ComplEx

Definition

Complex embedding (ComplEx) is a Knowledge Graph embedding method. It extends the idea of DistMult in a vector space to the complex domain.

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

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

ComplEx cannot model transitive relations