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"""
The :mod:`sklearn.pls` module implements Partial Least Squares (PLS).
"""
# Author: Edouard Duchesnay <edouard.duchesnay@cea.fr>
# License: BSD 3 clause
import warnings
from abc import ABCMeta, abstractmethod
import numpy as np
from scipy.linalg import pinv2, svd
from scipy.sparse.linalg import svds
from ..base import BaseEstimator, RegressorMixin, TransformerMixin
from ..base import MultiOutputMixin
from ..utils import check_array, check_consistent_length
from ..utils.extmath import svd_flip
from ..utils.validation import check_is_fitted, FLOAT_DTYPES
from ..utils.validation import _deprecate_positional_args
from ..exceptions import ConvergenceWarning
__all__ = ['PLSCanonical', 'PLSRegression', 'PLSSVD']
def _nipals_twoblocks_inner_loop(X, Y, mode="A", max_iter=500, tol=1e-06,
norm_y_weights=False):
"""Inner loop of the iterative NIPALS algorithm.
Provides an alternative to the svd(X'Y); returns the first left and right
singular vectors of X'Y. See PLS for the meaning of the parameters. It is
similar to the Power method for determining the eigenvectors and
eigenvalues of a X'Y.
"""
for col in Y.T:
if np.any(np.abs(col) > np.finfo(np.double).eps):
y_score = col.reshape(len(col), 1)
break
x_weights_old = 0
ite = 1
X_pinv = Y_pinv = None
eps = np.finfo(X.dtype).eps
if mode == "B":
# Uses condition from scipy<1.3 in pinv2 which was changed in
# https://github.com/scipy/scipy/pull/10067. In scipy 1.3, the
# condition was changed to depend on the largest singular value
X_t = X.dtype.char.lower()
Y_t = Y.dtype.char.lower()
factor = {'f': 1E3, 'd': 1E6}
cond_X = factor[X_t] * eps
cond_Y = factor[Y_t] * eps
# Inner loop of the Wold algo.
while True:
# 1.1 Update u: the X weights
if mode == "B":
if X_pinv is None:
# We use slower pinv2 (same as np.linalg.pinv) for stability
# reasons
X_pinv = pinv2(X, check_finite=False, cond=cond_X)
x_weights = np.dot(X_pinv, y_score)
else: # mode A
# Mode A regress each X column on y_score
x_weights = np.dot(X.T, y_score) / np.dot(y_score.T, y_score)
# If y_score only has zeros x_weights will only have zeros. In
# this case add an epsilon to converge to a more acceptable
# solution
if np.dot(x_weights.T, x_weights) < eps:
x_weights += eps
# 1.2 Normalize u
x_weights /= np.sqrt(np.dot(x_weights.T, x_weights)) + eps
# 1.3 Update x_score: the X latent scores
x_score = np.dot(X, x_weights)
# 2.1 Update y_weights
if mode == "B":
if Y_pinv is None:
# compute once pinv(Y)
Y_pinv = pinv2(Y, check_finite=False, cond=cond_Y)
y_weights = np.dot(Y_pinv, x_score)
else:
# Mode A regress each Y column on x_score
y_weights = np.dot(Y.T, x_score) / np.dot(x_score.T, x_score)
# 2.2 Normalize y_weights
if norm_y_weights:
y_weights /= np.sqrt(np.dot(y_weights.T, y_weights)) + eps
# 2.3 Update y_score: the Y latent scores
y_score = np.dot(Y, y_weights) / (np.dot(y_weights.T, y_weights) + eps)
# y_score = np.dot(Y, y_weights) / np.dot(y_score.T, y_score) ## BUG
x_weights_diff = x_weights - x_weights_old
if np.dot(x_weights_diff.T, x_weights_diff) < tol or Y.shape[1] == 1:
break
if ite == max_iter:
warnings.warn('Maximum number of iterations reached',
ConvergenceWarning)
break
x_weights_old = x_weights
ite += 1
return x_weights, y_weights, ite
def _svd_cross_product(X, Y):
C = np.dot(X.T, Y)
U, s, Vh = svd(C, full_matrices=False)
u = U[:, [0]]
v = Vh.T[:, [0]]
return u, v
def _center_scale_xy(X, Y, scale=True):
