ComplEx

class ampligraph.latent_features.ComplEx(k=100, eta=2, epochs=100, batches_count=100, seed=0, embedding_model_params={'negative_corruption_entities': 'all'}, optimizer='adam', optimizer_params={'lr': 0.0005}, loss='nll', loss_params={}, regularizer=None, regularizer_params={}, verbose=False)

Complex embeddings (ComplEx)

The ComplEx model [TWR+16] is an extension of the ampligraph.latent_features.DistMult bilinear diagonal model . ComplEx scoring function is based on the trilinear Hermitian dot product in \(\mathcal{C}\):

\[f_{ComplEx}=Re(\langle \mathbf{r}_p, \mathbf{e}_s, \overline{\mathbf{e}_o} \rangle)\]

Note that because embeddings are in \(\mathcal{C}\), ComplEx uses twice as many parameters as ampligraph.latent_features.DistMult.

Examples

>>> import numpy as np
>>> from ampligraph.latent_features import ComplEx
>>>
>>> model = ComplEx(batches_count=1, seed=555, epochs=20, k=10,
>>>             loss='pairwise', loss_params={'margin':1},
>>>             regularizer='LP', regularizer_params={'lambda':0.1})
>>> X = np.array([['a', 'y', 'b'],
>>>               ['b', 'y', 'a'],
>>>               ['a', 'y', 'c'],
>>>               ['c', 'y', 'a'],
>>>               ['a', 'y', 'd'],
>>>               ['c', 'y', 'd'],
>>>               ['b', 'y', 'c'],
>>>               ['f', 'y', 'e']])
>>> model.fit(X)
>>> model.predict(np.array([['f', 'y', 'e'], ['b', 'y', 'd']]))
[0.96325016, -0.17629346]
>>> model.get_embeddings(['f','e'], type='entity')
array([[-0.11257   , -0.09226837,  0.2829331 , -0.02094189,  0.02826234,
-0.3068198 , -0.41022655, -0.23714773, -0.00084166,  0.22521858,
-0.48155236,  0.29627186,  0.29841757,  0.16540456,  0.45836073,
 0.14025007, -0.03458257, -0.03813137,  0.35438442, -0.4733188 ],
[ 0.06088537,  0.13615245, -0.20476362,  0.20391239,  0.22199424,
 0.5762486 , -0.01087974,  0.39070424, -0.1372974 ,  0.39998057,
-0.5944237 ,  0.506474  ,  0.1255992 , -0.06021457, -0.26678884,
-0.18713273,  0.36862013,  0.07165384, -0.00845572, -0.16494963]],
dtype=float32)

Methods

__init__([k, eta, epochs, batches_count, …]) Initialize an EmbeddingModel
fit(X[, early_stopping, early_stopping_params]) Train a ComplEx model.
get_embeddings(entities[, type]) Get the embeddings of entities or relations.
predict(X[, from_idx, get_ranks]) Predict the scores of triples using a trained embedding model.
__init__(k=100, eta=2, epochs=100, batches_count=100, seed=0, embedding_model_params={'negative_corruption_entities': 'all'}, optimizer='adam', optimizer_params={'lr': 0.0005}, loss='nll', loss_params={}, regularizer=None, regularizer_params={}, verbose=False)

Initialize an EmbeddingModel

Also creates a new Tensorflow session for training.
Parameters:
  • k (int) – Embedding space dimensionality
  • eta (int) – The number of negatives that must be generated at runtime during training for each positive.
  • epochs (int) – The iterations of the training loop.
  • batches_count (int) – The number of batches in which the training set must be split during the training loop.
  • seed (int) – The seed used by the internal random numbers generator.
  • embedding_model_params (dict) –

    ComplEx-specific hyperparams:

    • ’negative_corruption_entities’ - Entities to be used for generation of corruptions while training. It can take the following values : all (default: all entities), batch (entities present in each batch), list of entities or an int (which indicates how many entities that should be used for corruption generation).
  • optimizer (string) – The optimizer used to minimize the loss function. Choose between ‘sgd’, ‘adagrad’, ‘adam’, ‘momentum’.
  • optimizer_params (dict) –

    Arguments specific to the optimizer, passed as a dictionary.

