Local Outlier Detection with Interpretation

Outlier detection aims at searching for a small set of objects that are inconsistent or considerably deviating from other objects in a dataset. Existing research focuses on outlier identification while omitting the equally important problem of outlier interpretation. This paper presents a novel method named LODI to address both problems at the same time. In LODI, we develop an approach that explores the quadratic entropy to adaptively select a set of neighboring instances, and a learning method to seek an optimal subspace in which an outlier is maximally separated from its neighbors. We show that this learning task can be optimally solved via the matrix eigen-decomposition and its solution contains all essential information to reveal which features in the original data space are the most important to interpret the exceptional properties of outliers. We demonstrate the appealing performance of LODI via a number of synthetic and real world datasets and compare its outlier detection rates against state-of-the-art algorithms.