# Risk Analysis and Countermeasures of Social Medical Insurance Based on Random Matrix Theory and Data Mining

Authors: Cuixia Chen
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Accelerating the reform of social medical insurance risk analysis is an urgent need to establish a complete social medical insurance system. Based on random matrix theory and data mining technology, this study constructs a social medical insurance risk analysis model. After determining the subject of the data warehouse and the relevant information of each subject, it starts to build a random matrix data warehouse, and solves the social medical insurance risk through the data fact table and dimension quantitative indicators. In the simulation process, the model uses the Oracle Warehouse Builder (OWB) software to create the data warehouse, and systematically analyzes and studies the construction process of each table; when creating the server through data mining, we run the repository as an administrator program to create data mining workspace, including creating OWB username and password. The experimental results show that after analyzing related technologies such as data warehouse, OLAP, and data mining, the accuracy rate of abnormality is 79.0%, and the recall rate is 85.8%. After using random matrix sampling technology to balance the dataset, the algorithm effect accuracy rate reaches 89.3%, which can effectively provide professional help for the social security fund supervision department and the medical insurance business management department.


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## Body

## 1. Introduction

At present, the functions of the medical insurance audit system are still mainly based on simple query, statistical analysis, multidimensional drilling, etc., and the system’s support for medical insurance supervision is very limited [1]. With the continuous increase in the number of insured persons and the trend of diversification and concealment of violations, the medical insurance supervision work dominated by manual random inspection and auditing is not effective [2]. The supervision of medical service behavior is directly related to the vital interests of the insured and the safety of the medical insurance fund, and affects whether the medical insurance system can develop sustainably and healthily [3]; effectively improving the information level of the current medical insurance audit system and providing decision support for medical insurance supervision are an important way to solve the current medical insurance fund loss caused by improper medical insurance supervision methods [4–6].Over the years, medical insurance informatization has collected and stored a large amount of data such as basic patient information, diagnosis and treatment prescription information, medical expense information, and reimbursement expense information [7], providing a data source for data analysis and mining. The researchers introduced random matrix theory, association rules, attribute reduction, and other technologies in data mining technology, trying to build an intelligent medical insurance audit system based on random matrix theory and association rules [8], using data mining technology combined with field medical service monitoring. The rules conduct in-depth analysis, mining and modeling of medical insurance data to realize real-time analysis, and screening of medical insurance settlement information. Many drawbacks such as unstable funding sources, lack of cost restraint mechanism, and low socialization degree are gradually exposed [9–11], especially in today’s rapid development of various economic components, and the establishment of a regional socialist market economic system is necessary. A new social insurance system is imperative. The most critical and also the most complicated and difficult to implement in the reform of the social insurance system is the basic medical insurance for employees, which involves the vital interests of the masses in all walks of life [12].Based on the above problems, this study takes the regional basic medical insurance system as the research object. The OLAP and data mining technology based on data warehouse are to process and analyze large-scale data, and to verify the hidden, unknown, or known regularity information. Therefore, this study selects two themes in the medical insurance business of social insurance for analysis and design. Combined with the information construction level of human resources and social security and the characteristics of medical insurance business, the technology of data warehouse is adopted to establish a theme-based data warehouse, conduct OLAP analysis and data mining, and provide ideas and methods for medical insurance big data research. Based on the advanced experience of foreign medical insurance informatization construction, this study designs a basic medical insurance system management service optimization platform model based on the function of social security card. The top-level design of the system helps to enrich and improve the informatization functions of the social security card. We integrate the data mining tool WEKA into the MyEclipse development environment, and realize the development of an intelligent medical insurance audit system based on random matrix theory and association rules using the theories, methods, and technologies obtained from the research. The main function of the system is knowledge base management, and the application of intelligent medical insurance audit system in medical insurance supervision is demonstrated by using model bases such as management and monitoring.


## 2. Related Work

At present, there is no unified definition for random matrix theory and data mining [13]. Researchers define data mining as the process of in-depth analysis of data through the application of advanced techniques to discover meaningful new relationships, patterns, and trends. These techniques include pattern recognition techniques, statistical techniques, and mathematical techniques [14–16].Owadally et al. [17] proposed that the risks faced by medical insurance are mainly manifested in five aspects, namely, economy, nature, politics, technology, and society. According to the characteristics and causes of these five aspects, several preventive suggestions and measures are put forward, which will affect the medical insurance fund. The factors of risk can be attributed to seven aspects, namely, economy, population, policy, payment method, internal management, medical expense increase, unreasonable expense, and gave perfect countermeasures; Jain et al. [18] proposed that the risks faced by medical insurance funds mainly exist in the process of supervision and use, such as the coverage of medical insurance is not complete enough; various supervision systems are not perfect; the fund balance rate is high; the settlement method is not very scientific; there are still irregularities in the use of funds; and there is still insurance fraud, put forward countermeasures and suggestions on the illegal operation and fund reform in the use of social security funds.Wu [19] comprehensively analyzed the latest technology and future development trend of web mining, studied the design of social security data warehouse, and put forward new ideas; Sharma and Jain [20] studied from the perspectives of preventing excessive treatment and controlling expenses. These studies mainly include the establishment of hospital medical insurance business decision support system and the application of data warehouse technology in cigarette quality management system. The data warehouse architecture and OLAP architecture of cigarette quality management system are proposed. The decision support system model was studied; by comparing the CBM, apriori, and ECLAT algorithms, it was proposed that the CBM algorithm performed better in detecting medical agglomeration [21]. Using data warehouse, data mining, OLAP, etc. as research tools, this study analyzes the total payment of medical insurance funds from a macroperspective, analyzes the medical insurance expenses for a single disease on a microlevel, and puts forward relevant suggestions [22, 23].