""" Center X, Y and scale if the scale parameter==True
Returns
-------
X, Y, x_mean, y_mean, x_std, y_std
"""
# center
x_mean = X.mean(axis=0)
X -= x_mean
y_mean = Y.mean(axis=0)
Y -= y_mean
# scale
if scale:
x_std = X.std(axis=0, ddof=1)
x_std[x_std == 0.0] = 1.0
X /= x_std
y_std = Y.std(axis=0, ddof=1)
y_std[y_std == 0.0] = 1.0
Y /= y_std
else:
x_std = np.ones(X.shape[1])
y_std = np.ones(Y.shape[1])
return X, Y, x_mean, y_mean, x_std, y_std
class _PLS(TransformerMixin, RegressorMixin, MultiOutputMixin, BaseEstimator,
metaclass=ABCMeta):
"""Partial Least Squares (PLS)
This class implements the generic PLS algorithm, constructors' parameters
allow to obtain a specific implementation such as:
- PLS2 regression, i.e., PLS 2 blocks, mode A, with asymmetric deflation
and unnormalized y weights such as defined by [Tenenhaus 1998] p. 132.
With univariate response it implements PLS1.
- PLS canonical, i.e., PLS 2 blocks, mode A, with symmetric deflation and
normalized y weights such as defined by [Tenenhaus 1998] (p. 132) and
[Wegelin et al. 2000]. This parametrization implements the original Wold
algorithm.
We use the terminology defined by [Wegelin et al. 2000].
This implementation uses the PLS Wold 2 blocks algorithm based on two
nested loops:
(i) The outer loop iterate over components.
(ii) The inner loop estimates the weights vectors. This can be done
with two algo. (a) the inner loop of the original NIPALS algo. or (b) a
SVD on residuals cross-covariance matrices.
n_components : int, number of components to keep. (default 2).
scale : boolean, scale data? (default True)
deflation_mode : str, "canonical" or "regression". See notes.
mode : "A" classical PLS and "B" CCA. See notes.
norm_y_weights : boolean, normalize Y weights to one? (default False)
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 : int (default 500)
The maximum number of iterations
of the NIPALS inner loop (used only if algorithm="nipals")
tol : non-negative real, default 1e-06
The tolerance used in the iterative algorithm.
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 effects.
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.
x_mean_ : array, [p]
X mean for each predictor.
y_mean_ : array, [q]
Y mean for each response variable.
x_std_ : array, [p]
X standard deviation for each predictor.
y_std_ : array, [q]
Y standard deviation for each response variable.
coef_ : array, [p, q]
The coefficients of the linear model: ``Y = X coef_ + Err``
n_iter_ : array-like
Number of iterations of the NIPALS inner loop for each
component. Not useful if the algorithm given is "svd".
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.
See also
--------
PLSCanonical
PLSRegression
CCA
PLS_SVD
"""
@abstractmethod
def __init__(self, n_components=2, *, scale=True,
deflation_mode="regression",
mode="A", algorithm="nipals", norm_y_weights=False,
max_iter=500, tol=1e-06, copy=True):
self.n_components = n_components
self.deflation_mode = deflation_mode
self.mode = mode
self.norm_y_weights = norm_y_weights
self.scale = scale
self.algorithm = algorithm
self.max_iter = max_iter
self.tol = tol
self.copy = copy
def fit(self, X, Y):
"""Fit model to data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and
n_features is the number of predictors.
Y : array-like of shape (n_samples, n_targets)
Target vectors, where n_samples is the number of samples and
n_targets is the number of response variables.
