scikits.learn.pls.PLSCanonical

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

PLS canonical. PLSCanonical inherits from PLS with mode=”A” and deflation_mode=”canonical”.

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

See also

CCA, PLSSVD

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 Y score. This performs a canonical symetric version of the PLS regression. But slightly different than the CCA. This is mode mostly used for modeling

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 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]]
>>> plsca = PLSCanonical()
>>> plsca.fit(X, Y, n_components=2)
PLSCanonical(scale=True, algorithm='nipals', max_iter=500, n_components=2,
       tol=1e-06, copy=True)
>>> X_c, Y_c = plsca.transform(X, Y)

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.

Methods

__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: X has to be normalize, do it on a copy or in place

with side effect!

Notes

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

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: 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. :