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Identifying anomalies in multi-dimensional datasets is an important task inmany real-world applications. A special case arises when anomalies are occludedin a small set of attributes, typically referred to as a subspace, and notnecessarily over the entire data space. In this paper, we propose a newsubspace analysis approach named Agglomerative Attribute Grouping (AAG) thataims to address this challenge by searching for subspaces that are comprised ofhighly correlative attributes. Such correlations among attributes represent asystematic interaction among the attributes that can better reflect thebehavior of normal observations and hence can be used to improve theidentification of two particularly interesting types of abnormal data samples:anomalies that are occluded in relatively small subsets of the attributes andanomalies that represent a new data class. AAG relies on a novelmulti-attribute measure, which is derived from information theory measures ofpartitions, for evaluating the "information distance" between groups of dataattributes. To determine the set of subspaces to use, AAG applies a variationof the well-known agglomerative clustering algorithm with the proposedmulti-attribute measure as the underlying distance function. Finally, the setof subspaces is used in an ensemble for anomaly detection. Extensive evaluationdemonstrates that, in the vast majority of cases, the proposed AAG method (i)outperforms classical and state-of-the-art subspace analysis methods when usedin anomaly detection ensembles, and (ii) generates fewer subspaces with a fewernumber of attributes each (on average), thus resulting in a faster trainingtime for the anomaly detection ensemble. Furthermore, in contrast to existingmethods, the proposed AAG method does not require any tuning of parameters.

A Non-Parametric Subspace Analysis Approach with Application to Anomaly Detection Ensembles