`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”.

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(copy=True, max_iter=500, n_components=1, scale=True, tol=1e-06)
>>> 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.
`predict`(X[, copy])	Apply the dimension reduction learned on the train data.
`score`(X, y[, sample_weight])	Returns 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]¶

fit(X, Y)[source]¶

Fit model to data.

Parameters:

X : array-like, shape = [n_samples, n_features]

Training vectors, where n_samples in the number of samples and n_features is the number of predictors.

Y : array-like of response, shape = [n_samples, n_targets]

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

fit_transform(X, y=None, **fit_params)[source]¶

Learn and apply the dimension reduction on the train data.

Parameters:

X : array-like of predictors, shape = [n_samples, p]

Training vectors, where n_samples in the number of samples and p is the number of predictors.

Y : array-like of response, shape = [n_samples, q], optional

Training vectors, where n_samples in the number of samples and q 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. :

get_params(deep=True)[source]¶

Get parameters for this estimator.

Parameters:

deep: boolean, optional :

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.

predict(X, copy=True)[source]¶

Apply the dimension reduction learned on the train data.

Parameters:

X : array-like of predictors, shape = [n_samples, p]

Training vectors, where n_samples in the number of samples and p 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]¶

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

The coefficient R^2 is defined as (1 - u/v), where u is the regression sum of squares ((y_true - y_pred) ** 2).sum() and v is the residual sum of squares ((y_true - y_true.mean()) ** 2).sum(). Best possible score is 1.0, lower values are worse.

Parameters:

X : array-like, shape = (n_samples, n_features)

Test samples.

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

True values for X.

sample_weight : array-like, shape = [n_samples], optional

Sample weights.

Returns:

score : float

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

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 former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.