sklearn.cross_decomposition
.PLSRegression¶

class
sklearn.cross_decomposition.
PLSRegression
(n_components=2, *, scale=True, max_iter=500, tol=1e06, copy=True)[source]¶ PLS regression
PLSRegression implements the PLS 2 blocks regression known as PLS2 or PLS1 in case of one dimensional response. This class inherits from _PLS with mode=”A”, deflation_mode=”regression”, norm_y_weights=False and algorithm=”nipals”.
Read more in the User Guide.
New in version 0.8.
 Parameters
 n_componentsint, default=2
Number of components to keep.
 scaleboolean, default=True
whether to scale the data
 max_iterint, default=500
the maximum number of iterations of the NIPALS inner loop (used only if algorithm=”nipals”)
 tolnonnegative real, default=1e06
Tolerance used in the iterative algorithm default 1e06.
 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_ndarray of shape (p, n_components)
X block weights vectors.
 y_weights_ndarray of shape (q, n_components)
Y block weights vectors.
 x_loadings_ndarray of shape (p, n_components)
X block loadings vectors.
 y_loadings_ndarray of shape (q, n_components)
Y block loadings vectors.
 x_scores_ndarray of shape (n_samples, n_components)
X scores.
 y_scores_ndarray of shape (n_samples, n_components)
Y scores.
 x_rotations_ndarray of shape (p, n_components)
X block to latents rotations.
 y_rotations_ndarray of shape (q, n_components)
Y block to latents rotations.
 x_mean_ndarray of shape (p,)
X mean for each predictor.
 y_mean_ndarray of shape (q,)
Y mean for each response variable.
 x_std_ndarray of shape (p,)
X standard deviation for each predictor.
 y_std_ndarray of shape (q,)
Y standard deviation for each response variable.
 coef_ndarray of shape (p, q)
The coefficients of the linear model:
Y = X coef_ + Err
 n_iter_ndarray of shape (n_components,)
Number of iterations of the NIPALS inner loop for each component.
Notes
Matrices:
T: x_scores_ U: y_scores_ W: x_weights_ C: y_weights_ P: x_loadings_ Q: y_loadings_
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.
For each component k, find weights u, v that optimizes:
max corr(Xk u, Yk v) * std(Xk u) std(Yk u)
, such thatu = 1
Note that it maximizes both the correlations between the scores and the intrablock 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 X score. This performs the PLS regression known as PLS2. This mode is prediction oriented.
This implementation provides the same results that 3 PLS packages provided in the R language (Rproject):
“mixOmics” with function pls(X, Y, mode = “regression”)
“plspm ” with function plsreg2(X, Y)
“pls” with function oscorespls.fit(X, Y)
References
Jacob A. Wegelin. A survey of Partial Least Squares (PLS) methods, with emphasis on the twoblock 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 PLSRegression >>> 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]] >>> pls2 = PLSRegression(n_components=2) >>> pls2.fit(X, Y) PLSRegression() >>> Y_pred = pls2.predict(X)
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
 Xarraylike of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and n_features is the number of predictors.
 Yarraylike 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
 Xarraylike of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and n_features is the number of predictors.
 yarraylike 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
 Xarraylike 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_reconstructedarraylike 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
 Xarraylike 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 inplace 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
 Xarraylike 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.
 yarraylike of shape (n_samples,) or (n_samples, n_outputs)
True values for X.
 sample_weightarraylike 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 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 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
 Xarraylike of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and n_features is the number of predictors.
 Yarraylike 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 inplace normalization.
 Returns
 x_scores if Y is not given, (x_scores, y_scores) otherwise.