Knowledge Graph Embeddings in Geometric Algebras

• URL: http://arxiv.org/abs/2010.00989v4
• Date: Mon, 22 Mar 2021 18:59:42 GMT
• Title: Knowledge Graph Embeddings in Geometric Algebras
• Authors: Chengjin Xu, Mojtaba Nayyeri, Yung-Yu Chen, Jens Lehmann
• Abstract summary: We introduce a novel geometric algebra-based KG embedding framework, GeomE. Our framework subsumes several state-of-the-art KG embedding approaches and is advantageous with its ability of modeling various key relation patterns. Experimental results on multiple benchmark knowledge graphs show that theproposed approach outperforms existing state-of-the-art models for link prediction.
• Score: 14.269860621624392
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Knowledge graph (KG) embedding aims at embedding entities and relations in a KG into a lowdimensional latent representation space. Existing KG embedding approaches model entities andrelations in a KG by utilizing real-valued , complex-valued, or hypercomplex-valued (Quaternionor 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 uti-lizes multivector representations and the geometric product to model entities and relations. Ourframework subsumes several state-of-the-art KG embedding approaches and is advantageouswith its ability of modeling various key relation patterns, including (anti-)symmetry, inversionand composition, rich expressiveness with higher degree of freedom as well as good general-ization capacity. Experimental results on multiple benchmark knowledge graphs show that theproposed approach outperforms existing state-of-the-art models for link prediction.

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