# sklearn.cross_decomposition.PLSCanonical¶

class sklearn.cross_decomposition.PLSCanonical(n_components=2, *, scale=True, algorithm='nipals', max_iter=500, tol=1e-06, copy=True)[source]

PLSCanonical implements the 2 blocks canonical PLS of the original Wold algorithm [Tenenhaus 1998] p.204, referred as PLS-C2A in [Wegelin 2000].

This class inherits from PLS with mode=”A” and deflation_mode=”canonical”, norm_y_weights=True and algorithm=”nipals”, but svd should provide similar results up to numerical errors.

Read more in the User Guide.

New in version 0.8.

Parameters
n_componentsint, default=2

Number of components to keep

scaleboolean, default=True

Option to scale data

algorithmstring, “nipals” or “svd”, default=’nipals’

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_iterint, default=500

the maximum number of iterations of the NIPALS inner loop (used only if algorithm=”nipals”)

tolnon-negative real, default=1e-06

the tolerance used in the iterative algorithm

copyboolean, default=True

Whether the deflation should be done on a copy. Let the default value to True unless you don’t care about side effect

Attributes
x_weights_array, shape = [p, n_components]

X block weights vectors.

y_weights_array, shape = [q, n_components]

Y block weights vectors.

x_scores_array, shape = [n_samples, n_components]

X scores.

y_scores_array, shape = [n_samples, n_components]

Y scores.

x_rotations_array, shape = [p, n_components]

X block to latents rotations.

y_rotations_array, shape = [q, n_components]

Y block to latents rotations.

coef_array of shape (p, q)

The coefficients of the linear model: Y = X coef_ + Err

n_iter_array-like

Number of iterations of the NIPALS inner loop for each component. Not useful if the algorithm provided is “svd”.

Notes

Matrices:

T: x_scores_
U: y_scores_
W: x_weights_
C: y_weights_


Are computed such that:

X = T P.T + Err and Y = U Q.T + Err
T[:, k] = Xk W[:, k] for k in range(n_components)
U[:, k] = Yk C[:, k] for k in range(n_components)
x_rotations_ = W (P.T W)^(-1)
y_rotations_ = C (Q.T C)^(-1)


where Xk and Yk are residual matrices at iteration k.

Slides explaining PLS

For each component k, find weights u, v that optimize:

max corr(Xk u, Yk v) * std(Xk u) std(Yk u), such that |u| = |v| = 1


Note that it maximizes both the correlations between the scores and the intra-block variances.

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. This performs a canonical symmetric version of the PLS regression. But slightly different than the CCA. This is mostly used for modeling.

This implementation provides the same results that the “plspm” package provided in the R language (R-project), using the function plsca(X, Y). Results are equal or collinear with the function pls(..., mode = "canonical") of the “mixOmics” package. The difference relies in the fact that mixOmics implementation does not exactly implement the Wold algorithm since it does not normalize y_weights to one.

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.

Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris: Editions Technic.

Examples

>>> from sklearn.cross_decomposition import PLSCanonical
>>> X = [[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [2.,5.,4.]]
>>> Y = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
>>> plsca = PLSCanonical(n_components=2)
>>> plsca.fit(X, Y)
PLSCanonical()
>>> X_c, Y_c = plsca.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. Transform data back to its original space. predict(X[, copy]) Apply the dimension reduction learned on the train data. score(X, y[, sample_weight]) Return 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.
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 and n_features is the number of predictors.

Yarray-like of 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(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 and n_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 and n_targets is the number of response variables.

Returns
x_scores if Y is not given, (x_scores, y_scores) otherwise.
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
paramsmapping of string to any

Parameter names mapped to their values.

inverse_transform(X)[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 and n_components is the number of pls components.

Returns
x_reconstructedarray-like of shape (n_samples, n_features)

Notes

This transformation will only be exact if n_components=n_features

predict(X, copy=True)[source]

Apply the dimension reduction learned on the train data.

Parameters
Xarray-like of 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(X, y, sample_weight=None)[source]

Return 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 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, shape = (n_samples, n_samples_fitted), where n_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 R2 score used when calling score on a regressor uses multioutput='uniform_average' from version 0.23 to keep consistent with default value of r2_score. This influences the score method of all the multioutput regressors (except for MultiOutputRegressor).

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 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
selfobject

Estimator instance.

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

Apply the dimension reduction learned on the train data.

Parameters
Xarray-like of 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 of shape (n_samples, n_targets), default=None

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.