metric_learn
.NCA¶

class
metric_learn.
NCA
(init='auto', n_components=None, max_iter=100, tol=None, verbose=False, preprocessor=None, random_state=None)[source]¶ Neighborhood Components Analysis (NCA)
NCA is a distance metric learning algorithm which aims to improve the accuracy of nearest neighbors classification compared to the standard Euclidean distance. The algorithm directly maximizes a stochastic variant of the leaveoneout knearest neighbors(KNN) score on the training set. It can also learn a lowdimensional linear transformation of data that can be used for data visualization and fast classification.
Read more in the User Guide.
Parameters:  initstring or numpy array, optional (default=’auto’)
Initialization of the linear transformation. Possible options are ‘auto’, ‘pca’, ‘identity’, ‘random’, and a numpy array of shape (n_features_a, n_features_b).
 ‘auto’
Depending on
n_components
, the most reasonable initialization will be chosen. Ifn_components <= n_classes
we use ‘lda’, as it uses labels information. If not, butn_components < min(n_features, n_samples)
, we use ‘pca’, as it projects data in meaningful directions (those of higher variance). Otherwise, we just use ‘identity’. ‘pca’
n_components
principal components of the inputs passed tofit()
will be used to initialize the transformation. (Seesklearn.decomposition.PCA
) ‘lda’
min(n_components, n_classes)
most discriminative components of the inputs passed tofit()
will be used to initialize the transformation. (Ifn_components > n_classes
, the rest of the components will be zero.) (Seesklearn.discriminant_analysis.LinearDiscriminantAnalysis
) ‘identity’
If
n_components
is strictly smaller than the dimensionality of the inputs passed tofit()
, the identity matrix will be truncated to the firstn_components
rows. ‘random’
The initial transformation will be a random array of shape
(n_components, n_features)
. Each value is sampled from the standard normal distribution. numpy array
n_features_b must match the dimensionality of the inputs passed to
fit()
and n_features_a must be less than or equal to that. Ifn_components
is not None, n_features_a must match it.
 n_componentsint or None, optional (default=None)
Dimensionality of reduced space (if None, defaults to dimension of X).
 max_iterint, optional (default=100)
Maximum number of iterations done by the optimization algorithm.
 tolfloat, optional (default=None)
Convergence tolerance for the optimization.
 verbosebool, optional (default=False)
Whether to print progress messages or not.
 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 initialize the random transformation. Ifinit='pca'
,random_state
is passed as an argument to PCA when initializing the transformation.
References
[1] J. Goldberger, G. Hinton, S. Roweis, R. Salakhutdinov. Neighbourhood Components Analysis. NIPS 2005. [2] Wikipedia entry on Neighborhood Components Analysis Examples
>>> import numpy as np >>> from metric_learn import NCA >>> from sklearn.datasets import load_iris >>> iris_data = load_iris() >>> X = iris_data['data'] >>> Y = iris_data['target'] >>> nca = NCA(max_iter=1000) >>> nca.fit(X, Y)
Attributes:  n_iter_
int
The number of iterations the solver has run.
 components_
numpy.ndarray
, shape=(n_components, n_features) The learned linear transformation
L
.
Methods
fit
(X, y)X: data matrix, (n x d) y: scalar labels, (n) 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__
(init='auto', n_components=None, max_iter=100, tol=None, verbose=False, preprocessor=None, random_state=None)[source]¶ Initialize self. See help(type(self)) for accurate signature.

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