Anomaly Detection In Incomplete Real-valued Information Systems Based On Granular Computing

Anomaly detection,also known as outlier detection,is an operation that can identify objects with different behaviors.It can be applied to many aspects such as public security,finance,medical treatment,and has a wide range of application scenarios and important theoretical research significance.In today’s data life,due to the instability of wireless data transmission,as well as the failure of data collection equipment,it is inevitable that an incomplete real-valued information system(IRVIS)with partial information value loss will occur.In order to address this issue,this article does not need to fill in missing data,but instead directly performs anomaly detection in the IRVIS,improving the richness of application scenarios for anomaly detection,which is of great significance in real life.Therefore,this paper proposes two anomaly detection algorithms in IRVIS.The first anomaly detection algorithm is the inner boundary＿degree of exception algorithm,abbreviated as IB＿DE anomaly detection algorithm.It regards the size of the inner boundary set as the size of the information granule g.Firstly,a distance degree formula suitable for calculating the distance between two information values on each attribute in IRVIS is introduced,and the parameter λ to control the distance is given.Then,according to the distance degree,the tolerance relations on the object set are defined,and the the tolerance classes,the λ-lower and λ-upper approximations in IRVIS are obtained.Next,the inner boundary under each conditional attribute in an IRVIS is presented.The more inner boundaries an object belongs to,the more likely it is to be an outlier.Next,an IB＿DE anomaly detection algorithm based inner boundary in IRVIS is proposed,which calculates the degree of exception of each object in IRVIS.Finally,through experiments on different datasets in the UCI machine learning repository,the IB＿DE anomaly detection algorithm is compared with different anomaly detection algorithms.The experimental results show that IB＿DE anomaly detection algorithm has good anomaly detection effect in IRVIS.It is worth mentioning that in the performance evaluation analysis of different anomaly detection algorithms,this article uses ROC curves and AUC ranking averages to further illustrate advantages of IB＿DE anomaly detection algorithm.The second anomaly detection algorithm is the outlier factor anomaly detection algorithm,which is abbreviated as the OF anomaly detection algorithm.First of all,the same method introduces the distance degree formula suitable for calculating the distance between two information values on each attribute in an IRVIS,and gives the parameters λ to control the distance.Then,the tolerance relationship on the object set is defined according to the distance degree,and the tolerance class of each object is obtained,which is regarded as each information granule g.Then,the approximate accuracy and uncertainty of each information granule g are obtained by the λ-lower and λ-upper approximations in an IRVIS.Next,the calculation formula of outlier factor for each object in IRVIS is given according to the uncertainty of different information granule g.Next,an OF anomaly detection algorithm in IRVIS based on outlier factor is proposed.This algorithm calculates the outlier factor for each object in IRVIS separately.The larger the outlier factor,the more likely the object is to be an outlier.Finally,through experiments on different datasets in the UCI machine learning repository,the OF anomaly detection algorithm is compared with different anomaly detection algorithms to verify the superiority of the OF anomaly detection algorithm used in IRVIS.