A rough set approach to outlier detection

This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, redistribution , reselling , loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden. The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss, actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material. " One person's noise is another person's signal " (Knorr and Ng 1998). In recent years, much attention has been given to the problem of outlier detection, whose aim is to detect outliers— objects who behave in an unexpected way or have abnormal properties. Detecting such outliers is important for many applications such as criminal activities in electronic commerce, computer intrusion attacks, terrorist threats, agricultural pest infestations. In this paper, we suggest to exploit the framework of rough sets for detecting outliers. We propose a novel definition of outliers—RMF (rough membership function)-based outliers, by virtue of the notion of rough membership function in rough set theory. An algorithm to find such outliers is also given. And the effectiveness of RMF-based method is demonstrated on two publicly available data sets. 1. Introduction Knowledge discovery in databases (KDD), or data mining, is an important issue in the development of data-and knowledge-base systems. Usually, knowledge discovery tasks can be classified into four general categories: (a) dependency detection, (b) class identification, (c) class description, and (d) outlier/exception detection (Knorr and Ng 1998). In contrast to most KDD tasks, such as clustering and classification, outlier detection aims to find small groups of data objects that are exceptional when compared with the rest large amount of data, in terms of certain sets of properties. For many applications, such as fraud detection in E-commerce, it is more interesting to find the rare events than to find the common ones. Studying the extraordinary behaviours of outliers can help us uncover the valuable information hidden behind them. Recently researchers have begun focusing on outlier detection and attempted to design algorithms for tasks such as fraud detection (Bolton and Hand 2002), identification of computer network …