Embedding Knowledge Graphs Based on Transitivity and Antisymmetry of
  Rules
  Representation learning of knowledge graphs encodes entities and relation
types into a continuous low-dimensional vector space, learns embeddings of
entities and relation types. Most existing methods only concentrate on
knowledge triples, ignoring logic rules which contain rich background
knowledge. Although there has been some work aiming at leveraging both
knowledge triples and logic rules, they ignore the transitivity and
antisymmetry of logic rules. In this paper, we propose a novel approach to
learn knowledge representations with entities and ordered relations in
knowledges and logic rules. The key idea is to integrate knowledge triples and
logic rules, and approximately order the relation types in logic rules to
utilize the transitivity and antisymmetry of logic rules. All entries of the
embeddings of relation types are constrained to be non-negative. We translate
the general constrained optimization problem into an unconstrained optimization
problem to solve the non-negative matrix factorization. Experimental results
show that our model significantly outperforms other baselines on knowledge
graph completion task. It indicates that our model is capable of capturing the
transitivity and antisymmetry information, which is significant when learning
embeddings of knowledge graphs.
