Definition

Knowledge graph (KG) is a structured representation of information that organizes data in the form of entities and their relationships. Commonly, knowledge graphs are massive and incomplete. So, knowledge graph completion (KG completion) is an important task.

Knowledge Graph Completion Task

Edges in KG are represented as triplets $⟨ h, r, t ⟩$ , where $h$ is a head, $r$ is a relation, and $t$ is a tail. Given a triplet $⟨ h, r, t ⟩$ , the goal of KG completion is that the embedding of $(h, r)$ should be close to the embedding of $t$ . A score function is high if input triplet $⟨ h, r, t ⟩$ is probable, otherwise low.

Relation Patterns in Knowledge Graph

Types of relations embedding models can represent

Model	Score	Embedding	Symmetric	Antisymmetric	Inverse	Transitive	1-to-N
TransE	$- ∥ h + r - t ∥$	$h, r, t \in R^{d}$	$\times$	$\circ$	$\circ$	$\circ$	$\times$
TransR	$- ∥ M_{r} h + r - M_{r} t ∥$	$h, t \in R^{d}$ $r \in R^{k}$ $M_{r} \in R^{k \times d}$	$\circ$	$\circ$	$\circ$	$\circ$	$\circ$
DistMult	$h^{⊺} diag (r) t$	$h, r, t \in R^{d}$	$\circ$	$\times$	$\times$	$\times$	$\times$
ComplEx	$Re (h^{⊺} diag (r) \overline{t})$	$h, r, t \in C^{d}$	$\circ$	$\circ$	$\circ$	$\times$	$\circ$