sklearn.cross_decomposition.CCA

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

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_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.

intercept_ndarray of shape (n_targets,)

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

New 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.

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_feature_names_out([input_features])	Get output feature names for transformation.
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.

property coef_

The coefficients of the linear model.

fit(X, Y)

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)

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)

Get output feature names for transformation.

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_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.

inverse_transform(X, Y=None)

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.

predict(X, copy=True)

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)

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)

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)

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.

Examples using sklearn.cross_decomposition.CCA

Compare cross decomposition methods

Compare cross decomposition methods

Multilabel classification

Multilabel classification