# metric_learn.RCA

class metric_learn.RCA(n_components=None, preprocessor=None)[source]

Relevant Components Analysis (RCA)

RCA learns a full rank Mahalanobis distance metric based on a weighted sum of in-chunklets covariance matrices. It applies a global linear transformation to assign large weights to relevant dimensions and low weights to irrelevant dimensions. Those relevant dimensions are estimated using “chunklets”, subsets of points that are known to belong to the same class.

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).

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]

Noam Shental, et al. Adjustment learning and relevant component analysis . ECCV 2002.

Examples

>>> from metric_learn import RCA
>>> X = [[-0.05,  3.0],[0.05, -3.0],
>>>     [0.1, -3.55],[-0.1, 3.55],
>>>     [-0.95, -0.05],[0.95, 0.05],
>>>     [0.4,  0.05],[-0.4, -0.05]]
>>> chunks = [0, 0, 1, 1, 2, 2, 3, 3]
>>> rca = RCA()
>>> rca.fit(X, chunks)

Attributes:
components_numpy.ndarray, shape=(n_components, n_features)

The learned linear transformation L.

Methods

 fit(X, chunks) Learn the RCA model. fit_transform(X[, y]) Fit to data, then transform it. Returns a copy of the Mahalanobis matrix learned by the metric learner. Get metadata routing of this object. 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. score_pairs(pairs) Returns the learned Mahalanobis distance between pairs. set_fit_request(*[, chunks]) Request metadata passed to the fit method. set_output(*[, transform]) Set output container. set_params(**params) Set the parameters of this estimator. Embeds data points in the learned linear embedding space.
__init__(n_components=None, preprocessor=None)[source]
fit(X, chunks)[source]

Learn the RCA model.

Parameters:
data(n x d) data matrix

Each row corresponds to a single instance

chunks(n,) array of ints

When chunks[i] == -1, point i doesn’t belong to any chunklet. When chunks[i] == j, point i belongs to chunklet j.

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:
Xarray-like of shape (n_samples, n_features)

Input samples.

yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None

Target values (None for unsupervised transformations).

**fit_paramsdict

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 metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

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.

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.

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.

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.

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.

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_fit_request(*, chunks: = '$UNCHANGED$') RCA

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:
chunksstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

Metadata routing for chunks parameter in fit.

Returns:
selfobject

The updated object.

set_output(*, transform=None)

Set output container.

See Introducing the set_output API for an example on how to use the API.

Parameters:
transform{“default”, “pandas”}, default=None

Configure output of transform and fit_transform.

• “default”: Default output format of a transformer

• “pandas”: DataFrame output

• None: Transform configuration is unchanged

Returns:
selfestimator instance

Estimator instance.

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.

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.RCA

Algorithms walkthrough

Algorithms walkthrough