## Learning to Locate Relative Outliers

S. Li & I.W. Tsang; JMLR W&CP 20:47–62,
2011.

### Abstract

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.

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