# -*- coding: utf-8 -*-
"""Implementation of structured model (SE)."""
from typing import Any, ClassVar, Mapping, Optional
from class_resolver import Hint
from torch.nn import functional
from ..nbase import ERModel
from ...constants import DEFAULT_EMBEDDING_HPO_EMBEDDING_DIM_RANGE
from ...nn.init import xavier_uniform_, xavier_uniform_norm_
from ...nn.modules import SEInteraction
from ...typing import Constrainer, Initializer
__all__ = [
"SE",
]
[docs]class SE(ERModel):
r"""An implementation of the Structured Embedding (SE) published by [bordes2011]_.
SE applies role- and relation-specific projection matrices
$\textbf{M}_{r}^{h}, \textbf{M}_{r}^{t} \in \mathbb{R}^{d \times d}$ to the head and tail
entities' embeddings before computing their differences. Then, the $l_p$ norm is applied
and the result is negated such that smaller differences are considered better.
.. math::
f(h, r, t) = - \|\textbf{M}_{r}^{h} \textbf{e}_h - \textbf{M}_{r}^{t} \textbf{e}_t\|_p
By employing different projections for the embeddings of the head and tail entities, SE explicitly differentiates
the role of an entity as either the subject or object.
---
name: Structured Embedding
citation:
author: Bordes
year: 2011
link: https://www.aaai.org/ocs/index.php/AAAI/AAAI11/paper/download/3659/3898
"""
#: The default strategy for optimizing the model's hyper-parameters
hpo_default: ClassVar[Mapping[str, Any]] = dict(
embedding_dim=DEFAULT_EMBEDDING_HPO_EMBEDDING_DIM_RANGE,
scoring_fct_norm=dict(type=int, low=1, high=2),
)
def __init__(
self,
*,
embedding_dim: int = 50,
scoring_fct_norm: int = 1,
entity_initializer: Hint[Initializer] = xavier_uniform_,
entity_constrainer: Hint[Constrainer] = functional.normalize,
entity_constrainer_kwargs: Optional[Mapping[str, Any]] = None,
relation_initializer: Hint[Initializer] = xavier_uniform_norm_,
**kwargs,
) -> None:
r"""Initialize SE.
:param embedding_dim: The entity embedding dimension $d$. Is usually $d \in [50, 300]$.
:param scoring_fct_norm: The $l_p$ norm. Usually 1 for SE.
:param entity_initializer: Entity initializer function. Defaults to :func:`pykeen.nn.init.xavier_uniform_`
:param entity_constrainer: Entity constrainer function. Defaults to :func:`torch.nn.functional.normalize`
:param entity_constrainer_kwargs: Keyword arguments to be used when calling the entity constrainer
:param relation_initializer: Relation initializer function. Defaults to
:func:`pykeen.nn.init.xavier_uniform_norm_`
:param kwargs:
Remaining keyword arguments to forward to :class:`pykeen.models.EntityEmbeddingModel`
"""
super().__init__(
interaction=SEInteraction(
p=scoring_fct_norm,
power_norm=False,
),
entity_representations_kwargs=dict(
shape=embedding_dim,
initializer=entity_initializer,
constrainer=entity_constrainer,
constrainer_kwargs=entity_constrainer_kwargs,
),
relation_representations_kwargs=[
dict(
shape=(embedding_dim, embedding_dim),
initializer=relation_initializer,
),
dict(
shape=(embedding_dim, embedding_dim),
initializer=relation_initializer,
),
],
**kwargs,
)