Learning to Locate Relative Outliers

Outliers usually spread across regions of low density. However, due to the absence or scarcity of outliers, designing a robust detector to sift outliers from a given dataset is still very challenging. In this paper, we consider to identify relative outliers from the target dataset with respect to another reference dataset of normal data. Particularly, we employ Maximum Mean Discrepancy (MMD) for matching the distribution between these two datasets and present a novel learning framework to learn a relative outlier detector. The learning task is formulated as a Mixed Integer Programming (MIP) problem, which is computationally hard. To this end, we propose an effective procedure to find a largely violated labeling vector for identifying relative outliers from abundant normal patterns, and its convergence is also presented. Then, a set of largely violated labeling vectors are combined by multiple kernel learning methods to robustly locate relative outliers. Comprehensive empirical studies on real-world datasets verify that our proposed relative outlier detection outperforms existing methods.