A Unified Subspace Outlier Ensemble Framework for Outlier Detection in High Dimensional Spaces

Abstract

The task of outlier detection is to find small groups of data objects that are exceptional when compared with rest large amount of data. Detection of such outliers is important for many applications such as fraud detection and customer migration. Most such applications are high dimensional domains in which the data may contain hundreds of dimensions. However, the outlier detection problem itself is not well defined and none of the existing definitions are widely accepted, especially in high dimensional space. In this paper, our first contribution is to propose a unified framework for outlier detection in high dimensional spaces from an ensemble-learning viewpoint. In our new framework, the outlying-ness of each data object is measured by fusing outlier factors in different subspaces using a combination function. Accordingly, we show that all existing researches on outlier detection can be regarded as special cases in the unified framework with respect to the set of subspaces considered and the type of combination function used. In addition, to demonstrate the usefulness of the ensemble-learning based outlier detection framework, we developed a very simple and fast algorithm, namely SOE1 (Subspace Outlier Ensemble using 1-dimensional Subspaces) in which only subspaces with one dimension is used for mining outliers from large categorical datasets. The SOE1 algorithm needs only two scans over the dataset and hence is very appealing in real data mining applications. Experimental results on real datasets and large synthetic datasets show that: (1) SOE1 has comparable performance with respect to those state-of-art outlier detection algorithms on identifying true outliers and (2) SOE1 can be an order of magnitude faster than one of the fastest outlier detection algorithms known so far.