    Supported keys:

    • ’lr’ (float): learning rate (used by all the optimizers). Default: 0.1.
    • ’momentum’ (float): learning momentum (only used when optimizer=momentum). Default: 0.9.

    Example: optimizer_params={'lr': 0.01}

  • loss (string) –

    The type of loss function to use during training.

    • ’pairwise’ the model will use pairwise margin-based loss function.
    • ’nll’ the model will use negative loss likelihood.
    • ’absolute_margin’ the model will use absolute margin likelihood.
    • ’self_adversarial’ the model will use adversarial sampling loss function.
  • loss_params (dict) –

    Dictionary of loss-specific hyperparameters. See loss functions documentation for additional details.

    Example: optimizer_params={'lr': 0.01} if loss='pairwise'.

  • regularizer (string) –

    The regularization strategy to use with the loss function.

    • None: the model will not use any regularizer (default)
    • ’LP’: the model will use L1, L2 or L3 based on the value of regularizer_params['p'] (see below).
  • regularizer_params (dict) –

    Dictionary of regularizer-specific hyperparameters. See the regularizers documentation for additional details.

    Example: regularizer_params={'lambda': 1e-5, 'p': 2} if regularizer='LP'.

  • verbose (bool) – Verbose mode
fit(X, early_stopping=False, early_stopping_params={})

Train a ComplEx model.

The model is trained on a training set X using the training protocol described in [TWR+16].
Parameters:
  • X (ndarray, shape [n, 3]) – The training triples
  • early_stopping (bool) – Flag to enable early stopping (default:False)
  • early_stopping_params (dictionary) –

    Dictionary of hyperparameters for the early stopping heuristics.

    The following string keys are supported:

    • ’x_valid’: ndarray, shape [n, 3] : Validation set to be used for early stopping.
    • ’criteria’: string : criteria for early stopping ‘hits10’, ‘hits3’, ‘hits1’ or ‘mrr’(default).
    • ’x_filter’: ndarray, shape [n, 3] : Positive triples to use as filter if a ‘filtered’ early stopping criteria is desired (i.e. filtered-MRR if ‘criteria’:’mrr’). Note this will affect training time (no filter by default).
    • ’burn_in’: int : Number of epochs to pass before kicking in early stopping (default: 100).
    • check_interval’: int : Early stopping interval after burn-in (default:10).
    • ’stop_interval’: int : Stop if criteria is performing worse over n consecutive checks (default: 3)
    • ’corruption_entities’: List of entities to be used for corruptions. If ‘all’, it uses all entities (default: ‘all’)
    • ’corrupt_side’: Specifies which side to corrupt. ‘s’, ‘o’, ‘s+o’ (default)

    Example: early_stopping_params={x_valid=X['valid'], 'criteria': 'mrr'}
get_embeddings(entities, type='entity')

Get the embeddings of entities or relations.

Parameters:
  • entities (array-like, dtype=int, shape=[n]) – The entities (or relations) of interest. Element of the vector must be the original string literals, and not internal IDs.
  • type (string) – If ‘entity’, the entities argument will be considered as a list of knowledge graph entities (i.e. nodes). If set to ‘relation’, they will be treated as relation types instead (i.e. predicates).
Returns:

embeddings – An array of k-dimensional embeddings.
Return type:

ndarray, shape [n, k]
predict(X, from_idx=False, get_ranks=False)

Predict the scores of triples using a trained embedding model.

The function returns raw scores generated by the model.

Note

To obtain probability estimates, use a logistic sigmoid:

>>> model.fit(X)
>>> y_pred = model.predict(np.array([['f', 'y', 'e'], ['b', 'y', 'd']]))
>>> print(y_pred)
array([1.2052395, 1.5818497], dtype=float32)
>>> from scipy.special import expit
>>> expit(y_pred)
array([0.7694556 , 0.82946634], dtype=float32)
Parameters:
  • X (ndarray, shape [n, 3]) – The triples to score.
  • from_idx (bool) – If True, will skip conversion to internal IDs. (default: False).
  • get_ranks (bool) – Flag to compute ranks by scoring against corruptions (default: False).
Returns:

  • scores_predict (ndarray, shape [n]) – The predicted scores for input triples X.
  • rank (ndarray, shape [n]) – Ranks of the triples (only returned if get_ranks=True.