9.12.3. sklearn.pls.CCA

class sklearn.pls.CCA(n_components=2, scale=True, algorithm='nipals', max_iter=500, tol=9.9999999999999995e-07, copy=True)

CCA Canonical Correlation Analysis. CCA inherits from PLS with mode=”B” and deflation_mode=”canonical”.

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] :

Training vectors, where n_samples in the number of samples and q is the number of response variables.

n_components: int, (default 2). :

number of components to keep.

scale: boolean, (default True) :

whether to scale the data?

algorithm: str, “nipals” or “svd” :

The algorithm used to estimate the weights. It will be called n_components times, i.e. once for each iteration of the outer loop.

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

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.pls import PLSCanonical, PLSRegression, 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(algorithm='nipals', 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)
predict(X[, copy])	Apply the dimension reduction learned on the train data.
set_params(**params)	Set the parameters of the estimator.
transform(X[, Y, copy])	Apply the dimension reduction learned on the train data.

__init__(n_components=2, scale=True, algorithm='nipals', max_iter=500, tol=9.9999999999999995e-07, copy=True)

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 require the estimation of a p x q matrix, which may be an issue in high dimensional space.

set_params(**params)

Set the parameters of the 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. :