"""An implementation of TransH
"""
import logging
import numpy as np
import tensorflow as tf
from ..base_model.TranslatingModel import TranslatingModel
from ...score import LpDistancePow
from ...loss import PairwiseHingeLoss
from ...ns_strategy import UniformStrategy
from ...constraint import normalized_embeddings, soft_constraint
logging.getLogger().setLevel(logging.INFO)
[docs]class TransH(TranslatingModel):
"""An implementation of TransH from `[wang 2014] <https://ojs.aaai.org/index.php/AAAI/article/view/8870>`_.
TransH overcomes the problems of TransE in modeling reflexive/one-to-many/many-to-one/many-to-many relations
by enabling an entity to have distributed representations when involved in different relations.
TransH represents each relation :math:`r` the relation-specific translation vector :math:`\\textbf{r}_r`
in the relation-specific hyperplane :math:`\\textbf{w}_r`, and project head and tail embeddings on to this
hyperplane, expecting the projected embeddings can be connected by the relation tranalation vector
:math:`\\textbf{r}_r`:
.. math::
{\\textbf{e}_h}_{\perp} + \\textbf{r}_r \\approx {\\textbf{e}_t}_{\perp}
{\\textbf{e}_h}_{\perp} = \\textbf{e}_h - \\textbf{w}_r^T \\textbf{e}_h\\textbf{w}_r
{\\textbf{e}_t}_{\perp} = \\textbf{e}_t - \\textbf{w}_r^T \\textbf{e}_t\\textbf{w}_r
where :math:`\\textbf{e}_i \in \mathbb{R}^k` are vector representations of the entities,
:math:`\\textbf{r}_i \in \mathbb{R}^k` are relation translation vectors,
and :math:`\\textbf{w}_i \in \mathbb{R}^k` are relation hyperplanes.
The score of :math:`(h,r,t)` is:
.. math::
f(h,r,t) = s({\\textbf{e}_h}_{\perp} + \\textbf{r}_r, {\\textbf{e}_t}_{\perp})
where :math:`s` is a scoring function (:py:mod:`KGE.score`) that scores the plausibility of matching between :math:`(translation, predicate)`. \n
By default, using :py:mod:`KGE.score.LpDistancePow`, negative squared L2-distance:
.. math::
s({\\textbf{e}_h}_{\perp} + \\textbf{r}_r, {\\textbf{e}_t}_{\perp}) =
- \left\| {\\textbf{e}_h}_{\perp} + \\textbf{r}_r - {\\textbf{e}_t}_{\perp} \\right\|_2^2
You can change to L1-distance by giving :code:`score_fn=LpDisrancePow(p=1)` in :py:func:`__init__`,
or change any score function you like by specifying :code:`score_fn` in :py:func:`__init__`.
If :code:`constraint=True` given in :py:func:`__init__`, conduct following constraints: \n
1. renormalized :math:`\left\| \\textbf{w}_i \\right\|_2 = 1` to have unit length every iteration \n
2. :math:`\left\| \\textbf{e}_i \\right\|_2 \leq 1` \n
3. :math:`\left| \mathbf{w}_{r}^T \mathbf{r}_{r} \\right| /\left\|\mathbf{r}_{r}\\right\|_2 \leq \epsilon` to guarantees the translation vector :math:`\\textbf{r}_r` is in the hyperplane \n
constraint 2 & 3 are realized by :py:func:`soft constraint <KGE.constraint.soft_constraint>` described in
`original TransH paper <https://ojs.aaai.org/index.php/AAAI/article/view/8870>`_:
.. math::
regularization~term = \lambda
\left\{ \sum_i \left[\| \\textbf{e}_i \|_{2}^{2}-1 \\right]_+ + \sum_i \left[ \\frac{\left(\ \\textbf{w}_{i}^T \\textbf{r}_{i} \\right)^2}{\left\| \\textbf{r}_{i} \\right\|_2^2}-\epsilon^2 \\right]_{+} \\right\}
"""
[docs] def __init__(self, embedding_params, negative_ratio, corrupt_side,
score_fn=LpDistancePow(p=2), loss_fn=PairwiseHingeLoss(margin=1),
ns_strategy=UniformStrategy, constraint=True, constraint_weight=1.0, n_workers=1):
"""Initialized TransH
Parameters
----------
embedding_params : dict
embedding dimension parameters, should have key :code:`'embedding_size'` for embedding dimension :math:`k`
negative_ratio : int
number of negative sample
corrupt_side : str
corrupt from which side while trainging, can be :code:`'h'`, :code:`'t'`, or :code:`'h+t'`
score_fn : function, optional
scoring function, by default :py:mod:`KGE.score.LpDistancePow`
loss_fn : class, optional
loss function class :py:mod:`KGE.loss.Loss`, by default :py:mod:`KGE.loss.PairwiseHingeLoss`
ns_strategy : function, optional
negative sampling strategy, by default :py:func:`KGE.ns_strategy.uniform_strategy`
constraint : bool, optional
conduct constraint or not, by default True
constraint_weight : float, optional
regularization weight :math:`\lambda`, by default 1.0
n_workers : int, optional
number of workers for negative sampling, by default 1
"""
super(TransH, self).__init__(embedding_params, negative_ratio, corrupt_side,
score_fn, loss_fn, ns_strategy, n_workers)
self.constraint = constraint
self.constraint_weight = constraint_weight
def _init_embeddings(self, seed):
"""Initialized the TransH embeddings.
