# metric_learn.SCML¶

class metric_learn.SCML(beta=1e-05, basis='triplet_diffs', n_basis=None, gamma=0.005, max_iter=10000, output_iter=500, batch_size=10, verbose=False, preprocessor=None, random_state=None)[source]

Sparse Compositional Metric Learning (SCML)

SCML learns an squared Mahalanobis distance from triplet constraints by optimizing sparse positive weights assigned to a set of $$K$$ rank-one PSD bases. This can be formulated as an optimization problem with only $$K$$ parameters, that can be solved with an efficient stochastic composite scheme.

Read more in the User Guide.

Warning

SCML is still a bit experimental, don’t hesitate to report if something fails/doesn’t work as expected.

Parameters: beta: float (default=1e-5)L1 regularization parameter. basisstring or array-like, optional (default=’triplet_diffs’)Set of bases to construct the metric. Possible options are ‘triplet_diffs’, and an array-like of shape (n_basis, n_features). ‘triplet_diffs’The basis set is constructed from the differences between points of n_basis positive or negative pairs taken from the triplets constrains. array-likeA matrix of shape (n_basis, n_features), that will be used as the basis set for the metric construction. n_basisint, optionalNumber of basis to be yielded. In case it is not set it will be set based on basis. If no value is selected a default will be computed based on the input. gamma: float (default = 5e-3)Learning rate for the optimization algorithm. max_iterint (default = 100000)Number of iterations for the algorithm. output_iterint (default = 5000)Number of iterations to check current weights performance and output this information in case verbose is True. verbosebool, optionalIf True, prints information while learning. preprocessorarray-like, shape=(n_samples, n_features) or callableThe preprocessor to call to get triplets from indices. If array-like, triplets 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.

metric_learn.SCML_Supervised
The supervised version of the algorithm.
Supervised versions of weakly-supervised algorithms
The section of the project documentation that describes the supervised version of weakly supervised estimators.

References

 [1] Y. Shi, A. Bellet and F. Sha. Sparse Compositional Metric Learning.. (AAAI), 2014.
 [2] Adapted from original Matlab implementation._.

Examples

>>> from metric_learn import SCML
>>> triplets = [[[1.2, 7.5], [1.3, 1.5], [6.2, 9.7]],
>>>             [[1.3, 4.5], [3.2, 4.6], [5.4, 5.4]],
>>>             [[3.2, 7.5], [3.3, 1.5], [8.2, 9.7]],
>>>             [[3.3, 4.5], [5.2, 4.6], [7.4, 5.4]]]
>>> scml = SCML()
>>> scml.fit(triplets)

Attributes: components_numpy.ndarray, shape=(n_features, n_features)The linear transformation L deduced from the learned Mahalanobis metric (See function _components_from_basis_weights.)

Methods

 decision_function(triplets) Predicts differences between sample distances in input triplets. fit(triplets) Learn the SCML model. get_mahalanobis_matrix() Returns a copy of the Mahalanobis matrix learned by the metric learner. get_metric() Returns a function that takes as input two 1D arrays and outputs the learned metric score on these two points. get_params([deep]) Get parameters for this estimator. predict(triplets) Predicts the ordering between sample distances in input triplets. score(triplets) Computes score on input triplets. score_pairs(pairs) Returns the learned Mahalanobis distance between pairs. set_params(**params) Set the parameters of this estimator. transform(X) Embeds data points in the learned linear embedding space.
__init__(beta=1e-05, basis='triplet_diffs', n_basis=None, gamma=0.005, max_iter=10000, output_iter=500, batch_size=10, verbose=False, preprocessor=None, random_state=None)

Initialize self. See help(type(self)) for accurate signature.

decision_function(triplets)

Predicts differences between sample distances in input triplets.

For each triplet (X_a, X_b, X_c) in the samples, computes the difference between the learned distance of the second pair (X_a, X_c) minus the learned distance of the first pair (X_a, X_b). The higher it is, the more probable it is that the pairs in the triplets are presented in the right order, i.e. that the label of the triplet is 1. The lower it is, the more probable it is that the label of the triplet is -1.

Parameters: tripletarray-like, shape=(n_triplets, 3, n_features) or (n_triplets, 3)3D array of triplets to predict, with each row corresponding to three points, or 2D array of indices of triplets if the metric learner uses a preprocessor. decision_functionnumpy.ndarray of floats, shape=(n_constraints,)Metric differences.
fit(triplets)[source]

Learn the SCML model.

Parameters: tripletsarray-like, shape=(n_constraints, 3, n_features) or (n_constraints, 3)3D array-like of triplets of points or 2D array of triplets of indicators. Triplets are assumed to be ordered such that: d(triplets[i, 0],triplets[i, 1]) < d(triplets[i, 0], triplets[i, 2]). selfobjectReturns 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_metric()

Returns a function that takes as input two 1D arrays and outputs the learned metric score on these two points.

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_funfunctionThe function described above.

score_pairs
a method that returns the metric 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=TrueIf True, will return the parameters for this estimator and contained subobjects that are estimators. paramsmapping of string to anyParameter names mapped to their values.
predict(triplets)

Predicts the ordering between sample distances in input triplets.

For each triplets, returns 1 if the first element is closer to the second than to the last and -1 if not.

Parameters: tripletsarray-like, shape=(n_triplets, 3, n_features) or (n_triplets, 3)3D array of triplets to predict, with each row corresponding to three points, or 2D array of indices of triplets if the metric learner uses a preprocessor. predictionnumpy.ndarray of floats, shape=(n_constraints,)Predictions of the ordering of pairs, for each triplet.
score(triplets)

Computes score on input triplets.

Returns the accuracy score of the following classification task: a triplet (X_a, X_b, X_c) is correctly classified if the predicted similarity between the first pair (X_a, X_b) is higher than that of the second pair (X_a, X_c)

Parameters: tripletsarray-like, shape=(n_triplets, 3, n_features) or (n_triplets, 3)3D array of triplets to score, with each row corresponding to three points, or 2D array of indices of triplets if the metric learner uses a preprocessor. scorefloatThe triplets 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).

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

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_params(**params)

Set the parameters of this estimator.

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

Parameters: **paramsdictEstimator parameters. selfobjectEstimator instance.
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. X_embeddednumpy.ndarray, shape=(n_samples, n_components)The embedded data points.