`metric_learn`.ITML

class metric_learn.ITML(gamma=1.0, max_iter=1000, tol=0.001, prior='identity', verbose=False, preprocessor=None, random_state=None, convergence_threshold='deprecated')[source]

Information Theoretic Metric Learning (ITML)

ITML minimizes the (differential) relative entropy, aka Kullback-Leibler divergence, between two multivariate Gaussians subject to constraints on the associated Mahalanobis distance, which can be formulated into a Bregman optimization problem by minimizing the LogDet divergence subject to linear constraints. This algorithm can handle a wide variety of constraints and can optionally incorporate a prior on the distance function. Unlike some other methods, ITML does not rely on an eigenvalue computation or semi-definite programming.

Read more in the User Guide.

Parameters:

gammafloat, optional (default=1.0)

Value for slack variables

max_iterint, optional (default=1000)

Maximum number of iteration of the optimization procedure.

tolfloat, optional (default=1e-3)

Convergence tolerance.

priorstring or numpy array, optional (default=’identity’)

The Mahalanobis matrix to use as a prior. Possible options are ‘identity’, ‘covariance’, ‘random’, and a numpy array of shape (n_features, n_features). For ITML, the prior should be strictly positive definite (PD).

‘identity’: An identity matrix of shape (n_features, n_features).
‘covariance’: The inverse covariance matrix.
‘random’: The prior will be a random SPD matrix of shape (n_features, n_features), generated using sklearn.datasets.make_spd_matrix.
numpy array: A positive definite (PD) matrix of shape (n_features, n_features), that will be used as such to set the prior.

verbosebool, optional (default=False)

If True, prints information while learning

preprocessorarray-like, shape=(n_samples, n_features) or callable

The preprocessor to call to get tuples from indices. If array-like, tuples will be formed like this: X[indices].

random_stateint or numpy.RandomState or None, optional (default=None)

A pseudo random number generator object or a seed for it if int. If prior='random', random_state is used to set the prior.

convergence_thresholdRenamed to tol. Will be deprecated in 0.7.0

References

[1]

Jason V. Davis, et al. Information-theoretic Metric Learning. ICML 2007.

Examples

>>> from metric_learn import ITML
>>> pairs = [[[1.2, 7.5], [1.3, 1.5]],
>>>         [[6.4, 2.6], [6.2, 9.7]],
>>>         [[1.3, 4.5], [3.2, 4.6]],
>>>         [[6.2, 5.5], [5.4, 5.4]]]
>>> y = [1, 1, -1, -1]
>>> # in this task we want points where the first feature is close to be
>>> # closer to each other, no matter how close the second feature is
>>> itml = ITML()
>>> itml.fit(pairs, y)

Attributes:

bounds_numpy.ndarray, shape=(2,): Bounds on similarity, aside slack variables, s.t. d(a, b) < bounds_[0] for all given pairs of similar points a and b, and d(c, d) > bounds_[1] for all given pairs of dissimilar points c and d, with d the learned distance. If not provided at initialization, bounds_[0] and bounds_[1] are set at train time to the 5th and 95th percentile of the pairwise distances among all points present in the input pairs.
n_iter_int: The number of iterations the solver has run.
components_numpy.ndarray, shape=(n_features, n_features): The linear transformation L deduced from the learned Mahalanobis metric (See function components_from_metric.)
threshold_float: If the distance metric between two points is lower than this threshold, points will be classified as similar, otherwise they will be classified as dissimilar.

Methods

`calibrate_threshold`(pairs_valid, y_valid[, ...])	Decision threshold calibration for pairwise binary classification
`decision_function`(pairs)	Returns the decision function used to classify the pairs.
`fit`(pairs, y[, bounds, calibration_params])	Learn the ITML model.
`get_mahalanobis_matrix`()	Returns a copy of the Mahalanobis matrix learned by the metric learner.
`get_metadata_routing`()	Get metadata routing of this object.
`get_metric`()	Returns a function that takes as input two 1D arrays and outputs the value of the learned metric on these two points.
`get_params`([deep])	Get parameters for this estimator.
`pair_distance`(pairs)	Returns the learned Mahalanobis distance between pairs.
`pair_score`(pairs)	Returns the opposite of the learned Mahalanobis distance between pairs.
`predict`(pairs)	Predicts the learned metric between input pairs.
`score`(pairs, y)	Computes score of pairs similarity prediction.
`score_pairs`(pairs)	Returns the learned Mahalanobis distance between pairs.
`set_decision_function_request`(*[, pairs])	Request metadata passed to the `decision_function` method.
`set_fit_request`(*[, bounds, ...])	Request metadata passed to the `fit` method.
`set_params`(**params)	Set the parameters of this estimator.
`set_predict_request`(*[, pairs])	Request metadata passed to the `predict` method.
`set_score_request`(*[, pairs])	Request metadata passed to the `score` method.
`set_threshold`(threshold)	Sets the threshold of the metric learner to the given value threshold.
`transform`(X)	Embeds data points in the learned linear embedding space.