## 3. Construction of Social Medical Insurance Risk Analysis Model Based on Random Matrix Theory and Data Mining

### 3.1. Random Matrix Solution Set Distribution

We consider the intersection point P of the four matrices of the random matrix solution set. According to our division,P is included in all four subsets. In the clustering process of any subset, the r neighborhood of point P is actually a 1/4 circular area, so the local density of point P is miscalculated during the subset clustering process, which may lead to the original Ps that are core points are identified as outliers or boundary points. Therefore, for each matrix, when calculating its subset, an area with a width of r needs to be additionally expanded, as shown by the red solid line, so that the adjacent subsets have a coincident area with a width of 2r, ensuring that for any sample point, its neighborhood can be completely covered by at least one subset.(1)M′qx,px=M′qx,p1M′qx,p3M′qx,p2M′qx,pi,g′qx,px,x=1−gt−t2,1−logt−t2−1.Matrix correlation analysis is a simple and practical analysis technique, which is to find the correlation or correlation existing in a large number of datasets, thereby describing the laws and patterns of the simultaneous appearance of certain attributes in a thing. Associations are divided into simple associations, temporal associations, and causal associations. Generally, support, confidence, and lift are used to measure the relevance of association rules.(2)maxM′q1+M′q2+M′qi−M′qx=px−1,mint,t−1maxt,t−1=1/2x+5t/11−1/2x+6t/11.Matrix prediction is to obtain a prediction model by learning the correlation between the input value and the output value of the sample data (historical data), and the model predicts the output value of the future input value and uses the prediction variance to assess the accuracy of model predictions. Time-series patterns describe and model recurring regularities or trends based on time or other series. Like predictive analysis, it uses known data to predict future values.If there arek, then k samples are arbitrarily selected from the sample as the center (initial centroid) of the k categories. The distance between each sample and the center is divided into the nearest class. In this way, k clusters are obtained, the centers of k clusters are recalculated again, and the previous process is repeated until no samples are redivided and finally convergence is achieved.(3)∏qi−qi−11−in−iZi−1+,⋯,+1n−iZi=1−in−ii−n−⋯,−1,f=1−in−iZi−1−1+in−iZi+1,i,j=1,2,3,…,n.Matrix biases may contain potentially interesting knowledge such as outliers outside clusters, deviations of observations from expectations, anomalous instances in classification, and exceptions that do not satisfy rules. In enterprise crisis management and its early warning, managers are more interested in unexpected rules. The mining of unexpected rules can help to detect anomalies in time, and analyze and identify the reasons for the anomalies, so that preventive measures can be taken in time.(4)∑i,j=1,2,…,n1n−iZi−1n−iZj−1n−iZi−j−logzizj=1−i−j.It can select the appropriate data from the original data as the object data, and the extraction should follow the principles of relevance, reliability, real time, and integrity. At the same time, the extracted sample data are explored, reviewed, and processed to ensure the quality of prediction. Data exploration mainly includes the following: outlier analysis, correlation analysis, missing value analysis, sample cross-validation, etc. The essence of this division method is to mutually use orthogonal hyperplanes to cut the original space, and it is only necessary to ensure that adjacent subsets have 2r overlapping intervals in each dimension to be divided. But for high-dimensional data, if such a segmentation is made in each dimension, it will quickly encounter the curse of dimensionality. Clearly, there is an exponential relationship between the number of subdatasets and the dimensionality, and as the dimensionality gets higher and higher, the number of subdatasets in Figure 1 will quickly balloon to unacceptably astronomical numbers. Therefore, dimension selection is required before segmentation.Figure 1
Random matrix solution topology.Matrix application integration consists of a set of interfaces and management. One is to complete the organization of application functions, that is, to establish the binding relationship between frameworks, models, and logic for business processing, to form functional modules and to define the control and configuration information of the modules; the execution authority of the system role completes the corresponding relationship between the business role and the execution module. The database includes “fact tables,” which contain data items that users need to analyze when building the database, and there is a “dimension table” for each dimension. Each tuple in the “fact table” contains a foreign key to each “dimension table” and some corresponding measurement data. The “dimension table” records the attributes of this dimension. In addition to the data included in the fact table for analysis, there are one or more foreign keywords, which are the link between the fact table and the data dimension table. In each dimension table, in addition to the primary key of each dimension, there are also some other attribute fields that describe the dimension. The analytical process of executing a query in a data warehouse model takes a lot of time to find data in the relevant tables. The star model enables the complex query of the data warehouse to be completed directly through the hierarchical comparison, drill-up, drill-down, and other operations of each dimension.


### 3.2. Data Mining Residual Analysis

Because the data sampled by data mining residuals often contain many noisy, incomplete, or even inconsistent data, which may affect the mining results, it is necessary to preprocess the data objects to improve the data quality and make the subsequent mining results more accurate. Data preprocessing includes steps such as data integration, data selection, data cleaning, and data transformation. Each nonleaf node represents a test on a feature attribute; each branch represents the output of the feature attribute on a certain value range; and each random matrix leaf node stores a category. The decision random matrix algorithm constructs a high-precision, small-scale decision-making random matrix to discover the classification knowledge contained in the dataset in Table1.Table 1
Data mining residuals.
Data onto the coordinate axisOverfitting for a small number of samplesRandom matrix classification knowledge0.110.880.120.190.120.990.100.320.000.550.220.350.220.210.660.640.660.740.320.560.320.340.010.300.010.090.810.41In each dimension, we project the full amount of data onto the coordinate axis, then divide the coordinate axis intok intervals, and make the overlapping length of adjacent intervals 2r, and we count the number of sample points that fall into each interval and calculate the variance. Small variance means that the distribution of data in each interval is more balanced, which is the preferred object. According to the idea of random oversampling, some samples will overlap in the balanced dataset, and the more unbalanced the categories in the original dataset, the greater the overlap ratio. When the scale of the dataset is relatively large, especially the number of rows and columns are given. In the case of more than 3,000, we pointed out the most time-consuming steps in the PCA algorithm, and demonstrated the important role of three random matrices and greedy algorithms in reducing the matrix decomposition time in the PCA dimensionality reduction process.


