MQuadE: a Unified Model for Knowledge Fact Embedding

The task of knowledge graph embedding (KGE) tries to find appropriate representations for entities and relations and appropriate mathematical computations between the representations to approximate the symbolic and logical relationships between entities. One major challenge for KGE is that the relations in real-world knowledge bases exhibit complex behaviors: they can be injective (1-1) or non-injective (1-N, N-1, or N-N), symmetry or skew-symmetry; one relation may be the inversion of another relation; one relation may be the composition of other two relations (where the composition can be either Abelian or non-Abelian). To our knowledge, there has not been any theoretical guarantee that these complex behaviors can be modeled by existing KGE methods. This paper proposes a method called MQuadE to tackle the challenge in KGE modeling. In MQuadE, we represent a fact triple (h, r, t), that is, (head entity, relation, tail entity), in the knowledge graph with a matrix quadruple (H, R, R,T ), where H and T are the representations of h and t respectively and < R, R > is the pair of representation of r . MQuadE projects the head entity into HR and the tail entity into RT , then assumes that HR and RT are similar for true facts and dissimilar for false facts. We prove that MQuadE, as a unified model for KGE, is able to model the generally concerned types of relations (symmetric, skew-symmetric, injective, non-injective, inversion, Abelian composition, non-Abelian composition). Experiments on link prediction and triple classification show that MQuadE outperforms many previous knowledge graph embedding methods, especially on 1-N, N-1, and N-N relations.