Implementation:Scikit learn Scikit learn PLSRegression

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Cross Decomposition, Regression
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for Partial Least Squares regression provided by scikit-learn.

Description

PLSRegression, also known as PLS2 or PLS1 depending on the number of targets, is a cross-decomposition method that projects both the predictors (X) and the response (y) into a lower-dimensional space of latent variables while maximizing the covariance between them. It combines dimensionality reduction with regression, making it particularly effective when predictors are highly collinear or when there are more features than samples. The module also provides PLSCanonical and PLSSVD as related cross-decomposition algorithms.

Usage

Use PLSRegression when you have high-dimensional, possibly collinear predictor variables and need to build a regression model. It is commonly applied in chemometrics, spectroscopy, genomics, and neuroimaging where the number of features often exceeds the number of samples and ordinary least squares regression would be ill-conditioned.

Code Reference

Source Location

Repository: scikit-learn
File: sklearn/cross_decomposition/_pls.py

Signature

class PLSRegression(_PLS):
    def __init__(
        self,
        n_components=2,
        *,
        scale=True,
        max_iter=500,
        tol=1e-06,
        copy=True,
    ):

Import

from sklearn.cross_decomposition import PLSRegression

I/O Contract

Inputs

Name	Type	Required	Description
n_components	int	No	Number of components to keep. Should be in [1, n_features] (default=2).
scale	bool	No	Whether to scale X and y (default=True).
max_iter	int	No	Maximum number of iterations for the power method (default=500).
tol	float	No	Convergence tolerance for the power method (default=1e-06).
copy	bool	No	Whether to copy X and y in fit before centering/scaling (default=True).

Outputs

Name	Type	Description
x_weights_	ndarray of shape (n_features, n_components)	Left singular vectors of the cross-covariance matrices.
y_weights_	ndarray of shape (n_targets, n_components)	Right singular vectors of the cross-covariance matrices.
x_loadings_	ndarray of shape (n_features, n_components)	Loadings of X.
y_loadings_	ndarray of shape (n_targets, n_components)	Loadings of y.
x_scores_	ndarray of shape (n_samples, n_components)	Transformed training samples.
y_scores_	ndarray of shape (n_samples, n_components)	Transformed training targets.
x_rotations_	ndarray of shape (n_features, n_components)	Projection matrix used to transform X.
y_rotations_	ndarray of shape (n_targets, n_components)	Projection matrix used to transform y.
coef_	ndarray of shape (n_targets, n_features)	Coefficients of the linear model.
intercept_	ndarray of shape (n_targets,)	Intercepts of the linear model.
n_features_in_	int	Number of features seen during fit.

Usage Examples

Basic Usage

import numpy as np
from sklearn.cross_decomposition import PLSRegression

X = np.array([[1, 2, 3], [4, 5, 6], [7, 8, 9], [10, 11, 12]], dtype=float)
y = np.array([1, 2, 3, 4], dtype=float)

pls = PLSRegression(n_components=2)
pls.fit(X, y)
X_transformed = pls.transform(X)
y_pred = pls.predict(X)
print(X_transformed.shape)  # (4, 2)
print(y_pred.shape)  # (4, 1)
print(pls.coef_.shape)  # (1, 3)

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