### 3.3. Analysis of Random Matrix Indicators

In the random matrix index analysis and detection problem studied in this study, the abnormal data are precisely the minority class, so we need to balance the dataset before using the classification algorithm. There are two main types of processing for unbalanced datasets, mainly using oversampling and undersampling. After the data model of the data warehouse is defined, the data from different data sources will be loaded into the data warehouse, and then, the system will run the corresponding synthesis program according to the data model to synthesize the data and create indexes to optimize the access efficiency. The multidimensional analysis request of the end user is dynamically translated into SQL request by the ROLAP engine; then, the SQL request is processed by the relational database, and finally, the query result is returned to the user after multidimensional processing.Objects typically have highly compressed index and pointer structures. Each object in Figure2 consists of cells that are grouped into groups, and the cell blocks are accessed by computing offsets. In MDDB, data management is mainly based on dimension and dimension members. Most MDDB products also provide unit-level control, and data blocking can reach unit block level. These management and control tasks are implemented by the data management layer in the MDDB and are generally not easy to bypass. The ROLAP is based on the traditional relational database system; security and access control are based on tables; and blocking is based on tables and pages. Since these are not directly related to the multidimensional concept in the application, the ROLAP tool must manage the security and access control by itself. Therefore, it is possible to bypass the security mechanism of ROLAP and directly access the database through its existing route.Figure 2
Unit index analysis of random matrix clustering into groups.According to the law revealed by the experiment, the outlier set in Figure3 can be used as the abnormal cluster to exclude most of the normal data, which is equivalent to a coarse-grained screening. The algorithm results of DBSCAN are meaningful, so even clustering with unlabeled data is not affected. In this outlier set, it can be found that the proportion of normal data has been greatly reduced, and the proportion of categories can already be considered to belong to the normal category. Inspired by this, the outlier part obtained by the clustering algorithm can be sampled, and this sampling is based on the density.Figure 3
Random matrix outlier set index.


### 3.4. Data Module Identification

In this study, we use the Oracle Warehouse Builder (OWB) software to create the data warehouse, and conduct a systematic analysis and research on the construction process of each table. When creating a server through OWB, run the Repository Assistant program as an administrator to create the OWB workspace. The main work is to create the OWB username and password, define the storage space of the table, and select the basic language to store the metadata of the data warehouse. Clustering essentially acts as a coarse-grained anomaly screening. From the perspective of further improving the accuracy, it is only necessary to sample the part of the outliers. When reading a transaction in a dataset, this kind of algorithm processes all itemsets contained in the transaction, so the algorithm calculates the support number of all itemsets in datasetD. For each transaction containing n items, 2n − 1 item sets will be generated. When the number of items contained in the dataset D is large, the number of candidate itemsets calculated and stored will be very large. When the number of itemsets is relatively small, a search algorithm can be used to mine association rules.(5)px,ti,j=x−titj,x−ti−1tj,x−titj−1,x−ti−1tj−1,∑x−ti−1/tj−11−i−j=1−i1−ti−1/tj−1.The algorithm only needs to scan the entire dataset twice, and the DIC algorithm can find all frequent itemsets by scanning the dataset twice when the data block is properly divided. The number of candidate itemsets of the dataset partitioning algorithm is generally larger than that of the apriori algorithm, and the dataset partitioning algorithm is the basis of various parallel association rule mining algorithms and distributed association rule mining algorithms.(6)1+i+jij1−i+j=i+j11i−j−1,∑g′qx−∑px=∑pxt−t2,∑qxgt−t2−1.The frequent itemsets inD are used as candidate itemsets, and then, the dataset D is scanned to determine the frequent itemsets. How to calculate the negative boundary to retrieve some missing frequent itemsets is the key to the sampling algorithm. The sampling algorithm is suitable for association rule mining in the environment where the mining efficiency is high, but the mining accuracy is not high.(7)11−n∑x−ti−1tj−1⊄∑x−ti−1tj−1,11−n∑x<ti−1x<∑x−tj−1.Because ROLAP uses relational tables to simulate multidimensional data, its access is more complicated than MOLAP. First, the user’s analysis request is converted into a SQL request by the ROLAP server and then handed over to the RDBMS for processing, and the processing result is returned to the user after multidimensional processing. When detailed data or other data are required, it is accessed through the MDDB. But MOLAP does not directly provide various OLAP functions on detailed data.(8)∑x+ti−1>i−1−x,1−tj−1∈xt.The attribute fields recorded in the database are abstracted according to the classification method, and the established hierarchical structure is called a conceptual random matrix. A method utilizing conceptual random matrix boosting can greatly condense the records in the database. The conceptual random matrix promotion of multiple attribute fields will result in a highly generalized knowledge base table, which is then converted into rules.Since the proportion of the original categories is too large, we need to discard a considerable amount of normal data, which may cause the loss of information of the normal samples in Figure4, resulting in insufficient recognition ability for normal samples. Therefore, in order to minimize the bias that information reduction brings to the classifier, we comprehensively use the data discarded by sampling twice to verify the decision random matrix. In particular, in addition to using out-of-bag validation errors for all base classifiers, the samples that were removed in the density-based sampling stage were also added to the validation set.Figure 4
Identification of data module attribute fields.


