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
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
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 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)
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. - __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, sample_weight=None)¶
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.
sample_weight : array-like, shape = [n_samples], optional
Sample weights.
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. :