Localized angle-based unsupervised outlier detection

The angle-based outlier detection (ABOD) is proposed to tackle the “curse of dimensionality” that exists in distance-related or density-related outlier detectors. However, ABOD may fail on multimodal datasets since it only considers global information. Furthermore, ABOD needs to calculate the angles between difference vectors from an instance to each pair of instances in the dataset except itself. Its time complexity reaches O (n3). In order to address these two issues, this paper proposes localized angle-based outlier detection (LABOD) which first finds the influence set, and then calculates the variance of angles between the difference vector from an instance to the mean of its neighbors in the influence set and the difference vectors from the instance to its neighbors in the influence set. The influence set consists of the nearest neighbor set and the reverse nearest neighbor set. Because the variance is defined by the angles in a local region, the proposed method can overcome the drawbacks of ABOD. The experiments performed on both synthetic and benchmark datasets demonstrate that LABOD is superior to ABOD.