### 3.5. Medical Insurance Risk Clustering

We sort out the clustering results of each medical insurance risk sample point in all partitions; if it is marked as a core point at least once, it is a core point; otherwise, if it is marked as a boundary point at least once, it is a boundary point, and the rest are outliers. For the core point, we merge all the clusters associated with it into a new cluster and put all the sample points associated with it into the new cluster. The final global clustering result is achieved through the algorithm. Among them, the algorithm outputs all the cluster information to be merged, and the mapping information of local clusters and global clusters can be obtained through the union search algorithm: the medical insurance management center is the center of the information system, and it is connected to two medical institutions (including fixed-point clusters), forming a huge medical insurance computer management network system covering the overall planning area, realizing the storage, processing, statistics and query, sharing, exchange, etc. The development and improvement of insurance provide protection.It can be seen from the results in Figure5 that the random matrix algorithm is inferior to other algorithms in terms of accuracy and recall, especially from the AUC value, which is only slightly better than random guessing, because the random matrix algorithm is more sensitive to data, and there are more normal data, so that the classification hyperplane tends to divide the samples into normal data. The advantage of logistic regression is that its generalization ability is better, and its AUC value is second only to the random matrix, which means that it can also achieve better classification results for different classification thresholds. The characteristic of the decision random matrix is that its accuracy rate is high, reaching 0.865, but the AUC value is only 0.772, indicating that it may have overfitting. In general, random matrices have good performance in Figure 6 in all aspects. The fact table contains a large amount of data without redundancy and is composed of data values; the dimension table stores text and time data. When designing a multidimensional data model, the fact table represents the topic at the center and the model is built around the topic.Figure 5
Mapping information of local clusters of medical insurance risks.Figure 6
Clustering of medical insurance risk training set.It can be seen that as the number of random matrices increases, the AUC value is stable at around 10.88%, and the small fluctuation can be considered as negligible error. According to the definition of ROC curve and AUC value, an AUC value of 1 is a perfect result, but it is difficult to achieve in practice; if it is above 0.9, it indicates that it is an excellent classifier; if it is between 0.7 and 0.9, the result is better; 0.7 is less effective, and less than 0.5 means that the classifier is not as effective as random guessing and cannot be used at all. If the 10-fold cross-validation is not used but the training set is directly used as the test set, then for the random matrix algorithm, the precision and recall rates obtained by us are both 100%, which means that all data points are correctly classified, and the classifier information in the dataset is learned. Dimensionality reduction methods are usually divided into linear dimensionality reduction and nonlinear dimensionality reduction. Linear dimensionality reduction assumes that the high-dimensional data are located in a global linear structure so that the low-dimensional data after dimensionality reduction can maintain the linear relationship between data points.


## 3.1. Random Matrix Solution Set Distribution

We consider the intersection point P of the four matrices of the random matrix solution set. According to our division,P is included in all four subsets. In the clustering process of any subset, the r neighborhood of point P is actually a 1/4 circular area, so the local density of point P is miscalculated during the subset clustering process, which may lead to the original Ps that are core points are identified as outliers or boundary points. Therefore, for each matrix, when calculating its subset, an area with a width of r needs to be additionally expanded, as shown by the red solid line, so that the adjacent subsets have a coincident area with a width of 2r, ensuring that for any sample point, its neighborhood can be completely covered by at least one subset.(1)M′qx,px=M′qx,p1M′qx,p3M′qx,p2M′qx,pi,g′qx,px,x=1−gt−t2,1−logt−t2−1.Matrix correlation analysis is a simple and practical analysis technique, which is to find the correlation or correlation existing in a large number of datasets, thereby describing the laws and patterns of the simultaneous appearance of certain attributes in a thing. Associations are divided into simple associations, temporal associations, and causal associations. Generally, support, confidence, and lift are used to measure the relevance of association rules.(2)maxM′q1+M′q2+M′qi−M′qx=px−1,mint,t−1maxt,t−1=1/2x+5t/11−1/2x+6t/11.Matrix prediction is to obtain a prediction model by learning the correlation between the input value and the output value of the sample data (historical data), and the model predicts the output value of the future input value and uses the prediction variance to assess the accuracy of model predictions. Time-series patterns describe and model recurring regularities or trends based on time or other series. Like predictive analysis, it uses known data to predict future values.If there arek, then k samples are arbitrarily selected from the sample as the center (initial centroid) of the k categories. The distance between each sample and the center is divided into the nearest class. In this way, k clusters are obtained, the centers of k clusters are recalculated again, and the previous process is repeated until no samples are redivided and finally convergence is achieved.(3)∏qi−qi−11−in−iZi−1+,⋯,+1n−iZi=1−in−ii−n−⋯,−1,f=1−in−iZi−1−1+in−iZi+1,i,j=1,2,3,…,n.Matrix biases may contain potentially interesting knowledge such as outliers outside clusters, deviations of observations from expectations, anomalous instances in classification, and exceptions that do not satisfy rules. In enterprise crisis management and its early warning, managers are more interested in unexpected rules. The mining of unexpected rules can help to detect anomalies in time, and analyze and identify the reasons for the anomalies, so that preventive measures can be taken in time.(4)∑i,j=1,2,…,n1n−iZi−1n−iZj−1n−iZi−j−logzizj=1−i−j.It can select the appropriate data from the original data as the object data, and the extraction should follow the principles of relevance, reliability, real time, and integrity. At the same time, the extracted sample data are explored, reviewed, and processed to ensure the quality of prediction. Data exploration mainly includes the following: outlier analysis, correlation analysis, missing value analysis, sample cross-validation, etc. The essence of this division method is to mutually use orthogonal hyperplanes to cut the original space, and it is only necessary to ensure that adjacent subsets have 2r overlapping intervals in each dimension to be divided. But for high-dimensional data, if such a segmentation is made in each dimension, it will quickly encounter the curse of dimensionality. Clearly, there is an exponential relationship between the number of subdatasets and the dimensionality, and as the dimensionality gets higher and higher, the number of subdatasets in Figure 1 will quickly balloon to unacceptably astronomical numbers. Therefore, dimension selection is required before segmentation.Figure 1
Random matrix solution topology.Matrix application integration consists of a set of interfaces and management. One is to complete the organization of application functions, that is, to establish the binding relationship between frameworks, models, and logic for business processing, to form functional modules and to define the control and configuration information of the modules; the execution authority of the system role completes the corresponding relationship between the business role and the execution module. The database includes “fact tables,” which contain data items that users need to analyze when building the database, and there is a “dimension table” for each dimension. Each tuple in the “fact table” contains a foreign key to each “dimension table” and some corresponding measurement data. The “dimension table” records the attributes of this dimension. In addition to the data included in the fact table for analysis, there are one or more foreign keywords, which are the link between the fact table and the data dimension table. In each dimension table, in addition to the primary key of each dimension, there are also some other attribute fields that describe the dimension. The analytical process of executing a query in a data warehouse model takes a lot of time to find data in the relevant tables. The star model enables the complex query of the data warehouse to be completed directly through the hierarchical comparison, drill-up, drill-down, and other operations of each dimension.


