HLoOP—Hyperbolic 2-Space Local Outlier Probabilities

Abstract

Hyperbolic geometry has recently garnered considerable attention in machine learning due to its ability to embed hierarchical graph structures with low distortions for further downstream processing. This paper introduces a simple framework to detect local outliers for datasets grounded in hyperbolic 2-space, which is referred to as Hyperbolic Local Outlier Probability (HLoOP). Within a Euclidean space, well-known techniques for local outlier detection are based on the Local Outlier Factor (LOF) and its variant, the LoOP (Local Outlier Probability), which incorporates probabilistic concepts to model the outlier level of a data vector. The proposed HLoOP combines the notion of finding nearest neighbors, density-based outlier scoring with a probabilistic, statistically oriented approach. Therefore, the method computes the Riemmanian distance of a data point to its nearest neighbors following a Gaussian probability density function expressed in a hyperbolic space. This is achieved by defining a Gaussian cumulative distribution in this space. The proposed HLoOP algorithm is tested on the WordNet dataset and desmonstrated promising results. The code and data will be made available upon request for reproducibility.

Keywords

• Outlier detection
• hyperbolic embedding
• LoOP
• HLoOP