  Hyperbolic geometry has recently garnered considerable attention in machine
learning due to its capacity 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
referred to as HLoOP (Hyperbolic Local Outlier Probability). 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 developed HLoOP combines the idea of finding nearest neighbors,
density-based outlier scoring with a probabilistic, statistically oriented
approach. Therefore, the method consists in computing 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 HLoOP algorithm is tested
on the WordNet dataset yielding promising results. Code and data will be made
available on request for reproductibility.
