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.

该文章引入了一种简单框架，用于在超休克 2 空间中检测局部异常值，称为 HLoOP (Hyperbolic Local Outlier Probability)。通过在超休克空间中计算数据点到其最近邻的 Riemmanian 距离，并利用高斯概率密度函数将其与局部异常因子相结合，该方法在 WordNet 数据集上取得了令人期待的结果。