Outlier detection for incomplete real-valued data via rough set theory and granular computing

Outlier detection is an important topic in data mining. An information system (IS) is a database that shows relationships between objects and attributes. A real-valued information system (RVIS) is an IS whose information values are real numbers. People often encounter missing values during data processing. A RVIS with the miss values is an incomplete real-valued information system (IRVIS). Due to the presence of the missing values, the distance between two information values is difficult to determine, so the existing outlier detection rarely considered an IS with the miss values. This paper investigates outlier detection for an IRVIS via rough set theory and granular computing. Firstly, the distance between two information values on each attribute of an IRVIS is introduced, and the parameter lambda to control the distance is given. Then, the tolerance relation on the object set is defined according to the distance, and the tolerance class is obtained, which is regarded as an information granule. After then, lambda-lower and lambda-upper approximations in an IRVIS are put forward. Next, the outlier factor of every object in an IRVIS is presented. Finally, outlier detection method for IRVIS via rough set theory and granular computing is proposed, and the corresponding algorithms is designed. Through the experiments, the proposed method is compared with other methods. The experimental results show that the designed algorithm is more effective than some existing algorithms in an IRVIS. It is worth mentioning that for comprehensive comparison, ROC curve and AUC value are used to illustrate the advantages of the proposed method.