TransR

Definition

Translating embeddings in relational space (TransR) is a Knowledge Graph embedding method. it extends the ieda of TransE model by introducing separate embedding space for entities and relations.

For a triplet $⟨h,r,t⟩$, let $\mathbf{h},\mathbf{t}\in {\mathbb{R}}^d$ be vectors in the entity space, and $\mathbf{r}\in {\mathbb{R}}^k$ be a vector in relation space.

The objective of TransR is finding the vectors satisfying the equality ${\mathbf{h}}_r+\mathbf{r}={\mathbf{t}}_r$ where ${\mathbf{h}}_r:=M_r\mathbf{h}$ and ${\mathbf{t}}_r:=M_r\mathbf{t}$ are the projections of $\mathbf{h}$ and $\mathbf{t}$ in the relation space, and $M_r\in {\mathbb{R}}^{k\times d}$ is the projection matrix of $r$.

The entity score function is defined as $f_r(h,t)=-||{\mathbf{h}}_r+\mathbf{r}-{\mathbf{t}}_r||$