"""
# copy since this will contains the residuals (deflated) matrices
check_consistent_length(X, Y)
X = self._validate_data(X, dtype=np.float64, copy=self.copy,
ensure_min_samples=2)
Y = check_array(Y, dtype=np.float64, copy=self.copy, ensure_2d=False)
if Y.ndim == 1:
Y = Y.reshape(-1, 1)
n = X.shape[0]
p = X.shape[1]
q = Y.shape[1]
if self.n_components < 1 or self.n_components > p:
raise ValueError('Invalid number of components: %d' %
self.n_components)
if self.algorithm not in ("svd", "nipals"):
raise ValueError("Got algorithm %s when only 'svd' "
"and 'nipals' are known" % self.algorithm)
if self.algorithm == "svd" and self.mode == "B":
raise ValueError('Incompatible configuration: mode B is not '
'implemented with svd algorithm')
if self.deflation_mode not in ["canonical", "regression"]:
raise ValueError('The deflation mode is unknown')
# Scale (in place)
X, Y, self.x_mean_, self.y_mean_, self.x_std_, self.y_std_ = (
_center_scale_xy(X, Y, self.scale))
# Residuals (deflated) matrices
Xk = X
Yk = Y
# Results matrices
self.x_scores_ = np.zeros((n, self.n_components))
self.y_scores_ = np.zeros((n, self.n_components))
self.x_weights_ = np.zeros((p, self.n_components))
self.y_weights_ = np.zeros((q, self.n_components))
self.x_loadings_ = np.zeros((p, self.n_components))
self.y_loadings_ = np.zeros((q, self.n_components))
self.n_iter_ = []
# NIPALS algo: outer loop, over components
Y_eps = np.finfo(Yk.dtype).eps
for k in range(self.n_components):
if np.all(np.dot(Yk.T, Yk) < np.finfo(np.double).eps):
# Yk constant
warnings.warn('Y residual constant at iteration %s' % k)
break
# 1) weights estimation (inner loop)
# -----------------------------------
if self.algorithm == "nipals":
# Replace columns that are all close to zero with zeros
Yk_mask = np.all(np.abs(Yk) < 10 * Y_eps, axis=0)
Yk[:, Yk_mask] = 0.0
x_weights, y_weights, n_iter_ = \
_nipals_twoblocks_inner_loop(
X=Xk, Y=Yk, mode=self.mode, max_iter=self.max_iter,
tol=self.tol, norm_y_weights=self.norm_y_weights)
self.n_iter_.append(n_iter_)
elif self.algorithm == "svd":
x_weights, y_weights = _svd_cross_product(X=Xk, Y=Yk)
# Forces sign stability of x_weights and y_weights
# Sign undeterminacy issue from svd if algorithm == "svd"
# and from platform dependent computation if algorithm == 'nipals'
x_weights, y_weights = svd_flip(x_weights, y_weights.T)
y_weights = y_weights.T
# compute scores
x_scores = np.dot(Xk, x_weights)
if self.norm_y_weights:
y_ss = 1
else:
y_ss = np.dot(y_weights.T, y_weights)
y_scores = np.dot(Yk, y_weights) / y_ss
# test for null variance
if np.dot(x_scores.T, x_scores) < np.finfo(np.double).eps:
warnings.warn('X scores are null at iteration %s' % k)
