sklearn.cross_decomposition.CCA¶
- class sklearn.cross_decomposition.CCA(n_components=2, scale=True, max_iter=500, tol=1e-06, copy=True)¶
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 (used only if algorithm=”nipals”)
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
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 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)
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. 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) 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)¶
- fit(X, Y)¶
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)¶
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
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)¶
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)¶
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
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)¶
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,)
True values for X.
Returns : score : float
R^2 of self.predict(X) wrt. y.
- set_params(**params)¶
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.
Returns : self :
- transform(X, Y=None, copy=True)¶
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.
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
Whether to copy X and Y, or perform in-place normalization.
Returns : x_scores if Y is not given, (x_scores, y_scores) otherwise. :