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.
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 : nonnegative real
Tolerance used in the iterative algorithm default 1e06.
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
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.
coef_: array, [p, q] :
The coefficients of the linear model:
Y = X coef_ + Err
n_iter_ : arraylike
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.
Slides explaining PLS <http://www.eigenvector.com/Docs/Wise_pls_properties.pdf>
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(copy=True, max_iter=500, n_components=2, scale=True, tol=1e06) >>> 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. predict
(X[, copy])Apply the dimension reduction learned on the train data. score
(X, y[, sample_weight])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. 
fit
(X, Y)[source]¶ Fit model to data.
Parameters: X : arraylike, shape = [n_samples, n_features]
Training vectors, where n_samples in the number of samples and n_features is the number of predictors.
Y : arraylike 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)[source]¶ Learn and apply the dimension reduction on the train data.
Parameters: X : arraylike of predictors, shape = [n_samples, p]
Training vectors, where n_samples in the number of samples and p is the number of predictors.
Y : arraylike 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, 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. :

get_params
(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.
Returns: params : mapping of string to any
Parameter names mapped to their values.

predict
(X, copy=True)[source]¶ Apply the dimension reduction learned on the train data.
Parameters: X : arraylike 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, 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]¶ 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 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 : arraylike, shape = (n_samples, n_features)
Test samples.
y : arraylike, shape = (n_samples) or (n_samples, n_outputs)
True values for X.
sample_weight : arraylike, shape = [n_samples], optional
Sample weights.
Returns: score : float
R^2 of self.predict(X) wrt. y.

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 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)[source]¶ Apply the dimension reduction learned on the train data.
Parameters: X : arraylike of predictors, shape = [n_samples, p]
Training vectors, where n_samples in the number of samples and p is the number of predictors.
Y : arraylike 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, 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. :