sklearn.cross_decomposition
.CCA¶
- class sklearn.cross_decomposition.CCA(n_components=2, *, scale=True, max_iter=500, tol=1e-06, copy=True)[source]¶
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
andY
.- 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 thantol
, whereu
corresponds to the left singular vector.- copybool, default=True
Whether to copy
X
andY
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 asY = 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)[source]¶
Fit model to data.
- Parameters
- Xarray-like of shape (n_samples, n_features)
Training vectors, where
n_samples
is the number of samples andn_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 andn_targets
is the number of response variables.
- Returns
- selfobject
Fitted model.
- fit_transform(X, y=None)[source]¶
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 andn_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 andn_targets
is the number of response variables.
- Returns
- selfndarray of shape (n_samples, n_components)
Return
x_scores
ifY
is not given,(x_scores, y_scores)
otherwise.
- get_feature_names_out(input_features=None)[source]¶
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)[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
- paramsdict
Parameter names mapped to their values.
- inverse_transform(X, Y=None)[source]¶
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 andn_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 andn_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 whenY
is given.
Notes
This transformation will only be exact if
n_components=n_features
.
- predict(X, copy=True)[source]¶
Predict targets of given samples.
- Parameters
- Xarray-like of shape (n_samples, n_features)
Samples.
- copybool, default=True
Whether to copy
X
andY
, 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)[source]¶
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 ofy
, 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)
, wheren_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 usesmultioutput='uniform_average'
from version 0.23 to keep consistent with default value ofr2_score
. This influences thescore
method of all the multioutput regressors (except forMultiOutputRegressor
).
- set_params(**params)[source]¶
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)[source]¶
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
andY
, or perform in-place normalization.
- Returns
- x_scores, y_scoresarray-like or tuple of array-like
Return
x_scores
ifY
is not given,(x_scores, y_scores)
otherwise.