≤1,si1=1.
Among them,si represents the ith row vector of matrix S. The second term in formula (26) is the regular term, and γ is the regularization parameter. In the clustering process, the ideal composition S is that the number of its connected domains is equal to the number of cluster categories. However, in most cases, only graph structures with a connected domain of 1 can be obtained by solving formula (26).
If the similarity matrixS˜ is assumed to have c connected domains, then its normalized Laplacian matrix L˜S˜=I−DS˜−1/2S˜DS˜−1/2 has the following properties:Theorem 1.
The number of zero eigenvalues of the Laplace matrix L˜S˜ is equal to the number of connected domains of the similarity matrix S˜.According to Theorem1, the number of nonzero eigenvalues of a matrix L˜S˜ is equal to the rank of the matrix. In order to obtain S˜ with c connected domains, we add a rank constraint to formula (26).(27)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2s.t.0≤sij≤1,si1=1,rankL˜S=n+n1−c.However, the optimization problem (27) with added rank constraints is still difficult to solve. We assume that σkL˜S represents the k-th smallest eigenvalue of L˜S. Since L˜S is a positive semi-definite matrix, σkL˜S≥0. Problem (27) can be transformed into:(28)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2+λ∑k=1cσkL˜Ss.t.0≤sij≤1,si1=1.When the parameterλ is large enough, formulas (28) and (27) are equal.According to KyFan’s theorem, we have:(29)∑k=1cσkL˜S=minF∈ℝn+1||,FTF=ITrFTL˜sF.Then, problem (28) can be rewritten as(30)minS,F∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2+λTrFTL˜SFs.t.0≤sij≤1,si1=1,F∈ℝn+n1×c,FTF=I.Compared with equation (27) and (30) is obviously easier to solve. Observing problem (30), we can see that there are two variables S and F that need to be optimized, which can be solved by alternately updating the two variables.(1)
FixS to update FWhenS is fixed, formula (30) can be rewritten as(31)minF∈ℝn+m×,FTTrFTL˜SF.Among them,L˜S=I−DS−1/2SDS−1/2 is the normalized Laplacian matrix and F and DS represent the form of the block matrix:(32)F=F¯F˜,D=DS100DS2.SubstitutingL˜S=I−DS−1/2SDS−1/2 and (32) into (31), we get:(33)maxF¯TF¯+F¯TF˜=ITrF¯TDS1−1/2PDS2−1/2F˜.According to Lemma1, the F matrix can be updated by singular value decomposition of matrix DS1−1/2SDS2−1/2.(2)
FixF to update SWhenF is fixed, formula (30) can be rewritten as(34)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22sij+γSF2+λTrFTL˜SFs.t.0≤sij≤1,si1=1.Considering that the Laplace matrixL˜S has the following properties:(35)TrFTL˜SF=12∑i=1n+n1∑j=1n+n1fidi−fjdj22sij.Substituting (35) into (34), we get:(36)minS∑i=1n+n1∑j=1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sijs.t.0≤sij≤1,si1=1.Among them, the parameterα=λ/2.Considering the definition of similarity graph matrixS in (25), formula (36) can be rewritten as(37)mins∑i=1n∑j=n+1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sij+∑i=n+1n+n1∑j=1nu˜i−u˜j22+γsij+αfidi−fjdj22sijs.t.0≤sij≤1,si1=1.Since(38)∑i=1n∑j=n+1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sij=∑i=n+1n+n1∑j=1nu˜i−u˜j22+γsij+αfidi−fjdj22sij.Formula (37) can be rewritten as(39)minS∑i=1n∑j=n+1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sijs.t.0≤sij≤1,si1=1.The updates of each row si in formula (39) are independent of each other, so we can optimize each row separately. Problem (39) is equivalent to optimization:(40)minsi∑j=n+1n+n1u˜i−u˜j22+γsij+αfidi−fjdj22sijs.t.0≤sij≤1,si1=1.liju=u˜i−u˜j22,lijf=fi/di−fj/dj22,lij=liju+αlijf, then formula (40) can be rewritten as(41)minsisi+12γli22,s.t.0≤sij≤1,si1=1.It can be proved that the optimal update method ofsij is(42)sij=−lij2γi+η+.Among them,γ,γi, and η are Lagrange multipliers, and their solution methods are(43)γi=k2li,k+1−12∑j=1klij,γ=1n∑i=1nγi,η=1k+12kγi∑j=1klij.Among them,k is the number of neighbors. So far, we have obtained the closed-form solution of the S-optimized update in equation (34).(3)
Iteratively update F and S until the objective function (29) converges.We assume that the input data areX∈ℝn×d, where n and d represent the data volume and data dimension, respectively. The time complexity of the clustering method proposed in this chapter mainly includes two parts. n1,t,k, and t1 represent the number of pinpoints, the number of k-means clustering iterations, the number of neighbors, and the number of optimization iterations, respectively. The time complexity mainly includes two aspects, data joint spectral embedding and fast adaptive nearest neighbor clustering based on block diagonal needle graph.(1)
Data joint spectral embedding(a)
The time complexity required to selectn1 needle points from the data points using the k-means method is Onn1dt;(b)
The time complexity required to obtain the bipartite graph matrixZ between the data point and the pin point is Onn1d;(c)
The time complexity of the singular value decomposition ofDA1−1/2ZDA2−1/2 is Onn1k+n12k.(2)
Fast adaptive neighbor clustering based on block diagonal matrix graph(a)
The time complexity required to select n1 pinpoints from the fast spectral embedding data U using the k-means method is Onn1ct; a.(b)
The time complexity required to initialize the matrix S is Onn1c;(c)
The time complexity required for the iterative update process is On13+n12n+nn1kt1.


