DistMult

Definition

DistMult is a Knowledge Graph embedding method representing entities and relations as vectors in same low-dimensional space. It uses a bilinear scoring function with a diagonal matrix for each relation.

For a triplet $⟨h,r,t⟩$, let $\mathbf{h},\mathbf{r},\mathbf{t}\in {\mathbb{R}}^d$ be embedding vectors.

The score function of DistMult is defined as $f_r(h,t)={\mathbf{h}}^{⊺}\mathrm{diag}(\mathbf{r})\mathbf{t}=\sum _{i=1}^d{\mathbf{h}}_i{\mathbf{r}}_i{\mathbf{t}}_i$

DistMult cannot model antisymmetric, inverse, and transitive relations.