## 3.2. Data Mining Residual Analysis

Because the data sampled by data mining residuals often contain many noisy, incomplete, or even inconsistent data, which may affect the mining results, it is necessary to preprocess the data objects to improve the data quality and make the subsequent mining results more accurate. Data preprocessing includes steps such as data integration, data selection, data cleaning, and data transformation. Each nonleaf node represents a test on a feature attribute; each branch represents the output of the feature attribute on a certain value range; and each random matrix leaf node stores a category. The decision random matrix algorithm constructs a high-precision, small-scale decision-making random matrix to discover the classification knowledge contained in the dataset in Table1.Table 1
Data mining residuals.
Data onto the coordinate axisOverfitting for a small number of samplesRandom matrix classification knowledge0.110.880.120.190.120.990.100.320.000.550.220.350.220.210.660.640.660.740.320.560.320.340.010.300.010.090.810.41In each dimension, we project the full amount of data onto the coordinate axis, then divide the coordinate axis intok intervals, and make the overlapping length of adjacent intervals 2r, and we count the number of sample points that fall into each interval and calculate the variance. Small variance means that the distribution of data in each interval is more balanced, which is the preferred object. According to the idea of random oversampling, some samples will overlap in the balanced dataset, and the more unbalanced the categories in the original dataset, the greater the overlap ratio. When the scale of the dataset is relatively large, especially the number of rows and columns are given. In the case of more than 3,000, we pointed out the most time-consuming steps in the PCA algorithm, and demonstrated the important role of three random matrices and greedy algorithms in reducing the matrix decomposition time in the PCA dimensionality reduction process.


## 3.3. Analysis of Random Matrix Indicators

In the random matrix index analysis and detection problem studied in this study, the abnormal data are precisely the minority class, so we need to balance the dataset before using the classification algorithm. There are two main types of processing for unbalanced datasets, mainly using oversampling and undersampling. After the data model of the data warehouse is defined, the data from different data sources will be loaded into the data warehouse, and then, the system will run the corresponding synthesis program according to the data model to synthesize the data and create indexes to optimize the access efficiency. The multidimensional analysis request of the end user is dynamically translated into SQL request by the ROLAP engine; then, the SQL request is processed by the relational database, and finally, the query result is returned to the user after multidimensional processing.Objects typically have highly compressed index and pointer structures. Each object in Figure2 consists of cells that are grouped into groups, and the cell blocks are accessed by computing offsets. In MDDB, data management is mainly based on dimension and dimension members. Most MDDB products also provide unit-level control, and data blocking can reach unit block level. These management and control tasks are implemented by the data management layer in the MDDB and are generally not easy to bypass. The ROLAP is based on the traditional relational database system; security and access control are based on tables; and blocking is based on tables and pages. Since these are not directly related to the multidimensional concept in the application, the ROLAP tool must manage the security and access control by itself. Therefore, it is possible to bypass the security mechanism of ROLAP and directly access the database through its existing route.Figure 2
Unit index analysis of random matrix clustering into groups.According to the law revealed by the experiment, the outlier set in Figure3 can be used as the abnormal cluster to exclude most of the normal data, which is equivalent to a coarse-grained screening. The algorithm results of DBSCAN are meaningful, so even clustering with unlabeled data is not affected. In this outlier set, it can be found that the proportion of normal data has been greatly reduced, and the proportion of categories can already be considered to belong to the normal category. Inspired by this, the outlier part obtained by the clustering algorithm can be sampled, and this sampling is based on the density.Figure 3
Random matrix outlier set index.


## 3.4. Data Module Identification

In this study, we use the Oracle Warehouse Builder (OWB) software to create the data warehouse, and conduct a systematic analysis and research on the construction process of each table. When creating a server through OWB, run the Repository Assistant program as an administrator to create the OWB workspace. The main work is to create the OWB username and password, define the storage space of the table, and select the basic language to store the metadata of the data warehouse. Clustering essentially acts as a coarse-grained anomaly screening. From the perspective of further improving the accuracy, it is only necessary to sample the part of the outliers. When reading a transaction in a dataset, this kind of algorithm processes all itemsets contained in the transaction, so the algorithm calculates the support number of all itemsets in datasetD. For each transaction containing n items, 2n − 1 item sets will be generated. When the number of items contained in the dataset D is large, the number of candidate itemsets calculated and stored will be very large. When the number of itemsets is relatively small, a search algorithm can be used to mine association rules.(5)px,ti,j=x−titj,x−ti−1tj,x−titj−1,x−ti−1tj−1,∑x−ti−1/tj−11−i−j=1−i1−ti−1/tj−1.The algorithm only needs to scan the entire dataset twice, and the DIC algorithm can find all frequent itemsets by scanning the dataset twice when the data block is properly divided. The number of candidate itemsets of the dataset partitioning algorithm is generally larger than that of the apriori algorithm, and the dataset partitioning algorithm is the basis of various parallel association rule mining algorithms and distributed association rule mining algorithms.(6)1+i+jij1−i+j=i+j11i−j−1,∑g′qx−∑px=∑pxt−t2,∑qxgt−t2−1.The frequent itemsets inD are used as candidate itemsets, and then, the dataset D is scanned to determine the frequent itemsets. How to calculate the negative boundary to retrieve some missing frequent itemsets is the key to the sampling algorithm. The sampling algorithm is suitable for association rule mining in the environment where the mining efficiency is high, but the mining accuracy is not high.(7)11−n∑x−ti−1tj−1⊄∑x−ti−1tj−1,11−n∑x<ti−1x<∑x−tj−1.Because ROLAP uses relational tables to simulate multidimensional data, its access is more complicated than MOLAP. First, the user’s analysis request is converted into a SQL request by the ROLAP server and then handed over to the RDBMS for processing, and the processing result is returned to the user after multidimensional processing. When detailed data or other data are required, it is accessed through the MDDB. But MOLAP does not directly provide various OLAP functions on detailed data.(8)∑x+ti−1>i−1−x,1−tj−1∈xt.The attribute fields recorded in the database are abstracted according to the classification method, and the established hierarchical structure is called a conceptual random matrix. A method utilizing conceptual random matrix boosting can greatly condense the records in the database. The conceptual random matrix promotion of multiple attribute fields will result in a highly generalized knowledge base table, which is then converted into rules.Since the proportion of the original categories is too large, we need to discard a considerable amount of normal data, which may cause the loss of information of the normal samples in Figure4, resulting in insufficient recognition ability for normal samples. Therefore, in order to minimize the bias that information reduction brings to the classifier, we comprehensively use the data discarded by sampling twice to verify the decision random matrix. In particular, in addition to using out-of-bag validation errors for all base classifiers, the samples that were removed in the density-based sampling stage were also added to the validation set.Figure 4
Identification of data module attribute fields.


