metric_learn
.LSML_Supervised¶

class
metric_learn.
LSML_Supervised
(tol=0.001, max_iter=1000, prior='identity', num_constraints=None, weights=None, verbose=False, preprocessor=None, random_state=None)[source]¶ Supervised version of Least Squaredresidual Metric Learning (LSML)
LSML_Supervised
creates quadruplets from labeled samples by taking two samples from the same class, and two samples from different classes. This way it builds quadruplets where the two first points must be more similar than the two last points.Parameters:  tolfloat, optional (default=1e3)
Convergence tolerance of the optimization procedure.
 max_iterint, optional (default=1000)
Number of maximum iterations of the optimization procedure.
 priorstring or numpy array, optional (default=’identity’)
Prior to set for the metric. Possible options are ‘identity’, ‘covariance’, ‘random’, and a numpy array of shape (n_features, n_features). For LSML, 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 initial Mahalanobis matrix will be a random positive definite (PD) matrix of shape
(n_features, n_features)
, generated usingsklearn.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.
 num_constraints: int, optional (default=None)
Number of constraints to generate. If None, default to
20 * num_classes**2
. weights(num_constraints,) array of floats, optional (default=None)
Relative weight given to each constraint. If None, defaults to uniform weights.
 verbosebool, optional (default=False)
If True, prints information while learning
 preprocessorarraylike, shape=(n_samples, n_features) or callable
The preprocessor to call to get tuples from indices. If arraylike, 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
init='random'
,random_state
is used to set the random prior. In any case,random_state
is also used to randomly sample constraints from labels.
Examples
>>> from metric_learn import LSML_Supervised >>> from sklearn.datasets import load_iris >>> iris_data = load_iris() >>> X = iris_data['data'] >>> Y = iris_data['target'] >>> lsml = LSML_Supervised(num_constraints=200) >>> lsml.fit(X, Y)
Attributes:  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 functioncomponents_from_metric
.)
Methods
fit
(X, y)Create constraints from labels and learn the LSML model. fit_transform
(X[, y])Fit to data, then transform it. 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. 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__
(tol=0.001, max_iter=1000, prior='identity', num_constraints=None, weights=None, verbose=False, preprocessor=None, random_state=None)[source]¶ Initialize self. See help(type(self)) for accurate signature.

fit
(X, y)[source]¶ Create constraints from labels and learn the LSML model.
Parameters:  X(n x d) matrix
Input data, where each row corresponds to a single instance.
 y(n) arraylike
Data labels.

fit_transform
(X, y=None, **fit_params)¶ Fit to data, then transform it.
Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.
Parameters:  X{arraylike, sparse matrix, dataframe} of shape (n_samples, n_features)
 yndarray of shape (n_samples,), default=None
Target values.
 **fit_paramsdict
Additional fit parameters.
Returns:  X_newndarray array of shape (n_samples, n_features_new)
Transformed array.

get_mahalanobis_matrix
()¶ Returns a copy of the Mahalanobis matrix learned by the metric learner.
Returns:  M
numpy.ndarray
, shape=(n_features, n_features) The copy of the learned Mahalanobis matrix.
 M

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 scikitlearn’s estimators.Returns:  metric_funfunction
The function described above.
See also
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=True
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:  paramsmapping of string to any
Parameter names mapped to their values.

score_pairs
(pairs)¶ Returns the learned Mahalanobis distance between pairs.
This distance is defined as: \(d_M(x, x') = \sqrt{(xx')^T M (xx')}\) where
M
is the learned Mahalanobis matrix, for every pair of pointsx
andx'
. 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 \(x_e = L x\) (SeeMahalanobisMixin
).Parameters:  pairsarraylike, 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:  scores
numpy.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_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:  **paramsdict
Estimator parameters.
Returns:  selfobject
Estimator instance.

transform
(X)¶ Embeds data points in the learned linear embedding space.
Transforms samples in
X
intoX_embedded
, samples inside a new embedding space such that:X_embedded = X.dot(L.T)
, whereL
is the learned linear transformation (SeeMahalanobisMixin
).Parameters:  X
numpy.ndarray
, shape=(n_samples, n_features) The data points to embed.
Returns:  X_embedded
numpy.ndarray
, shape=(n_samples, n_components) The embedded data points.
 X