sklearn.cross_decomposition
.CCA¶

class
sklearn.cross_decomposition.
CCA
(n_components=2, scale=True, max_iter=500, tol=1e06, 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_componentsint, (default 2).
number of components to keep.
 scaleboolean, (default True)
whether to scale the data?
 max_iteran integer, (default 500)
the maximum number of iterations of the NIPALS inner loop
 tolnonnegative real, default 1e06.
the tolerance used in the iterative algorithm
 copyboolean
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_arraylike
Number of iterations of the NIPALS inner loop for each component.
See also
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 twoblock 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
(self, X, Y)Fit model to data.
fit_transform
(self, X[, y])Learn and apply the dimension reduction on the train data.
get_params
(self[, deep])Get parameters for this estimator.
inverse_transform
(self, X)Transform data back to its original space.
predict
(self, X[, copy])Apply the dimension reduction learned on the train data.
score
(self, X, y[, sample_weight])Return the coefficient of determination R^2 of the prediction.
set_params
(self, \*\*params)Set the parameters of this estimator.
transform
(self, X[, Y, copy])Apply the dimension reduction learned on the train data.

__init__
(self, n_components=2, scale=True, max_iter=500, tol=1e06, copy=True)[source]¶ Initialize self. See help(type(self)) for accurate signature.

fit
(self, X, Y)[source]¶ Fit model to data.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and n_features is the number of predictors.
 Yarraylike 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
(self, X, y=None)[source]¶ Learn and apply the dimension reduction on the train data.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and n_features is the number of predictors.
 yarraylike 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
(self, 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
 paramsmapping of string to any
Parameter names mapped to their values.

inverse_transform
(self, X)[source]¶ Transform data back to its original space.
 Parameters
 Xarraylike 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_reconstructedarraylike of shape (n_samples, n_features)
Notes
This transformation will only be exact if n_components=n_features

predict
(self, X, copy=True)[source]¶ Apply the dimension reduction learned on the train data.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and n_features is the number of predictors.
 copyboolean, default True
Whether to copy X and Y, or perform inplace normalization.
Notes
This call requires the estimation of a p x q matrix, which may be an issue in high dimensional space.

score
(self, 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
 Xarraylike 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.
 yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for X.
 sample_weightarraylike of shape (n_samples,), default=None
Sample weights.
 Returns
 scorefloat
R^2 of self.predict(X) wrt. y.
Notes
The R2 score used when calling
score
on a regressor will usemultioutput='uniform_average'
from version 0.23 to keep consistent withr2_score
. This will influence thescore
method of all the multioutput regressors (except forMultiOutputRegressor
). To specify the default value manually and avoid the warning, please either callr2_score
directly or make a custom scorer withmake_scorer
(the builtin scorer'r2'
usesmultioutput='uniform_average'
).

set_params
(self, **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
 **paramsdict
Estimator parameters.
 Returns
 selfobject
Estimator instance.

transform
(self, X, Y=None, copy=True)[source]¶ Apply the dimension reduction learned on the train data.
 Parameters
 Xarraylike of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and n_features is the number of predictors.
 Yarraylike 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.
 copyboolean, default True
Whether to copy X and Y, or perform inplace normalization.
 Returns
 x_scores if Y is not given, (x_scores, y_scores) otherwise.