TransH

class TransH(*, embedding_dim=50, scoring_fct_norm=2, entity_initializer=<function uniform_>, relation_initializer=<function uniform_>, **kwargs)

Bases: pykeen.models.base.EntityRelationEmbeddingModel

An implementation of TransH [wang2014].

This model extends pykeen.models.TransE by applying the translation from head to tail entity in a relational-specific hyperplane in order to address its inability to model one-to-many, many-to-one, and many-to-many relations.

In TransH, each relation is represented by a hyperplane, or more specifically a normal vector of this hyperplane \(\textbf{w}_{r} \in \mathbb{R}^d\) and a vector \(\textbf{d}_{r} \in \mathbb{R}^d\) that lies in the hyperplane. To compute the plausibility of a triple \((h,r,t)\in \mathbb{K}\), the head embedding \(\textbf{e}_h \in \mathbb{R}^d\) and the tail embedding \(\textbf{e}_t \in \mathbb{R}^d\) are first projected onto the relation-specific hyperplane:

\[ \begin{align}\begin{aligned}\textbf{e'}_{h,r} = \textbf{e}_h - \textbf{w}_{r}^\top \textbf{e}_h \textbf{w}_r\\\textbf{e'}_{t,r} = \textbf{e}_t - \textbf{w}_{r}^\top \textbf{e}_t \textbf{w}_r\end{aligned}\end{align} \]

where \(\textbf{h}, \textbf{t} \in \mathbb{R}^d\). Then, the projected embeddings are used to compute the score for the triple \((h,r,t)\):

\[f(h, r, t) = -\|\textbf{e'}_{h,r} + \textbf{d}_r - \textbf{e'}_{t,r}\|_{p}^2\]

See also

• OpenKE implementation of TransH

Initialize TransH.

Parameters

• embedding_dim (int) – The entity embedding dimension \(d\). Is usually \(d \in [50, 300]\).

• scoring_fct_norm (int) – The \(l_p\) norm applied in the interaction function. Is usually 1 or 2..

• entity_initializer (Union[str, Callable[[FloatTensor], FloatTensor], None]) – Entity initializer function. Defaults to torch.nn.init.uniform_()

• relation_initializer (Union[str, Callable[[FloatTensor], FloatTensor], None]) – Relation initializer function. Defaults to torch.nn.init.uniform_()

• kwargs – Remaining keyword arguments to forward to pykeen.models.EntityRelationEmbeddingModel

Attributes Summary

hpo_default	The default strategy for optimizing the model's hyper-parameters
regularizer_default_kwargs	The settings used by [wang2014] for TransH

Methods Summary

post_parameter_update()	Has to be called after each parameter update.
regularize_if_necessary(*tensors)	Update the regularizer's term given some tensors, if regularization is requested.
score_h(rt_batch, **kwargs)	Forward pass using left side (head) prediction.
score_hrt(hrt_batch, **kwargs)	Forward pass.
score_t(hr_batch, **kwargs)	Forward pass using right side (tail) prediction.

Attributes Documentation

hpo_default: ClassVar[Mapping[str, Any]] = {'embedding_dim': {'high': 256, 'low': 16, 'q': 16, 'type': <class 'int'>}, 'scoring_fct_norm': {'high': 2, 'low': 1, 'type': <class 'int'>}}

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

regularizer_default_kwargs: ClassVar[Mapping[str, Any]] = {'epsilon': 1e-05, 'weight': 0.05}

The settings used by [wang2014] for TransH

Methods Documentation

post_parameter_update()

Has to be called after each parameter update.

Return type

None

regularize_if_necessary(*tensors)

Update the regularizer’s term given some tensors, if regularization is requested.

Return type

None

score_h(rt_batch, **kwargs)

Forward pass using left side (head) prediction.

This method calculates the score for all possible heads for each (relation, tail) pair.

Parameters

• rt_batch (LongTensor) – shape: (batch_size, 2), dtype: long The indices of (relation, tail) pairs.

• slice_size – >0 The divisor for the scoring function when using slicing.

• mode – The pass mode, which is None in the transductive setting and one of “training”, “validation”, or “testing” in the inductive setting.

Return type

FloatTensor

Returns

shape: (batch_size, num_entities), dtype: float For each r-t pair, the scores for all possible heads.

score_hrt(hrt_batch, **kwargs)

Forward pass.

This method takes head, relation and tail of each triple and calculates the corresponding score.

Parameters

• hrt_batch (LongTensor) – shape: (batch_size, 3), dtype: long The indices of (head, relation, tail) triples.

• mode – The pass mode, which is None in the transductive setting and one of “training”, “validation”, or “testing” in the inductive setting.

Return type

FloatTensor

Returns

shape: (batch_size, 1), dtype: float The score for each triple.

score_t(hr_batch, **kwargs)

Forward pass using right side (tail) prediction.

This method calculates the score for all possible tails for each (head, relation) pair.

Parameters

• hr_batch (LongTensor) – shape: (batch_size, 2), dtype: long The indices of (head, relation) pairs.

• slice_size – >0 The divisor for the scoring function when using slicing.

• mode – The pass mode, which is None in the transductive setting and one of “training”, “validation”, or “testing” in the inductive setting.

Return type

FloatTensor

Returns

shape: (batch_size, num_entities), dtype: float For each h-r pair, the scores for all possible tails.