Detecting outliers from pairwise proximities: Proximity isolation forests

Because outliers are very different from the rest of the data, it is natural to represent outliers by their distances to other objects. Furthermore, there are many scenarios in which only pairwise distances are known, and feature-based outlier detection methods cannot directly be applied. Considering these ob- servations, and given the success of Isolation Forests for (feature-based) outlier detection, we propose Proximity Isolation Forest, a proximity-based extension. The methodology only requires a set of pairwise distances to work, making it suitable for different types of data. Analogously to Isolation Forest, outliers are detected via their early isolation in the trees; to encode the isolation we design nine training strate- gies, both random and optimized. We thoroughly evaluate the proposed approach on fifteen datasets, successfully assessing its robustness and suitability for the task; additionally we compare favourably to alternative proximity-based methods.