metric_learn.LFDA

class metric_learn.LFDA(n_components=None, k=None, embedding_type='weighted', preprocessor=None)[source]

Local Fisher Discriminant Analysis for Supervised Dimensionality Reduction

LFDA is a linear supervised dimensionality reduction method. It is particularly useful when dealing with multimodality, where one ore more classes consist of separate clusters in input space. The core optimization problem of LFDA is solved as a generalized eigenvalue problem.

Read more in the User Guide.

Parameters:
n_componentsint or None, optional (default=None)

Dimensionality of reduced space (if None, defaults to dimension of X).

kint, optional (default=None)

Number of nearest neighbors used in local scaling method. If None, defaults to min(7, n_features - 1).

embedding_typestr, optional (default: ‘weighted’)

Type of metric in the embedding space.

‘weighted’

weighted eigenvectors

‘orthonormalized’

orthonormalized

‘plain’

raw eigenvectors

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].

References

[1]Masashi Sugiyama. Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis. JMLR 2007.
[2]Yuan Tang. Local Fisher Discriminant Analysis on Beer Style Clustering.

Examples

>>> import numpy as np
>>> from metric_learn import LFDA
>>> from sklearn.datasets import load_iris
>>> iris_data = load_iris()
>>> X = iris_data['data']
>>> Y = iris_data['target']
>>> lfda = LFDA(k=2, dim=2)
>>> lfda.fit(X, Y)
Attributes:
components_numpy.ndarray, shape=(n_components, n_features)

The learned linear transformation L.

Methods

fit(X, y) Fit the LFDA 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__(n_components=None, k=None, embedding_type='weighted', preprocessor=None)[source]

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

fit(X, y)[source]

Fit the LFDA model.

Parameters:
X(n, d) array-like

Input data.

y(n,) array-like

Class labels, one per point of data.

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{array-like, 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:
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_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: \(d_M(x, x') = \sqrt{(x-x')^T M (x-x')}\) 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 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 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.LFDA