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。

HLoOP -- 双曲空间局部异常概率

HLoOP -- Hyperbolic 2-space Local Outlier Probabilities

Knowledge base completion (KBC) aims to predict missing information in a
knowledge base.In this paper, we address the out-of-knowledge-base (OOKB)
entity problem in KBC:how to answer queries concerning test entities not
observed at training time. Existing embedding-based KBC models assume that all
test entities are available at training time, making it unclear how to obtain
embeddings for new entities without costly retraining. To solve the OOKB entity
problem without retraining, we use graph neural networks (Graph-NNs) to compute
the embeddings of OOKB entities, exploiting the limited auxiliary knowledge
provided at test time.The experimental results show the effectiveness of our
proposed model in the OOKB setting.Additionally, in the standard KBC setting in
which OOKB entities are not involved, our model achieves state-of-the-art
performance on the WordNet dataset. The code and dataset are available at
this https URL

本文介绍了一种利用图神经网络计算 OOBK 实体嵌入的知识库完整性完成（KBC）模型，并在 WordNet 数据集上实现了最先进的性能。