Recent years, Knowledge Graph Embeddings (KGEs) have shown promising
performance on link prediction tasks by mapping the entities and relations from
a Knowledge Graph (KG) into a geometric space and thus have gained increasing
attentions. In addition, many recent Knowledge Graphs involve evolving data,
e.g., the fact (\textit{Obama}, \textit{PresidentOf}, \textit{USA}) is valid
only from 2009 to 2017. This introduces important challenges for knowledge
representation learning since such temporal KGs change over time. In this work,
we strive to move beyond the complex or hypercomplex space for KGE and propose
a novel geometric algebra based embedding approach, GeomE, which uses
multivector representations and the geometric product to model entities and
relations. GeomE subsumes several state-of-the-art KGE models and is able to
model diverse relations patterns. On top of this, we extend GeomE to TGeomE for
temporal KGE, which performs 4th-order tensor factorization of a temporal KG
and devises a new linear temporal regularization for time representation
learning. Moreover, we study the effect of time granularity on the performance
of TGeomE models. Experimental results show that our proposed models achieve
the state-of-the-art performances on link prediction over four commonly-used
static KG datasets and four well-established temporal KG datasets across
various metrics.

本论文使用几何代数和张量分解提出了一种新的知识图谱表示学习方法 GeomE 和 TGeomE，用于解决深度学习中的时序数据问题。结果表明，该方法在四个常用的静态 KG 数据集和四个知名的时间 KG 数据集上实现了最先进的性能。