## 3. Analysis of the Impact of Intelligent Accounting Information Management Algorithm on Corporate Governance Information Transparency

The development characteristics selected in this paper include growth and volatility. Financial characteristics describe the performance of a listed corporate in a specific period, and the information it conveys is quite useful to stakeholders. The financial characteristics selected in this paper include profitability, financial risk, and loss in the previous year. Figure1 shows the relationship between the above-mentioned corporate characteristics and accounting information transparency, which has also become the basic analytical theoretical framework for this paper to study and verify this issue.Figure 1
Analysis framework of factors affecting accounting information transparency based on corporate characteristics.This article combines the supply chain of corporate financial reporting and the information transformation process (Figure2) in the capital market to understand the meaning of accounting transparency. Under the modern corporate system nurtured by the capital market, the separation of powers has resulted in information asymmetry, which has resulted in a supply and demand mechanism for information.Figure 2
Information transfer diagram of capital market.The corporate's internal and external governance mechanisms and the macro institutional environment have an impact on disclosure benefits and disclosure costs. In addition, management disclosure decisions are also influenced by its own motivations and corporate characteristics. Figure3 describes the influencing factors of information transparency and its mechanism of action.Figure 3
Influencing factors and mechanism of information transparency.Because accounting information has economic consequences, the provision of accounting information cannot be simply a technical issue, or accounting transparency can be achieved only by relying on a set of clear and scientific accounting standards. The realization of accounting transparency can only be expected when the relevant accounting environment can guarantee the quality of accounting information and the quality of disclosure. Moreover, a healthy corporate governance ecology can be used as a constraint and supervision mechanism to restrict the disclosure of accounting information of listed companies and ensure the high quality of accounting information. Its impact on accounting transparency can be shown in Figure4.Figure 4
The impact of corporate governance ecology on accounting transparency.The internal and external supervision mechanism of the corporate is an important check on the quality of accounting information. If the supervision mechanism cannot operate effectively, it will seriously affect the transparency of accounting information. Figure5 specifically lists the intermediate supervision links of listed companies' accounting information from management to users.Figure 5
Quality control link of accounting information.Management takes into account the impact of cost-benefit factors and rational brokerage assumptions that seek to avoid disadvantages. On the one hand, it may conceal internal control deficiencies. On the other hand, with the expansion of the power of the management, for the consideration of private interests, the management may manipulate the quality of accounting information by affecting the internal control of the enterprise or taking advantage of the defects of internal control, so that the disclosure of accounting information has greater discretionary power. At the same time, internal control is a necessary means to strengthen corporate governance, standardize internal processes, and supervise and restrain managers’ behavior. A sound and complete internal control system can effectively restrain the self-interested behavior of the management and play an important role in ensuring the effective operation of various departments of the enterprise and improving the quality of accounting information. This paper assumes that the corresponding logical structure is shown in Figure6.Figure 6
Logical structure diagram.On the basis of the above, the model proposed in this paper is verified, and the relationship between intelligent accounting information management technology and corporate governance information transparency is calculated. The statistical test results are shown in Figure7.Figure 7
The relationship between intelligent accounting information management technology and corporate governance information transparency.Through the above regression analysis, we can see that there is a linear correlation between the advanced degree of intelligent accounting information management technology and the transparency of corporate governance information. On this basis, the effect of the model proposed in this paper is verified, and the statistical results are shown in Table1.Table 1
Evaluation of the effect of intelligent accounting information management system.
NumEvaluation183.36284.35381.20490.89583.32689.64787.59881.66979.561081.451186.551281.651380.941484.631588.871686.901783.041889.321990.212084.782181.492287.122385.122488.562585.402690.862789.882886.812980.763081.003182.333284.323390.453483.473584.373683.713784.953887.673987.084083.224184.714290.224383.614486.564582.624679.694785.864879.16From the above research, we can see that the intelligent accounting information management system proposed in this paper can effectively improve the corporate's accounting information management effect.


## 4. Conclusion

In the study of economics, the problem of investor protection has always been troubled by scholars. There are many factors that affect the level of investor protection. In addition to macro factors, there are not only the efficiency factors of the securities market itself but also corporate-level governance and management factors. Moreover, many factors affect each other, and it is difficult to solve all problems at one time. Combining these factors, improving the transparency of corporate accounting information has become a key link to achieve investor protection. This paper analyzes the information transparency in the process of corporate governance based on intelligent accounting information technology. Through regression analysis, we can see that there is a linear correlation between the advanced degree of intelligent accounting information management technology and the transparency of corporate governance information. At the same time, the intelligent accounting information management system proposed in this paper can effectively improve the corporate's accounting information management effect.



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*Source: 2478926-2022-07-07.xml*