## 3.5. Medical Insurance Risk Clustering

We sort out the clustering results of each medical insurance risk sample point in all partitions; if it is marked as a core point at least once, it is a core point; otherwise, if it is marked as a boundary point at least once, it is a boundary point, and the rest are outliers. For the core point, we merge all the clusters associated with it into a new cluster and put all the sample points associated with it into the new cluster. The final global clustering result is achieved through the algorithm. Among them, the algorithm outputs all the cluster information to be merged, and the mapping information of local clusters and global clusters can be obtained through the union search algorithm: the medical insurance management center is the center of the information system, and it is connected to two medical institutions (including fixed-point clusters), forming a huge medical insurance computer management network system covering the overall planning area, realizing the storage, processing, statistics and query, sharing, exchange, etc. The development and improvement of insurance provide protection.It can be seen from the results in Figure5 that the random matrix algorithm is inferior to other algorithms in terms of accuracy and recall, especially from the AUC value, which is only slightly better than random guessing, because the random matrix algorithm is more sensitive to data, and there are more normal data, so that the classification hyperplane tends to divide the samples into normal data. The advantage of logistic regression is that its generalization ability is better, and its AUC value is second only to the random matrix, which means that it can also achieve better classification results for different classification thresholds. The characteristic of the decision random matrix is that its accuracy rate is high, reaching 0.865, but the AUC value is only 0.772, indicating that it may have overfitting. In general, random matrices have good performance in Figure 6 in all aspects. The fact table contains a large amount of data without redundancy and is composed of data values; the dimension table stores text and time data. When designing a multidimensional data model, the fact table represents the topic at the center and the model is built around the topic.Figure 5
Mapping information of local clusters of medical insurance risks.Figure 6
Clustering of medical insurance risk training set.It can be seen that as the number of random matrices increases, the AUC value is stable at around 10.88%, and the small fluctuation can be considered as negligible error. According to the definition of ROC curve and AUC value, an AUC value of 1 is a perfect result, but it is difficult to achieve in practice; if it is above 0.9, it indicates that it is an excellent classifier; if it is between 0.7 and 0.9, the result is better; 0.7 is less effective, and less than 0.5 means that the classifier is not as effective as random guessing and cannot be used at all. If the 10-fold cross-validation is not used but the training set is directly used as the test set, then for the random matrix algorithm, the precision and recall rates obtained by us are both 100%, which means that all data points are correctly classified, and the classifier information in the dataset is learned. Dimensionality reduction methods are usually divided into linear dimensionality reduction and nonlinear dimensionality reduction. Linear dimensionality reduction assumes that the high-dimensional data are located in a global linear structure so that the low-dimensional data after dimensionality reduction can maintain the linear relationship between data points.


## 4. Application and Analysis of Social Medical Insurance Risk Analysis Model Based on Random Matrix Theory and Data Mining

### 4.1. Random Matrix and Data Mining Feature Extraction

The random matrix data analysis unit is used to define transaction rules for mining results and evaluate behaviors that do not meet the thresholds of transaction rules according to the requirements of the mining project definition, and to provide analysis, query, and statistical interfaces for the end business users of the detection results. The logical structure of this unit includes the following: result presentation and data analysis module. The result display module is used to define the display mode of mining results and the visualization of the display of mining results; the data analysis module is used to define the mining results through the inference engine according to the defined rules selected in the rule management unit configured by the mining project.In the random matrix model based on density sampling, the training data are sampled from the outliers in the DBSCAN clustering results, so we use the other parts of the dataset except for the outliers as the test set. According to the clustering results, the test set consists of normal data, and the test set and training set do not overlap each other. After experiments, 99.9% of the data in the test set in Figure7 are correctly classified by the model, which shows that the analysis and detection process has strong generalization ability.Figure 7
Rule threshold feature extraction for data mining.A random matrix moves a row dimension into a column dimension or swaps a dimension on the page display with an off-page dimension (making it a new row or column). The architecture consists of application integration tools and a set of interface management tools. One is to complete the organization of application functions, that is, to establish the relationship between the framework and the model for business processing; the other is to assign the user’s execution authority to complete the correspondence between business roles and execution behaviors. The integration principle is to use the driver framework as the execution layer of the application, and define the model and logic that the framework should be bound to by invoking the framework assembled by the supporting platform, thereby completing the integration of business processing functions. Because the framework, model, and logic are isolated at different levels, the application system is assembled, which makes the dynamic evolution of the application system possible.


