sklearn.cross_decomposition.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.

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_scores_ndarray of shape (n_samples, n_components)

Attribute x_scores_ was deprecated in version 0.24.

y_scores_ndarray of shape (n_samples, n_components)

Attribute y_scores_ was deprecated in version 0.24.

x_rotations_ndarray of shape (n_features, n_components)

The projection matrix used to transform X.

y_rotations_ndarray of shape (n_features, n_components)

The projection matrix used to transform Y.

coef_ndarray of shape (n_features, n_targets)

The coefficients of the linear model such that Y is approximated as Y = X @ coef_.

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.

New 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)

Methods

fit(X, Y)

Fit model to data.

fit_transform(X[, y])

Learn and apply the dimension reduction on the train data.

get_params([deep])

Get parameters for this estimator.

inverse_transform(X[, Y])

Transform data back to its original space.

predict(X[, copy])

Predict targets of given samples.

score(X, y[, sample_weight])

Return the coefficient of determination of the prediction.

set_params(**params)

Set the parameters of this estimator.

transform(X[, Y, copy])

Apply the dimension reduction.

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_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, n_components)

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

Returns
X_reconstructedndarray of shape (n_samples, n_features)

Return the reconstructed X data.

Y_reconstructedndarray 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.

property norm_y_weights

DEPRECATED: Attribute norm_y_weights was deprecated in version 0.24 and will be removed in 1.1 (renaming of 0.26).

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 and Y, 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 the coefficient of determination of the prediction.

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) wrt. 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_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.

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.

property x_mean_

DEPRECATED: Attribute x_mean_ was deprecated in version 0.24 and will be removed in 1.1 (renaming of 0.26).

property x_scores_

Attribute x_scores_ was deprecated in version 0.24.

property x_std_

DEPRECATED: Attribute x_std_ was deprecated in version 0.24 and will be removed in 1.1 (renaming of 0.26).

property y_mean_

DEPRECATED: Attribute y_mean_ was deprecated in version 0.24 and will be removed in 1.1 (renaming of 0.26).

property y_scores_

Attribute y_scores_ was deprecated in version 0.24.

property y_std_

DEPRECATED: Attribute y_std_ was deprecated in version 0.24 and will be removed in 1.1 (renaming of 0.26).

Examples using sklearn.cross_decomposition.CCA