CCA#

class sklearn.cross_decomposition.CCA(n_components=2, *, scale=True, max_iter=500, tol=1e-06, copy=True)[source]#

Canonical Correlation Analysis, also known as “Mode B” PLS.

For a comparison between other cross decomposition algorithms, see Compare cross decomposition methods.

Read more in the User Guide.

Parameters:
n_componentsint, default=2

Number of components to keep. Should be in [1, min(n_samples, n_features, n_targets)].

scalebool, default=True

Whether to scale X and y.

max_iterint, default=500

The maximum number of iterations of the power method.

tolfloat, default=1e-06

The tolerance used as convergence criteria in the power method: the algorithm stops whenever the squared norm of u_i - u_{i-1} is less than tol, where u corresponds to the left singular vector.

copybool, default=True

Whether to copy X and y in fit before applying centering, and potentially scaling. If False, these operations will be done inplace, modifying both arrays.

Attributes:
x_weights_ndarray of shape (n_features, n_components)

The left singular vectors of the cross-covariance matrices of each iteration.

y_weights_ndarray of shape (n_targets, n_components)

The right singular vectors of the cross-covariance matrices of each iteration.

x_loadings_ndarray of shape (n_features, n_components)

The loadings of X.

y_loadings_ndarray of shape (n_targets, n_components)

The loadings of y.

x_rotations_ndarray of shape (n_features, n_components)

The projection matrix used to transform X.

y_rotations_ndarray of shape (n_targets, n_components)

The projection matrix used to transform y.

coef_ndarray of shape (n_targets, n_features)

The coefficients of the linear model such that y is approximated as y = X @ coef_.T + intercept_.

intercept_ndarray of shape (n_targets,)

The intercepts of the linear model such that y is approximated as y = X @ coef_.T + intercept_.

Added in version 1.1.

n_iter_list of shape (n_components,)

Number of iterations of the power method, for each component.

n_features_in_int

Number of features seen during fit.

feature_names_in_ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when X has feature names that are all strings.

Added in version 1.0.

See also

PLSCanonical

Partial Least Squares transformer and regressor.

PLSSvD

Partial Least Square SvD.

Examples

>>> from sklearn.cross_decomposition import CCA
>>> X = [[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [3.,5.,4.]]
>>> y = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
>>> cca = CCA(n_components=1)
>>> cca.fit(X, y)
CCA(n_components=1)
>>> X_c, y_c = cca.transform(X, y)
fit(X, y)[source]#

Fit model to data.

Parameters:
Xarray-like of shape (n_samples, n_features)

Training vectors, where n_samples is the number of samples and n_features is the number of predictors.

yarray-like of shape (n_samples,) or (n_samples, n_targets)

Target vectors, where n_samples is the number of samples and n_targets is the number of response variables.

Returns:
selfobject

Fitted model.

fit_transform(X, y=None)[source]#

Learn and apply the dimension reduction on the train data.

Parameters:
Xarray-like of shape (n_samples, n_features)

Training vectors, where n_samples is the number of samples and n_features is the number of predictors.

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

Target vectors, where n_samples is the number of samples and n_targets is the number of response variables.

Returns:
selfndarray of shape (n_samples, n_components)

Return x_scores if y is not given, (x_scores, y_scores) otherwise.

get_feature_names_out(input_features=None)[source]#

Get output feature names for transformation.

The feature names out will prefixed by the lowercased class name. For example, if the transformer outputs 3 features, then the feature names out are: ["class_name0", "class_name1", "class_name2"].

Parameters:
input_featuresarray-like of str or None, default=None

Only used to validate feature names with the names seen in fit.

Returns:
feature_names_outndarray of str objects

Transformed feature names.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:
routingMetadataRequest

A MetadataRequest encapsulating routing information.

get_params(deep=True)[source]#

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.

inverse_transform(X, y=None)[source]#

Transform data back to its original space.

Parameters:
Xarray-like of shape (n_samples, n_components)

New data, where n_samples is the number of samples and n_components is the number of pls components.

yarray-like of shape (n_samples,) or (n_samples, n_components)

New target, where n_samples is the number of samples and n_components is the number of pls components.

Returns:
X_originalndarray of shape (n_samples, n_features)

Return the reconstructed X data.

y_originalndarray of shape (n_samples, n_targets)

Return the reconstructed X target. Only returned when y is given.

Notes

This transformation will only be exact if n_components=n_features.

predict(X, copy=True)[source]#

Predict targets of given samples.

Parameters:
Xarray-like of shape (n_samples, n_features)

Samples.

copybool, default=True

Whether to copy X or perform in-place normalization.

Returns:
y_predndarray of shape (n_samples,) or (n_samples, n_targets)

Returns predicted values.

Notes

This call requires the estimation of a matrix of shape (n_features, n_targets), which may be an issue in high dimensional space.

score(X, y, sample_weight=None)[source]#

Return coefficient of determination on test data.

The coefficient of determination, \(R^2\), is defined as \((1 - \frac{u}{v})\), where \(u\) is the residual sum of squares ((y_true - y_pred)** 2).sum() and \(v\) is the total sum of squares ((y_true - y_true.mean()) ** 2).sum(). The best possible score is 1.0 and it can be negative (because the model can be arbitrarily worse). A constant model that always predicts the expected value of y, disregarding the input features, would get a \(R^2\) score of 0.0.

Parameters:
Xarray-like of shape (n_samples, n_features)

Test samples. For some estimators this may be a precomputed kernel matrix or a list of generic objects instead with shape (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

yarray-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.

sample_weightarray-like of shape (n_samples,), default=None

Sample weights.

Returns:
scorefloat

\(R^2\) of self.predict(X) w.r.t. y.

Notes

The \(R^2\) score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

set_output(*, transform=None)[source]#

Set output container.

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

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

Configure output of transform and fit_transform.

  • "default": Default output format of a transformer

  • "pandas": DataFrame output

  • "polars": Polars output

  • None: Transform configuration is unchanged

Added in version 1.4: "polars" option was added.

Returns:
selfestimator instance

Estimator instance.

set_params(**params)[source]#

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.

set_predict_request(*, copy: bool | None | str = '$UNCHANGED$') → CCA[source]#

Configure whether metadata should be requested to be passed to the predict method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to predict 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 predict.

  • 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.

Added in version 1.3.

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

Metadata routing for copy parameter in predict.

Returns:
selfobject

The updated object.

set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → CCA[source]#

Configure whether metadata should be requested to be passed to the score method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to score 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 score.

  • 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.

Added in version 1.3.

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

Metadata routing for sample_weight parameter in score.

Returns:
selfobject

The updated object.

set_transform_request(*, copy: bool | None | str = '$UNCHANGED$') → CCA[source]#

Configure whether metadata should be requested to be passed to the transform method.

Note that this method is only relevant when this estimator is used as a sub-estimator within a meta-estimator and metadata routing is enabled with enable_metadata_routing=True (see sklearn.set_config). Please check the User Guide on how the routing mechanism works.

The options for each parameter are:

  • True: metadata is requested, and passed to transform 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 transform.

  • 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.

Added in version 1.3.

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

Metadata routing for copy parameter in transform.

Returns:
selfobject

The updated object.

transform(X, y=None, copy=True)[source]#

Apply the dimension reduction.

Parameters:
Xarray-like of shape (n_samples, n_features)

Samples to transform.

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

Target vectors.

copybool, default=True

Whether to copy X and y, or perform in-place normalization.

Returns:
x_scores, y_scoresarray-like or tuple of array-like

Return x_scores if y is not given, (x_scores, y_scores) otherwise.