Outlier detection for set-valued data based on rough set theory and granular computing

Outlier detection has been broadly used in industrial practices such as public security and fraud detection, etc. Outlier detection from various perspectives against different backgrounds has been proposed. However, most of outlier detection consider categorical or numerical data. There are few researches on outlier detection for set-valued data, and a set-valued information system (SVIS) is a proper way of tackling the problem of missing values in data sets. This paper investigates outlier detection for set-valued data based on rough set theory (RST) and granular computing (GrC). First, the similarity between two information values in an SVIS is introduced and a variable parameter to control the similarity is given. Then, the tolerance relations on the object set are defined, and based on this tolerance relation, theta-lower and theta-upper approximations in an SVIS are put forward. Next, the outlier factor in an SVIS is presented and applied to various data sets. Finally, outlier detection method for set-valued data based on RST and GrC is proposed, and the corresponding algorithms are designed. Through numerical experiments based on UCI, the designed algorithm is compared with six other detection algorithms. The experimental results show the designed algorithm is arguably the best choice under the context of an SVIS. It is worth mentioning that for a comprehensive comparison, we use two criteria: AUC value and F-1 measure, to show the superiority of the designed algorithm.