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_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

tolnon-negative real, default 1e-06.

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_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(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.
predict(self, X[, copy])	Apply the dimension reduction learned on the train data.
score(self, X, y[, sample_weight])	Returns 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=1e-06, copy=True)[source]¶

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

fit(self, X, Y)[source]¶

Fit model to data.

Parameters

Xarray-like, 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, 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

Xarray-like, 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, 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

deepboolean, optional

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.

predict(self, X, copy=True)[source]¶

Apply the dimension reduction learned on the train data.

Parameters

Xarray-like, 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 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(self, X, y, sample_weight=None)[source]¶

Returns 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

Xarray-like, shape = (n_samples, n_features)

Test samples. For some estimators this may be a precomputed kernel matrix instead, shape = (n_samples, n_samples_fitted], where n_samples_fitted is the number of samples used in the fitting for the estimator.

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

True values for X.

sample_weightarray-like, shape = [n_samples], optional

Sample weights.

Returns

scorefloat

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(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.

Returns

self

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

Apply the dimension reduction learned on the train data.

Parameters

Xarray-like, 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, 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 in-place normalization.

Returns

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