Knowledge Graph Embeddings in Geometric Algebras
Chengjin Xu, Mojtaba Nayyeri, Yung-Yu Chen, Jens Lehmann · 2020
Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a low dimensional latent representation space.Existing KG embedding approaches model entities and relations in a KG by utilizing real-valued , complex-valued, or hypercomplex-valued (Quaternion or Octonion) representations, all of which are subsumed into a geometric algebra.In this work, we introduce a novel geometric algebra-based KG embedding framework, GeomE, which utilizes multivector representations and the geometric product to model entities and relations.Our framework subsumes several state-of-the-art KG embedding approaches and is advantageous with its ability of modeling various key relation patterns, including (anti-)symmetry, inversion and composition, rich expressiveness with higher degree of freedom as well as good generalization capacity.Experimental results on multiple benchmark knowledge graphs show that the proposed approach outperforms existing state-of-the-art models for link prediction.