Class PLSRegressionScikitsLearnNode

PLS regression (Also known PLS2 or PLS in case of one dimensional
response). PLSregression inherits from PLS with mode="A" and
deflation_mode="regression".
This node has been automatically generated by wrapping the ``scikits.learn.pls.PLSRegression`` class
from the ``sklearn`` library.  The wrapped instance can be accessed
through the ``scikits_alg`` attribute.
**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, number of components to keep. (default 2).

scale: boolean, scale data? (default True)

algorithm: str "nipals" or "svd" the algorithm used to estimate the
    weights, it will be called "n_components" time ie.: for each iteration
    of the outer loop.

max_iter: an integer, the maximum number of iterations (default 500) of the
    NIPALS inner loop (used only if algorithm="nipals")

tol: a not negative real, the tolerance used in the iterative algorithm
     default 1e-06.

copy: boolean, should the deflation been made 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 coeficients 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| = |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.

**Examples**

>>> from scikits.learn.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()
>>> pls2.fit(X, Y, n_components=2)
PLSRegression(scale=True, algorithm='nipals', max_iter=500, n_components=2,
       tol=1e-06, copy=True)
>>> Y_pred = pls2.predict(X)

**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.

Overrides: object.__init__

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.
This node has been automatically generated by wrapping the ``scikits.learn.pls.PLSRegression`` class
from the ``sklearn`` library.  The wrapped instance can be accessed
through the ``scikits_alg`` attribute.
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: X and Y have to be normalize, do it on a copy or in place
    with side effect!

Returns

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

Overrides: Node.execute

Overrides: Node.is_invertible

(inherited documentation)

Returns: bool

A boolean indication whether the node can be trained.

Overrides: Node.is_trainable

Overrides: Node.stop_training

(inherited documentation)