  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.