break
# 2) Deflation (in place)
# ----------------------
# Possible memory footprint reduction may done here: in order to
# avoid the allocation of a data chunk for the rank-one
# approximations matrix which is then subtracted to Xk, we suggest
# to perform a column-wise deflation.
#
# - regress Xk's on x_score
x_loadings = np.dot(Xk.T, x_scores) / np.dot(x_scores.T, x_scores)
# - subtract rank-one approximations to obtain remainder matrix
Xk -= np.dot(x_scores, x_loadings.T)
if self.deflation_mode == "canonical":
# - regress Yk's on y_score, then subtract rank-one approx.
y_loadings = (np.dot(Yk.T, y_scores)
/ np.dot(y_scores.T, y_scores))
Yk -= np.dot(y_scores, y_loadings.T)
if self.deflation_mode == "regression":
# - regress Yk's on x_score, then subtract rank-one approx.
y_loadings = (np.dot(Yk.T, x_scores)
/ np.dot(x_scores.T, x_scores))
Yk -= np.dot(x_scores, y_loadings.T)
# 3) Store weights, scores and loadings # Notation:
self.x_scores_[:, k] = x_scores.ravel() # T
self.y_scores_[:, k] = y_scores.ravel() # U
self.x_weights_[:, k] = x_weights.ravel() # W
self.y_weights_[:, k] = y_weights.ravel() # C
self.x_loadings_[:, k] = x_loadings.ravel() # P
self.y_loadings_[:, k] = y_loadings.ravel() # Q
# Such that: X = TP' + Err and Y = UQ' + Err
# 4) rotations from input space to transformed space (scores)
# T = X W(P'W)^-1 = XW* (W* : p x k matrix)
# U = Y C(Q'C)^-1 = YC* (W* : q x k matrix)
self.x_rotations_ = np.dot(
self.x_weights_,
pinv2(np.dot(self.x_loadings_.T, self.x_weights_),
check_finite=False))
if Y.shape[1] > 1:
self.y_rotations_ = np.dot(
self.y_weights_,
pinv2(np.dot(self.y_loadings_.T, self.y_weights_),
check_finite=False))
else:
self.y_rotations_ = np.ones(1)
if True or self.deflation_mode == "regression":
# FIXME what's with the if?
# Estimate regression coefficient
# Regress Y on T
# Y = TQ' + Err,
# Then express in function of X
# Y = X W(P'W)^-1Q' + Err = XB + Err
# => B = W*Q' (p x q)
self.coef_ = np.dot(self.x_rotations_, self.y_loadings_.T)
self.coef_ = self.coef_ * self.y_std_
return self
def transform(self, X, Y=None, copy=True):
"""Apply the dimension reduction learned on the train data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and
n_features is the number of predictors.
Y : array-like of shape (n_samples, n_targets)
Target vectors, where n_samples is the number of samples and
n_targets is the number of response variables.
copy : boolean, default True
Whether to copy X and Y, or perform in-place normalization.
Returns
-------
x_scores if Y is not given, (x_scores, y_scores) otherwise.
"""
check_is_fitted(self)
X = check_array(X, copy=copy, dtype=FLOAT_DTYPES)
# Normalize
X -= self.x_mean_
X /= self.x_std_
# Apply rotation
x_scores = np.dot(X, self.x_rotations_)
if Y is not None:
Y = check_array(Y, ensure_2d=False, copy=copy, dtype=FLOAT_DTYPES)
if Y.ndim == 1:
Y = Y.reshape(-1, 1)
Y -= self.y_mean_
Y /= self.y_std_
y_scores = np.dot(Y, self.y_rotations_)
return x_scores, y_scores
return x_scores
def inverse_transform(self, X):
"""Transform data back to its original space.
Parameters
----------
X : array-like of shape (n_samples, n_components)
New data, where n_samples is the number of samples
and n_components is the number of pls components.
Returns
-------
x_reconstructed : array-like of shape (n_samples, n_features)
Notes
-----
This transformation will only be exact if n_components=n_features
"""
check_is_fitted(self)
X = check_array(X, dtype=FLOAT_DTYPES)
# From pls space to original space
X_reconstructed = np.matmul(X, self.x_loadings_.T)
# Denormalize
X_reconstructed *= self.x_std_
X_reconstructed += self.x_mean_
return X_reconstructed
def predict(self, X, copy=True):
"""Apply the dimension reduction learned on the train data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and
n_features is the number of predictors.
copy : boolean, default True
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.