__init__(gamma=1.0, max_iter=1000, tol=0.001, prior='identity', verbose=False, preprocessor=None, random_state=None, convergence_threshold='deprecated')

calibrate_threshold(pairs_valid, y_valid, strategy='accuracy', min_rate=None, beta=1.0)

Decision threshold calibration for pairwise binary classification

Method that calibrates the decision threshold (cutoff point) of the metric learner. This threshold will then be used when calling the method predict. The methods for picking cutoff points make use of traditional binary classification evaluation statistics such as the true positive and true negative rates and F-scores. The threshold will be found to maximize the chosen score on the validation set (pairs_valid, y_valid).

See more in the User Guide.

Parameters:

strategystr, optional (default=’accuracy’)

The strategy to use for choosing the cutoff threshold.

‘accuracy’: Selects a decision threshold that maximizes the accuracy.
‘f_beta’: Selects a decision threshold that maximizes the f_beta score, with beta given by the parameter beta.
‘max_tpr’: Selects a decision threshold that yields the highest true positive rate with true negative rate at least equal to the value of the parameter min_rate.
‘max_tnr’: Selects a decision threshold that yields the highest true negative rate with true positive rate at least equal to the value of the parameter min_rate.

betafloat in [0, 1], optional (default=None)

Beta value to be used in case strategy == ‘f_beta’.

min_ratefloat in [0, 1] or None, (default=None)

In case strategy is ‘max_tpr’ or ‘max_tnr’ this parameter must be set to specify the minimal value for the true negative rate or true positive rate respectively that needs to be achieved.

pairs_validarray-like, shape=(n_pairs_valid, 2, n_features)

The validation set of pairs to use to set the threshold.

y_validarray-like, shape=(n_pairs_valid,)

The labels of the pairs of the validation set to use to set the threshold. They must be +1 for positive pairs and -1 for negative pairs.

See also

sklearn.calibration: scikit-learn’s module for calibrating classifiers

References

[1]

Receiver-operating characteristic (ROC) plots: a fundamental evaluation tool in clinical medicine, MH Zweig, G Campbell - Clinical chemistry, 1993

[2]

Most of the code of this function is from scikit-learn’s PR #10117

classes_ = array([0, 1])

decision_function(pairs)

Returns the decision function used to classify the pairs.

Returns the opposite of the learned metric value between samples in every pair, to be consistent with scikit-learn conventions. Hence it should ideally be low for dissimilar samples and high for similar samples. This is the decision function that is used to classify pairs as similar (+1), or dissimilar (-1).

Parameters:

pairsarray-like, shape=(n_pairs, 2, n_features) or (n_pairs, 2): 3D Array of pairs to predict, with each row corresponding to two points, or 2D array of indices of pairs if the metric learner uses a preprocessor.

Returns:

y_predictednumpy.ndarray of floats, shape=(n_constraints,): The predicted decision function value for each pair.

fit(pairs, y, bounds=None, calibration_params=None)[source]

Learn the ITML model.

The threshold will be calibrated on the trainset using the parameters calibration_params.

Parameters:

pairs: array-like, shape=(n_constraints, 2, n_features) or (n_constraints, 2): 3D Array of pairs with each row corresponding to two points, or 2D array of indices of pairs if the metric learner uses a preprocessor.
y: array-like, of shape (n_constraints,): Labels of constraints. Should be -1 for dissimilar pair, 1 for similar.
boundsarray-like of two numbers: Bounds on similarity, aside slack variables, s.t. d(a, b) < bounds_[0] for all given pairs of similar points a and b, and d(c, d) > bounds_[1] for all given pairs of dissimilar points c and d, with d the learned distance. If not provided at initialization, bounds_[0] and bounds_[1] will be set to the 5th and 95th percentile of the pairwise distances among all points present in the input pairs.
calibration_paramsdict or None: Dictionary of parameters to give to calibrate_threshold for the threshold calibration step done at the end of fit. If None is given, calibrate_threshold will use the default parameters.

