Embedding Knowledge Graphs Based on Transitivity and Antisymmetry of Rules

TL;DR

This paper introduces a novel knowledge graph embedding method that incorporates transitivity and antisymmetry of logic rules, improving the representation quality by leveraging background logical knowledge.

Contribution

It proposes a new approach that integrates logic rule properties into knowledge graph embeddings, addressing limitations of previous methods.

Findings

Outperforms baseline models on knowledge graph completion tasks.

Effectively captures transitivity and antisymmetry in logic rules.

Utilizes non-negative relation embeddings constrained through matrix factorization.

Abstract

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.