sklearn.cross_decomposition.PLSRegression¶

class sklearn.cross_decomposition.PLSRegression(n_components=2, scale=True, max_iter=500, tol=1e-06, 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_componentsint, (default 2)

Number of components to keep.

scaleboolean, (default True)

whether to scale the data

max_iteran integer, (default 500)

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

tolnon-negative real

Tolerance used in the iterative algorithm default 1e-06.

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, [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_array-like

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

For each component k, find weights u, v that optimizes: max corr(Xk u, Yk v) * std(Xk u) std(Yk u), such that |u| = 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 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 (R-project):

• “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 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.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(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, max_iter=500, tol=1e-06, copy=True)[source]¶

Initialize self. See help(type(self)) for accurate signature.

fit(self, X, Y)[source]¶

Fit model to data.

Parameters

Xarray-like, 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, 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

Xarray-like, 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, shape = [n_samples, n_targets]

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(self, deep=True)[source]¶

Get parameters for this estimator.

Parameters

deepboolean, optional

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.

predict(self, X, copy=True)[source]¶

Apply the dimension reduction learned on the train data.

Parameters

Xarray-like, 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(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

Xarray-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.

yarray-like, shape = (n_samples) or (n_samples, n_outputs)

True values for X.

sample_weightarray-like, shape = [n_samples], optional

Sample weights.

Returns

scorefloat

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 r2_score. This will influence the score method of all the multioutput regressors (except for MultiOutputRegressor). To specify the default value manually and avoid the warning, please either call r2_score directly or make a custom scorer with 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

Xarray-like, 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, shape = [n_samples, n_targets]

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.