### 4.2. Social Medical Insurance Risk Simulation

To create a medical insurance decision support system, we first need to establish and build a medical insurance data warehouse. The data warehouse is a data environment that faces data analysis processing. When designing a data warehouse system, it cannot be designed according to the original traditional database system development method. The medical insurance data warehouse developed in this project is based on SQL Server 7. Since this study mainly studies the two topics of medical insurance fund payment and individual account expenditure for single-disease expenses, the target attributes cannot be determined in advance. Therefore, in the research process of this study, we use the clustering algorithmK provided in Oracle Data Miner for data mining research and result analysis. It has the advantages of high classification accuracy, strong parallel distribution processing ability, and can effectively solve problems with large and complex data. The disadvantage is that a large number of parameters are required, and the output results are difficult to interpret, which affects the reliability and acceptability of the results and is not suitable for real-time analysis. The data changed in the text is synchronized to the target database in real time.The system in Figure8 supports comprehensive, real-time, and automatic auditing of medical insurance settlement information, effectively supervises and controls behaviors involving medical insurance fund expenditures, and returns the audit results to the medical insurance management information system in a timely manner. As a result, presettlement information is generated, and the payment of medical insurance funds is refused for drugs that involve illegal purchases, thus ensuring the safety of medical insurance funds and work efficiency. When performing data analysis, we mostly analyze the comprehensive-level data so that the analysis speed is faster: when the comprehensive-level data in Figure 9 cannot meet the requirements, it is necessary to analyze the detail-level data for analysis.Figure 8
Risk structure of social medical insurance.Figure 9
Training on social medical insurance risk dataset.In the MapReduce programming model of the random matrix, the complete original data are divided into different data blocks and sent to different Mappers, and the data on each Mapper are different from other Mappers. For sampling, there are different sampling strategies at this time. One method is to use bagging to train multiple decision random matrices directly on each Mapper and then combine the decision random matrices of all Mappers to form a random matrix. Our algorithm is generally faster than standard PCA. However, since the overall algorithm of PCA is a linear algorithm, and our S-curve is a nonlinear surface, the effect of dimensionality reduction is too small. It can be seen that there are black points and yellow points in the upper right corner of the graphs. The fusion of it, the so-called “head-to-foot” phenomenon, distorts the actual structure of the manifold.


### 4.3. Example Application and Analysis

The database server of this system adopts an IBM P650 series server, the CPU is dual-core 3.0, the memory is 2 G, the hard disk is 200 G, and the RAID5 disk array data backup is configured. The main switch of this network system design is Cisco 0375C24T-E Layer 3 switches, the floor switches are Cisco 2950 switches. At the same time, the firewall of NetScreen-204 is designed to ensure the security of the system. The system is divided into four layers: data acquisition layer, data preprocessing layer, data mining engine layer, and service and management layer. The data acquisition layer mainly solves the data source of the system and is an important basic layer of the system. This layer extracts the data in the medical insurance business database, including the insured person information, historical medical treatment and medication information, drug catalog information, and designated medical institution information. The data preprocessing layer in Table2 is to perform necessary processing on the extracted data, including data selection, data cleaning, data conversion, data loading, and other links to improve the quality of the data and make the results of data analysis and mining more accurate.Table 2
Data mining transformation algorithm.
Data mining textTransformation algorithm codex−ti−1/tj−1Double getlen (int dim){Management include1+i+jInt train labels[ntrain];tj−1 disk array dataInt train count [10] = {0};Backup is configured1−iDigit∗Dtrain = (Digit∗)malloc();Monitoring managementZi−1Fp = fopen(training file, “r”);Data acquisition layerx−tPrintf (“…load training digits.\n”);logzi/zjFor(i = 0; i < n train; i++)n−i of the systemDistance tmp = (Distance)in[index 1];The system andzi/zjIn[index 1] = in[index 2];It is an important basic layerIn[index 2] = tmp;Data source of{Int num 1, int num 2Mainly solves theZiInti, j, min;On the other hand, it uses data mining technology to build a system monitoring model based on an objective, fair, and relatively scientific clinical knowledge base of medicine combined with the current medical insurance policy regulations, so as to support the automatic review of medical insurance medical bills and realize strong regulation of health insurance funds.Since random matrix logics are different in different fields, they are encapsulated in the way of components, so that they have the same interface and different implementations. In this way, as can be seen from Figure10, in the realization of different business functions, which component to call can be determined according to the business type, and the called interface method will remain unchanged. Due to the extreme imbalance of the original dataset, the classification results are obviously biased toward the normal category, the accuracy rate for anomalies is only 74.0%, and the recall rate is only 55.8%, which cannot achieve the effect of analysis and detection. After using the sampling technology to balance the dataset, the algorithm effect increased and the accuracy rate reached 84.3%, but the abnormal recognition ability was still insufficient, and the recall rate was not as good as the analysis and detection method proposed in this study. The above experiments have verified the importance of the clustering algorithm in screening data in analysis and detection. Compared with traditional oversampling and undersampling, density-based sampling utilizes the local density information of data and is more purposeful in sampling. Although the classifier trained on the sampled data cannot achieve perfect results, it has been able to greatly reduce the scope of review and effectively reduce the review pressure.Figure 10
Encapsulation of local density information of random matrix.


## 4.1. Random Matrix and Data Mining Feature Extraction

The random matrix data analysis unit is used to define transaction rules for mining results and evaluate behaviors that do not meet the thresholds of transaction rules according to the requirements of the mining project definition, and to provide analysis, query, and statistical interfaces for the end business users of the detection results. The logical structure of this unit includes the following: result presentation and data analysis module. The result display module is used to define the display mode of mining results and the visualization of the display of mining results; the data analysis module is used to define the mining results through the inference engine according to the defined rules selected in the rule management unit configured by the mining project.In the random matrix model based on density sampling, the training data are sampled from the outliers in the DBSCAN clustering results, so we use the other parts of the dataset except for the outliers as the test set. According to the clustering results, the test set consists of normal data, and the test set and training set do not overlap each other. After experiments, 99.9% of the data in the test set in Figure7 are correctly classified by the model, which shows that the analysis and detection process has strong generalization ability.Figure 7
Rule threshold feature extraction for data mining.A random matrix moves a row dimension into a column dimension or swaps a dimension on the page display with an off-page dimension (making it a new row or column). The architecture consists of application integration tools and a set of interface management tools. One is to complete the organization of application functions, that is, to establish the relationship between the framework and the model for business processing; the other is to assign the user’s execution authority to complete the correspondence between business roles and execution behaviors. The integration principle is to use the driver framework as the execution layer of the application, and define the model and logic that the framework should be bound to by invoking the framework assembled by the supporting platform, thereby completing the integration of business processing functions. Because the framework, model, and logic are isolated at different levels, the application system is assembled, which makes the dynamic evolution of the application system possible.


