  Translation distance based knowledge graph embedding (KGE) methods, such as
TransE and RotatE, model the relation in knowledge graphs as translation or
rotation in the vector space. Both translation and rotation are injective; that
is, the translation or rotation of different vectors results in different
results. In knowledge graphs, different entities may have a relation with the
same entity; for example, many actors starred in one movie. Such a
non-injective relation pattern cannot be well modeled by the translation or
rotation operations in existing translation distance based KGE methods. To
tackle the challenge, we propose a translation distance-based KGE method called
SpaceE to model relations as linear transformations. The proposed SpaceE embeds
both entities and relations in knowledge graphs as matrices and SpaceE
naturally models non-injective relations with singular linear transformations.
We theoretically demonstrate that SpaceE is a fully expressive model with the
ability to infer multiple desired relation patterns, including symmetry,
skew-symmetry, inversion, Abelian composition, and non-Abelian composition.
Experimental results on link prediction datasets illustrate that SpaceE
substantially outperforms many previous translation distance based knowledge
graph embedding methods, especially on datasets with many non-injective
relations. The code is available based on the PaddlePaddle deep learning
platform https://www.paddlepaddle.org.cn.
