9.12.1. sklearn.pls.PLSRegression

class sklearn.pls.PLSRegression(n_components=2, scale=True, algorithm='nipals', max_iter=500, tol=9.9999999999999995e-07, copy=True)

PLS regression

PLSRegression inherits from PLS with mode=”A” and deflation_mode=”regression”. Also known PLS2 or PLS in case of one dimensional response.

Parameters :

X: array-like of predictors, shape = [n_samples, p] :

Training vectors, where n_samples in the number of samples and p is the number of predictors.

Y: array-like of response, shape = [n_samples, q] :

Training vectors, where n_samples in the number of samples and q is the number of response variables.

n_components: int, (default 2) :

Number of components to keep.

scale: boolean, (default True) :

whether to scale the 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 :

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

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

Notes

For each component k, find weights u, v that optimizes: max corr(Xk u, Yk v) * var(Xk u) var(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 X score. This performs the PLS regression known as PLS2. This mode is prediction oriented.

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.pls import PLSCanonical, PLSRegression, CCA
>>> 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(algorithm='nipals', copy=True, max_iter=500, n_components=2,
       scale=True, tol=1e-06)
>>> Y_pred = pls2.predict(X)

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.
coefs: array, [p, q]	The coeficients of the linear model: Y = X coefs + Err

Methods

fit(X, Y)
predict(X[, copy])	Apply the dimension reduction learned on the train data.
set_params(**params)	Set the parameters of the estimator.
transform(X[, Y, copy])	Apply the dimension reduction learned on the train data.

__init__(n_components=2, scale=True, algorithm='nipals', max_iter=500, tol=9.9999999999999995e-07, copy=True)

predict(X, copy=True)

Apply the dimension reduction learned on the train data. Parameters ———- X: array-like 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

Whether to copy X and Y, or perform in-place normalization.

Notes

This call require the estimation of a p x q matrix, which may be an issue in high dimensional space.

set_params(**params)

Set the parameters of the 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)

Apply the dimension reduction learned on the train data. Parameters ———- X: array-like of predictors, shape = [n_samples, p]

Training vectors, where n_samples in the number of samples and p is the number of predictors.

Y: array-like 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

Whether to copy X and Y, or perform in-place normalization.

Returns :x_scores if Y is not given, (x_scores, y_scores) otherwise. :