sklearn.cross_decomposition.CCA

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

CCA Canonical Correlation Analysis.

CCA inherits from PLS with mode=”B” and deflation_mode=”canonical”.

Read more in the User Guide.

Parameters

n_components : int, (default 2).

number of components to keep.

scale : boolean, (default True)

whether to scale the data?

max_iter : an integer, (default 500)

the maximum number of iterations of the NIPALS inner loop

tol : non-negative real, default 1e-06.

the tolerance used in the iterative algorithm

copy : boolean

Whether the deflation be done on a copy. Let the default value to True unless you don’t care about side effects

Attributes

x_weights_

(array, [p, n_components]) X block weights vectors.

y_weights_

(array, [q, n_components]) Y block weights vectors.

x_loadings_

(array, [p, n_components]) X block loadings vectors.

y_loadings_

(array, [q, n_components]) Y block loadings vectors.

x_scores_

(array, [n_samples, n_components]) X scores.

y_scores_

(array, [n_samples, n_components]) Y scores.

x_rotations_

(array, [p, n_components]) X block to latents rotations.

y_rotations_

(array, [q, n_components]) Y block to latents rotations.

n_iter_

(array-like) Number of iterations of the NIPALS inner loop for each component.

See also

PLSCanonical, PLSSVD

Notes

For each component k, find the weights u, v that maximizes max corr(Xk u, Yk v), such that |u| = |v| = 1

Note that it maximizes only the correlations between the scores.

The residual matrix of X (Xk+1) block is obtained by the deflation on the current X score: x_score.

The residual matrix of Y (Yk+1) block is obtained by deflation on the current Y score.

References

Jacob A. Wegelin. A survey of Partial Least Squares (PLS) methods, with emphasis on the two-block case. Technical Report 371, Department of Statistics, University of Washington, Seattle, 2000.

In french but still a reference: Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris: Editions Technic.

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)

Transform data back to its original space.

predict(X[, copy])

Apply the dimension reduction learned on the train data.

score(X, y[, sample_weight])

Return the coefficient of determination R^2 of the prediction.

set_params(**params)

Set the parameters of this estimator.

transform(X[, Y, copy])

Apply the dimension reduction learned on the train data.

__init__(n_components=2, scale=True, max_iter=500, tol=1e-06, copy=True)[source]

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

fit(X, Y)[source]

Fit model to data.

Parameters

X : array-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.

Y : array-like of shape (n_samples, n_targets)

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

fit_transform(X, y=None)[source]

Learn and apply the dimension reduction on the train data.

Parameters

X : array-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.

y : array-like of shape (n_samples, n_targets)

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

Returns

x_scores if Y is not given, (x_scores, y_scores) otherwise.

get_params(deep=True)[source]

Get parameters for this estimator.

Parameters

deep : bool, default=True

If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns

params : mapping of string to any

Parameter names mapped to their values.

inverse_transform(X)[source]

Transform data back to its original space.

Parameters

X : array-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.

Returns

x_reconstructed : array-like of shape (n_samples, n_features)

Notes

This transformation will only be exact if n_components=n_features

predict(X, copy=True)[source]

Apply the dimension reduction learned on the train data.

Parameters

X : array-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.

copy : boolean, default True

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

Notes

This call requires the estimation of a p x q matrix, which may be an issue in high dimensional space.

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

Return the coefficient of determination R^2 of the prediction.

The coefficient R^2 is defined as (1 - 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

X : array-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, shape = (n_samples, n_samples_fitted), where n_samples_fitted is the number of samples used in the fitting for the estimator.

y : array-like of shape (n_samples,) or (n_samples, n_outputs)

True values for X.

sample_weight : array-like of shape (n_samples,), default=None

Sample weights.

Returns

score : float

R^2 of self.predict(X) wrt. y.

Notes

The R2 score used when calling score on a regressor will use multioutput='uniform_average' from version 0.23 to keep consistent with r2_score. This will influence the score method of all the multioutput regressors (except for MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call r2_score directly or make a custom scorer with make_scorer (the built-in scorer 'r2' uses multioutput='uniform_average').

set_params(**params)[source]

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

**params : dict

Estimator parameters.

Returns

self : object

Estimator instance.

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

Apply the dimension reduction learned on the train data.

Parameters

X : array-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.

Y : array-like of shape (n_samples, n_targets)

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

copy : boolean, default True

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

Returns

x_scores if Y is not given, (x_scores, y_scores) otherwise.

Examples using sklearn.cross_decomposition.CCA