sklearn.cross_decomposition.PLSRegression¶

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

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”.

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

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| = 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 PLSCanonical, 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=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 coefficients of the linear model: Y = X coefs + Err

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)	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.

__init__(n_components=2, scale=True, max_iter=500, tol=1e-06, copy=True)¶

fit(X, Y)¶

Fit model to data.

Parameters :

X : array-like, shape = [n_samples, n_features]

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

Y : array-like 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)¶

Learn and apply the dimension reduction 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. :

get_params(deep=True)¶

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)¶

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

score(X, y)¶

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, lower values are worse.

Parameters :

X : array-like, shape = (n_samples, n_features)

Test samples.

y : array-like, shape = (n_samples,)

True values for X.

Returns :

score : float

R^2 of self.predict(X) wrt. y.

set_params(**params)¶

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)¶

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. :