# 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.

Parameters: n_components : int, (default 2). Number of components to keep scale : boolean, (default True) Option to scale data algorithm : string, “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, 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 x_weights_ : array, shape = [p, n_components] X block weights vectors. y_weights_ : array, shape = [q, n_components] Y block weights vectors. x_loadings_ : array, shape = [p, n_components] X block loadings vectors. y_loadings_ : array, shape = [q, n_components] Y block loadings 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. 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(algorithm='nipals', copy=True, max_iter=500, n_components=2,
scale=True, tol=1e-06)
>>> X_c, Y_c = plsca.transform(X, Y)


Methods

 fit(self, X, Y) Fit model to data. fit_transform(self, X[, y]) Learn and apply the dimension reduction on the train data. get_params(self[, deep]) Get parameters for this estimator. predict(self, X[, copy]) Apply the dimension reduction learned on the train data. score(self, X, y[, sample_weight]) Returns the coefficient of determination R^2 of the prediction. set_params(self, \*\*params) Set the parameters of this estimator. transform(self, X[, Y, copy]) Apply the dimension reduction learned on the train data.
__init__(self, n_components=2, scale=True, algorithm=’nipals’, max_iter=500, tol=1e-06, copy=True)[source]
fit(self, X, Y)[source]

Fit model to data.

Parameters: X : array-like, shape = [n_samples, n_features] Training vectors, where n_samples is the number of samples and n_features is the number of predictors. Y : array-like, 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(self, X, y=None)[source]

Learn and apply the dimension reduction on the train data.

Parameters: X : array-like, shape = [n_samples, n_features] Training vectors, where n_samples is the number of samples and n_features is the number of predictors. y : array-like, shape = [n_samples, n_targets] Target vectors, where n_samples is the number of samples and n_targets is the number of response variables. x_scores if Y is not given, (x_scores, y_scores) otherwise.
get_params(self, 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. params : mapping of string to any Parameter names mapped to their values.
predict(self, X, copy=True)[source]

Apply the dimension reduction learned on the train data.

Parameters: X : array-like, shape = [n_samples, n_features] Training vectors, where n_samples is the number of samples and n_features 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(self, 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 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: X : array-like, shape = (n_samples, n_features) Test samples. For some estimators this may be a precomputed kernel matrix instead, shape = (n_samples, n_samples_fitted], where n_samples_fitted is the number of samples used in the fitting for the estimator. 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. score : float R^2 of self.predict(X) wrt. y.

Notes

The R2 score used when calling score on a regressor will use multioutput='uniform_average' from version 0.23 to keep consistent with metrics.r2_score. This will influence the score method of all the multioutput regressors (except for multioutput.MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call metrics.r2_score directly or make a custom scorer with metrics.make_scorer (the built-in scorer 'r2' uses multioutput='uniform_average').

set_params(self, **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.

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

Apply the dimension reduction learned on the train data.

Parameters: X : array-like, shape = [n_samples, n_features] Training vectors, where n_samples is the number of samples and n_features is the number of predictors. Y : array-like, shape = [n_samples, n_targets] Target vectors, where n_samples is the number of samples and n_targets is the number of response variables. copy : boolean, default True Whether to copy X and Y, or perform in-place normalization. x_scores if Y is not given, (x_scores, y_scores) otherwise.