Returns:

selfobject: Returns the instance.

get_mahalanobis_matrix()

Returns a copy of the Mahalanobis matrix learned by the metric learner.

Returns:

Mnumpy.ndarray, shape=(n_features, n_features): The copy of the learned Mahalanobis matrix.

get_metadata_routing()

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest: A MetadataRequest encapsulating routing information.

get_metric()

Returns a function that takes as input two 1D arrays and outputs the value of the learned metric on these two points. Depending on the algorithm, it can return a distance or a similarity function between pairs.

This function will be independent from the metric learner that learned it (it will not be modified if the initial metric learner is modified), and it can be directly plugged into the metric argument of scikit-learn’s estimators.

Returns:

metric_funfunction: The function described above.

See also

pair_distance: a method that returns the distance between several pairs of points. Unlike get_metric, this is a method of the metric learner and therefore can change if the metric learner changes. Besides, it can use the metric learner’s preprocessor, and works on concatenated arrays.
pair_score: a method that returns the similarity score between several pairs of points. Unlike get_metric, this is a method of the metric learner and therefore can change if the metric learner changes. Besides, it can use the metric learner’s preprocessor, and works on concatenated arrays.

Examples

>>> from metric_learn import NCA
>>> from sklearn.datasets import make_classification
>>> from sklearn.neighbors import KNeighborsClassifier
>>> nca = NCA()
>>> X, y = make_classification()
>>> nca.fit(X, y)
>>> knn = KNeighborsClassifier(metric=nca.get_metric())
>>> knn.fit(X, y) 
KNeighborsClassifier(algorithm='auto', leaf_size=30,
  metric=<function MahalanobisMixin.get_metric.<locals>.metric_fun
          at 0x...>,
  metric_params=None, n_jobs=None, n_neighbors=5, p=2,
  weights='uniform')

get_params(deep=True)

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

pair_distance(pairs)

Returns the learned Mahalanobis distance between pairs.

This distance is defined as: $d_M(x, x') = \sqrt{(x-x')^T M (x-x')}$ where M is the learned Mahalanobis matrix, for every pair of points x and x'. This corresponds to the euclidean distance between embeddings of the points in a new space, obtained through a linear transformation. Indeed, we have also: $d_M(x, x') = \sqrt{(x_e - x_e')^T (x_e- x_e')}$, with $x_e = L x$ (See MahalanobisMixin).

Parameters:

pairsarray-like, shape=(n_pairs, 2, n_features) or (n_pairs, 2): 3D Array of pairs to score, with each row corresponding to two points, for 2D array of indices of pairs if the metric learner uses a preprocessor.

Returns:

scoresnumpy.ndarray of shape=(n_pairs,): The learned Mahalanobis distance for every pair.

See also

get_metric: a method that returns a function to compute the metric between two points. The difference with pair_distance is that it works on two 1D arrays and cannot use a preprocessor. Besides, the returned function is independent of the metric learner and hence is not modified if the metric learner is.
Mahalanobis Distances: The section of the project documentation that describes Mahalanobis Distances.

pair_score(pairs)

Returns the opposite of the learned Mahalanobis distance between pairs.

Parameters:

pairsarray-like, shape=(n_pairs, 2, n_features) or (n_pairs, 2): 3D Array of pairs to score, with each row corresponding to two points, for 2D array of indices of pairs if the metric learner uses a preprocessor.

Returns:

scoresnumpy.ndarray of shape=(n_pairs,): The opposite of the learned Mahalanobis distance for every pair.

See also

get_metric: a method that returns a function to compute the metric between two points. The difference with pair_score is that it works on two 1D arrays and cannot use a preprocessor. Besides, the returned function is independent of the metric learner and hence is not modified if the metric learner is.
Mahalanobis Distances: The section of the project documentation that describes Mahalanobis Distances.

predict(pairs)

Predicts the learned metric between input pairs. (For now it just calls decision function).

Returns the learned metric value between samples in every pair. It should ideally be low for similar samples and high for dissimilar samples.

Parameters:

pairsarray-like, shape=(n_pairs, 2, n_features) or (n_pairs, 2): 3D Array of pairs to predict, with each row corresponding to two points, or 2D array of indices of pairs if the metric learner uses a preprocessor.