## 4.2. Social Medical Insurance Risk Simulation

To create a medical insurance decision support system, we first need to establish and build a medical insurance data warehouse. The data warehouse is a data environment that faces data analysis processing. When designing a data warehouse system, it cannot be designed according to the original traditional database system development method. The medical insurance data warehouse developed in this project is based on SQL Server 7. Since this study mainly studies the two topics of medical insurance fund payment and individual account expenditure for single-disease expenses, the target attributes cannot be determined in advance. Therefore, in the research process of this study, we use the clustering algorithmK provided in Oracle Data Miner for data mining research and result analysis. It has the advantages of high classification accuracy, strong parallel distribution processing ability, and can effectively solve problems with large and complex data. The disadvantage is that a large number of parameters are required, and the output results are difficult to interpret, which affects the reliability and acceptability of the results and is not suitable for real-time analysis. The data changed in the text is synchronized to the target database in real time.The system in Figure8 supports comprehensive, real-time, and automatic auditing of medical insurance settlement information, effectively supervises and controls behaviors involving medical insurance fund expenditures, and returns the audit results to the medical insurance management information system in a timely manner. As a result, presettlement information is generated, and the payment of medical insurance funds is refused for drugs that involve illegal purchases, thus ensuring the safety of medical insurance funds and work efficiency. When performing data analysis, we mostly analyze the comprehensive-level data so that the analysis speed is faster: when the comprehensive-level data in Figure 9 cannot meet the requirements, it is necessary to analyze the detail-level data for analysis.Figure 8
Risk structure of social medical insurance.Figure 9
Training on social medical insurance risk dataset.In the MapReduce programming model of the random matrix, the complete original data are divided into different data blocks and sent to different Mappers, and the data on each Mapper are different from other Mappers. For sampling, there are different sampling strategies at this time. One method is to use bagging to train multiple decision random matrices directly on each Mapper and then combine the decision random matrices of all Mappers to form a random matrix. Our algorithm is generally faster than standard PCA. However, since the overall algorithm of PCA is a linear algorithm, and our S-curve is a nonlinear surface, the effect of dimensionality reduction is too small. It can be seen that there are black points and yellow points in the upper right corner of the graphs. The fusion of it, the so-called “head-to-foot” phenomenon, distorts the actual structure of the manifold.


## 4.3. Example Application and Analysis

The database server of this system adopts an IBM P650 series server, the CPU is dual-core 3.0, the memory is 2 G, the hard disk is 200 G, and the RAID5 disk array data backup is configured. The main switch of this network system design is Cisco 0375C24T-E Layer 3 switches, the floor switches are Cisco 2950 switches. At the same time, the firewall of NetScreen-204 is designed to ensure the security of the system. The system is divided into four layers: data acquisition layer, data preprocessing layer, data mining engine layer, and service and management layer. The data acquisition layer mainly solves the data source of the system and is an important basic layer of the system. This layer extracts the data in the medical insurance business database, including the insured person information, historical medical treatment and medication information, drug catalog information, and designated medical institution information. The data preprocessing layer in Table2 is to perform necessary processing on the extracted data, including data selection, data cleaning, data conversion, data loading, and other links to improve the quality of the data and make the results of data analysis and mining more accurate.Table 2
Data mining transformation algorithm.
Data mining textTransformation algorithm codex−ti−1/tj−1Double getlen (int dim){Management include1+i+jInt train labels[ntrain];tj−1 disk array dataInt train count [10] = {0};Backup is configured1−iDigit∗Dtrain = (Digit∗)malloc();Monitoring managementZi−1Fp = fopen(training file, “r”);Data acquisition layerx−tPrintf (“…load training digits.\n”);logzi/zjFor(i = 0; i < n train; i++)n−i of the systemDistance tmp = (Distance)in[index 1];The system andzi/zjIn[index 1] = in[index 2];It is an important basic layerIn[index 2] = tmp;Data source of{Int num 1, int num 2Mainly solves theZiInti, j, min;On the other hand, it uses data mining technology to build a system monitoring model based on an objective, fair, and relatively scientific clinical knowledge base of medicine combined with the current medical insurance policy regulations, so as to support the automatic review of medical insurance medical bills and realize strong regulation of health insurance funds.Since random matrix logics are different in different fields, they are encapsulated in the way of components, so that they have the same interface and different implementations. In this way, as can be seen from Figure10, in the realization of different business functions, which component to call can be determined according to the business type, and the called interface method will remain unchanged. Due to the extreme imbalance of the original dataset, the classification results are obviously biased toward the normal category, the accuracy rate for anomalies is only 74.0%, and the recall rate is only 55.8%, which cannot achieve the effect of analysis and detection. After using the sampling technology to balance the dataset, the algorithm effect increased and the accuracy rate reached 84.3%, but the abnormal recognition ability was still insufficient, and the recall rate was not as good as the analysis and detection method proposed in this study. The above experiments have verified the importance of the clustering algorithm in screening data in analysis and detection. Compared with traditional oversampling and undersampling, density-based sampling utilizes the local density information of data and is more purposeful in sampling. Although the classifier trained on the sampled data cannot achieve perfect results, it has been able to greatly reduce the scope of review and effectively reduce the review pressure.Figure 10
Encapsulation of local density information of random matrix.


## 5. Conclusions

This study sorts out the relevant theories and important algorithms of data mining technology, analyzes and studies the application of data mining technology in the field of medical insurance risk analysis, and proposes to introduce random matrix theory and data mining technology into the intelligent medical insurance audit system. Using data mining technology to process medical insurance data, extract valuable data, and apply it to medical insurance supervision, so as to achieve full coverage, real-time, and automatic inspection of medical insurance information and provide reliable services for medical insurance. On the basis of analyzing the applicability of data mining technology in medical insurance inspection system, an intelligent medical insurance inspection system architecture based on random matrix theory and association rules is proposed, including data acquisition layer, data preprocessing layer, and data mining engine layer. Then, the support base of the intelligent medical insurance audit system is designed, namely, knowledge base, rule base, and model base, and the association rule algorithm and attribute reduction algorithm are used to analyze the historical prescription information of the insured to discover common drug patterns for different diseases. The rule base covers payment policy review rules, diagnosis and treatment rationality review rules, clinical normative review rules, and abnormal medical behavior monitoring rules.



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*Source: 6429510-2022-07-18.xml*