TransD

class TransD(*, embedding_dim=50, relation_dim=None, interaction_kwargs=None, entity_initializer=<function xavier_uniform_>, relation_initializer=<pykeen.utils.compose object>, entity_constrainer=<function clamp_norm>, relation_constrainer=<function clamp_norm>, **kwargs)[source]

Bases: ERModel

An implementation of TransD from [ji2015].

TransD is an extension of pykeen.models.TransR that, like TransR, considers entities and relations as objects living in different vector spaces. However, instead of performing the same relation-specific projection for all entity embeddings, entity-relation-specific projection matrices \(\textbf{M}_{r,h}, \textbf{M}_{t,h} \in \mathbb{R}^{k \times d}\) are constructed.

To do so, all head entities, tail entities, and relations are represented by two vectors, \(\textbf{e}_h, \hat{\textbf{e}}_h, \textbf{e}_t, \hat{\textbf{e}}_t \in \mathbb{R}^d\) and \(\textbf{r}_r, \hat{\textbf{r}}_r \in \mathbb{R}^k\), respectively. The first set of embeddings is used for calculating the entity-relation-specific projection matrices:

\[ \begin{align}\begin{aligned}\textbf{M}_{r,h} = \hat{\textbf{r}}_r \hat{\textbf{e}}_h^{T} + \tilde{\textbf{I}}\\\textbf{M}_{r,t} = \hat{\textbf{r}}_r \hat{\textbf{e}}_t^{T} + \tilde{\textbf{I}}\end{aligned}\end{align} \]

where \(\tilde{\textbf{I}} \in \mathbb{R}^{k \times d}\) is a \(k \times d\) matrix with ones on the diagonal and zeros elsewhere. Next, \(\textbf{e}_h\) and \(\textbf{e}_t\) are projected into the relation space by means of the constructed projection matrices. Finally, the plausibility score for \((h,r,t) \in \mathbb{K}\) is given by:

\[f(h,r,t) = -\|\textbf{M}_{r,h} \textbf{e}_h + \textbf{r}_r - \textbf{M}_{r,t} \textbf{e}_t\|_{2}^2\]

See also

Initialize the model.

Parameters:
  • embedding_dim (int) – the (entity) embedding dimension

  • relation_dim (Optional[int]) – the relation embedding dimension. Defaults to embedding_dim.

  • interaction_kwargs (Optional[Mapping[str, Any]]) – additional keyword-based parameters passed to TransDInteraction.__init__()

  • entity_initializer (Union[str, Callable[[FloatTensor], FloatTensor], None]) – the entity representation initializer

  • relation_initializer (Union[str, Callable[[FloatTensor], FloatTensor], None]) – the relation representation initializer

  • entity_constrainer (Union[str, Callable[[FloatTensor], FloatTensor], None]) – the entity representation constrainer

  • relation_constrainer (Union[str, Callable[[FloatTensor], FloatTensor], None]) – the relation representation constrainer

  • kwargs – additional keyword-based parameters passed to ERModel.__init__()

Attributes Summary

hpo_default

The default strategy for optimizing the model's hyper-parameters

Attributes Documentation

hpo_default: ClassVar[Mapping[str, Any]] = {'embedding_dim': {'high': 256, 'low': 16, 'q': 16, 'type': <class 'int'>}, 'relation_dim': {'high': 256, 'low': 16, 'q': 16, 'type': <class 'int'>}}

The default strategy for optimizing the model’s hyper-parameters