Returns:

y_predictednumpy.ndarray of floats, shape=(n_constraints,): The predicted learned metric value between samples in every pair.

score(pairs, y)

Computes score of pairs similarity prediction.

Returns the roc_auc score of the fitted metric learner. It is computed in the following way: for every value of a threshold t we classify all pairs of samples where the predicted distance is inferior to t as belonging to the “similar” class, and the other as belonging to the “dissimilar” class, and we count false positive and true positives as in a classical roc_auc curve.

Parameters:

pairsarray-like, shape=(n_pairs, 2, n_features) or (n_pairs, 2): 3D Array of pairs, with each row corresponding to two points, or 2D array of indices of pairs if the metric learner uses a preprocessor.
yarray-like, shape=(n_constraints,): The corresponding labels.

Returns:

scorefloat: The roc_auc score.

score_pairs(pairs)

Returns the learned Mahalanobis distance between pairs.

This distance is defined as: $d_M(x, x') = \\sqrt{(x-x')^T M (x-x')}$ where M is the learned Mahalanobis matrix, for every pair of points x and x'. This corresponds to the euclidean distance between embeddings of the points in a new space, obtained through a linear transformation. Indeed, we have also: $d_M(x, x') = \\sqrt{(x_e - x_e')^T (x_e- x_e')}$, with $x_e = L x$ (See MahalanobisMixin).

Deprecated since version 0.7.0: Please use pair_distance instead.

Warning

This method will be removed in 0.8.0. Please refer to pair_distance or pair_score. This change will occur in order to add learners that don’t necessarily learn a Mahalanobis distance.

Parameters:

pairsarray-like, shape=(n_pairs, 2, n_features) or (n_pairs, 2): 3D Array of pairs to score, with each row corresponding to two points, for 2D array of indices of pairs if the metric learner uses a preprocessor.

Returns:

scoresnumpy.ndarray of shape=(n_pairs,): The learned Mahalanobis distance for every pair.

See also

get_metric: a method that returns a function to compute the metric between two points. The difference with score_pairs is that it works on two 1D arrays and cannot use a preprocessor. Besides, the returned function is independent of the metric learner and hence is not modified if the metric learner is.
Mahalanobis Distances: The section of the project documentation that describes Mahalanobis Distances.

set_decision_function_request(*, pairs: bool | None | str = '$UNCHANGED$') → ITML

Request metadata passed to the decision_function method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to decision_function if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to decision_function.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

pairsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for pairs parameter in decision_function.

Returns:

selfobject: The updated object.

Request metadata passed to the fit method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to fit if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to fit.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

boundsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for bounds parameter in fit.
calibration_paramsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for calibration_params parameter in fit.
pairsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for pairs parameter in fit.

Returns:

selfobject: The updated object.

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

set_predict_request(*, pairs: bool | None | str = '$UNCHANGED$') → ITML

Request metadata passed to the predict method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to predict if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to predict.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

pairsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for pairs parameter in predict.

Returns:

selfobject: The updated object.

set_score_request(*, pairs: bool | None | str = '$UNCHANGED$') → ITML

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config()). Please see User Guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANGED) retains the existing request. This allows you to change the request for some parameters and not others.

New in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

pairsstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED: Metadata routing for pairs parameter in score.

Returns:

selfobject: The updated object.

set_threshold(threshold)

Sets the threshold of the metric learner to the given value threshold.

See more in the User Guide.

Parameters:

thresholdfloat: The threshold value we want to set. It is the value to which the predicted distance for test pairs will be compared. If they are superior to the threshold they will be classified as similar (+1), and dissimilar (-1) if not.

Returns:

self_PairsClassifier: The pairs classifier with the new threshold set.

transform(X)

Embeds data points in the learned linear embedding space.

Transforms samples in X into X_embedded, samples inside a new embedding space such that: X_embedded = X.dot(L.T), where L is the learned linear transformation (See MahalanobisMixin).

Parameters:

Xnumpy.ndarray, shape=(n_samples, n_features): The data points to embed.

Returns:

X_embeddednumpy.ndarray, shape=(n_samples, n_components): The embedded data points.

Examples using `metric_learn.ITML`

Algorithms walkthrough

metric_learn.ITML

Examples using metric_learn.ITML

`metric_learn`.ITML

Examples using `metric_learn.ITML`