Reverse Nearest Neighbors in Unsupervised Distance-Based Outlier Detection

Outlier detection in high-dimensional data presents various challenges resulting from the curse of dimensionality. A prevailing view is that distance concentration, i.e., the tendency of distances in high-dimensional data to become indiscernible, hinders the detection of outliers by making distance-based methods label all points as almost equally good outliers. In this paper, we provide evidence supporting the opinion that such a view is too simple, by demonstrating that distance-based methods can produce more contrasting outlier scores in high-dimensional settings. Furthermore, we show that high dimensionality can have a different impact, by reexamining the notion of reverse nearest neighbors in the unsupervised outlier-detection context. Namely, it was recently observed that the distribution of points' reverse-neighbor counts becomes skewed in high dimensions, resulting in the phenomenon known as hubness. We provide insight into how some points (antihubs) appear very infrequently in k-NN lists of other points, and explain the connection between antihubs, outliers, and existing unsupervised outlier-detection methods. By evaluating the classic k-NN method, the angle-based technique designed for high-dimensional data, the density-based local outlier factor and influenced outlierness methods, and antihub-based methods on various synthetic and real-world data sets, we offer novel insight into the usefulness of reverse neighbor counts in unsupervised outlier detection.