If :code:`model_weight_initial` not given in :py:func:`train`, initialized embeddings randomly,
otherwise, initialized from :code:`model_weight_initial`.
Parameters
----------
seed : int
random seed
"""
if self._model_weights_initial is None:
assert self.embedding_params.get("embedding_size") is not None, "'embedding_size' should be given in embedding_params when using TransH"
limit = np.sqrt(6.0 / self.embedding_params["embedding_size"])
uniform_initializer = tf.initializers.RandomUniform(minval=-limit, maxval=limit, seed=seed)
ent_emb = tf.Variable(
uniform_initializer([len(self.metadata["ind2ent"]), self.embedding_params["embedding_size"]]),
name="entities_embedding", dtype=np.float32
)
rel_emb = tf.Variable(
uniform_initializer([len(self.metadata["ind2rel"]), self.embedding_params["embedding_size"]]),
name="relations_embedding", dtype=np.float32
)
rel_hyper = tf.Variable(
uniform_initializer([len(self.metadata["ind2rel"]), self.embedding_params["embedding_size"]]),
name="relations_hyperplane", dtype=np.float32
)
self.model_weights = {"ent_emb": ent_emb, "rel_emb": rel_emb, "rel_hyper": rel_hyper}
else:
self._check_model_weights(self._model_weights_initial)
self.model_weights = self._model_weights_initial
def _check_model_weights(self, model_weights):
"""Check the model_weights have necessary keys and dimensions
Parameters
----------
model_weights : dict
model weights to check.
"""
assert model_weights.get("ent_emb") is not None, "entity embedding should be given in model_weights with key 'ent_emb'"
assert model_weights.get("rel_emb") is not None, "relation embedding should be given in model_weights with key 'rel_emb'"
assert model_weights.get("rel_hyper") is not None, "relation hyperplane should be given in model_weights with key 'rel_hyper'"
assert list(model_weights["ent_emb"].shape) == [len(self.metadata["ind2ent"]), self.embedding_params["embedding_size"]], \
"shape of 'ent_emb' should be (len(metadata['ind2ent']), embedding_params['embedding_size'])"
assert list(model_weights["rel_emb"].shape) == [len(self.metadata["ind2rel"]), self.embedding_params["embedding_size"]], \
"shape of 'rel_emb' should be (len(metadata['ind2rel']), embedding_params['embedding_size'])"
assert list(model_weights["rel_hyper"].shape) == [len(self.metadata["ind2rel"]), self.embedding_params["embedding_size"]], \
"shape of 'rel_hyper' should be (len(metadata['ind2rel']), embedding_params['embedding_size'])"
[docs] def score_hrt(self, h, r, t):
""" Score the triplets :math:`(h,r,t)`.
If :code:`h` is :code:`None`, score all entities: :math:`(h_i, r, t)`. \n
If :code:`t` is :code:`None`, score all entities: :math:`(h, r, t_i)`. \n
:code:`h` and :code:`t` should not be :code:`None` simultaneously.
Parameters
----------
h : tf.Tensor or np.ndarray or None
index of heads with shape :code:`(n,)`
r : tf.Tensor or np.ndarray
index of relations with shape :code:`(n,)`
t : tf.Tensor or np.ndarray or None
index of tails with shape :code:`(n,)`
Returns
-------
tf.Tensor
triplets scores with shape :code:`(n,)`
"""
h,r,t = super(TransH, self).score_hrt(h,r,t)
h_emb = tf.nn.embedding_lookup(self.model_weights["ent_emb"], h)
r_emb = tf.nn.embedding_lookup(self.model_weights["rel_emb"], r)
r_hyper = tf.nn.embedding_lookup(self.model_weights["rel_hyper"], r)
t_emb = tf.nn.embedding_lookup(self.model_weights["ent_emb"], t)
h_emb = tf.expand_dims(h_emb, axis=-1)
r_hyper = tf.expand_dims(r_hyper, axis=-1)
t_emb = tf.expand_dims(t_emb, axis=-1)
h_proj = tf.squeeze(h_emb - tf.multiply(tf.matmul(r_hyper, h_emb, transpose_a=True), r_hyper))
t_proj = tf.squeeze(t_emb - tf.multiply(tf.matmul(r_hyper, t_emb, transpose_a=True), r_hyper))
return self.score_fn(h_proj + r_emb, t_proj)
def _constraint_loss(self, X):
"""Perform constraint if necessary.
Parameters
----------
X : batch_data
batch data
Returns
-------
tf.Tensor
regularization term with shape (1,)
"""
if self.constraint:
self.model_weights["rel_hyper"].assign(normalized_embeddings(X=self.model_weights["rel_hyper"], p=2, axis=1, value=1))
scale = soft_constraint(self.model_weights["ent_emb"], p=2, axis=-1, value=1)
orthogonal = tf.matmul(tf.expand_dims(self.model_weights["rel_hyper"], axis=-1),
tf.expand_dims(self.model_weights["rel_emb"], axis=-1),
transpose_a=True)
orthogonal = tf.pow(tf.squeeze(orthogonal) / tf.norm(self.model_weights["rel_emb"], axis=-1), 2) - 1e-18
orthogonal = tf.reduce_sum(tf.clip_by_value(orthogonal, 0, np.inf))
return self.constraint_weight * (scale + orthogonal)
else:
return 0