"""
check_is_fitted(self)
X = check_array(X, copy=copy, dtype=FLOAT_DTYPES)
# Normalize
X -= self.x_mean_
X /= self.x_std_
Ypred = np.dot(X, self.coef_)
return Ypred + self.y_mean_
def fit_transform(self, X, y=None):
"""Learn and apply the dimension reduction on the train data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and
n_features is the number of predictors.
y : array-like of shape (n_samples, n_targets)
Target vectors, where n_samples is the number of samples and
n_targets is the number of response variables.
Returns
-------
x_scores if Y is not given, (x_scores, y_scores) otherwise.
"""
return self.fit(X, y).transform(X, y)
def _more_tags(self):
return {'poor_score': True,
'requires_y': False}
class PLSRegression(_PLS):
"""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".
Read more in the :ref:`User Guide <cross_decomposition>`.
.. versionadded:: 0.8
Parameters
----------
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.
coef_ : array, [p, q]
The coefficients of the linear model: ``Y = X coef_ + Err``
n_iter_ : array-like
Number of iterations of the NIPALS inner loop for each
component.
Notes
-----
Matrices::
T: x_scores_
U: y_scores_
W: x_weights_
C: y_weights_
P: x_loadings_
Q: y_loadings_
Are computed such that::
X = T P.T + Err and Y = U Q.T + Err
T[:, k] = Xk W[:, k] for k in range(n_components)
U[:, k] = Yk C[:, k] for k in range(n_components)
x_rotations_ = W (P.T W)^(-1)
y_rotations_ = C (Q.T C)^(-1)
where Xk and Yk are residual matrices at iteration k.
`Slides explaining
PLS <http://www.eigenvector.com/Docs/Wise_pls_properties.pdf>`_
For each component k, find weights u, v that optimizes:
``max corr(Xk u, Yk v) * std(Xk u) std(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)
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()
>>> 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.
"""
@_deprecate_positional_args
def __init__(self, n_components=2, *, scale=True,
max_iter=500, tol=1e-06, copy=True):
super().__init__(
n_components=n_components, scale=scale,
deflation_mode="regression", mode="A",
norm_y_weights=False, max_iter=max_iter, tol=tol,
copy=copy)
class PLSCanonical(_PLS):
""" PLSCanonical implements the 2 blocks canonical PLS of the original Wold
algorithm [Tenenhaus 1998] p.204, referred as PLS-C2A in [Wegelin 2000].
This class inherits from PLS with mode="A" and deflation_mode="canonical",
norm_y_weights=True and algorithm="nipals", but svd should provide similar
results up to numerical errors.
Read more in the :ref:`User Guide <cross_decomposition>`.
.. versionadded:: 0.8
Parameters
----------
n_components : int, (default 2).
Number of components to keep
scale : boolean, (default True)
Option to scale 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, default 1e-06
the tolerance used in the iterative algorithm
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, shape = [p, n_components]
X block weights vectors.
y_weights_ : array, shape = [q, n_components]
Y block weights vectors.
x_loadings_ : array, shape = [p, n_components]
X block loadings vectors.
y_loadings_ : array, shape = [q, n_components]
Y block loadings vectors.
x_scores_ : array, shape = [n_samples, n_components]
X scores.
y_scores_ : array, shape = [n_samples, n_components]
Y scores.
x_rotations_ : array, shape = [p, n_components]
X block to latents rotations.
y_rotations_ : array, shape = [q, n_components]
Y block to latents rotations.
coef_ : array of shape (p, q)
The coefficients of the linear model: ``Y = X coef_ + Err``
n_iter_ : array-like
Number of iterations of the NIPALS inner loop for each
component. Not useful if the algorithm provided is "svd".
Notes
-----
Matrices::
T: x_scores_
U: y_scores_
W: x_weights_
C: y_weights_
P: x_loadings_
Q: y_loadings__
Are computed such that::
X = T P.T + Err and Y = U Q.T + Err
T[:, k] = Xk W[:, k] for k in range(n_components)
U[:, k] = Yk C[:, k] for k in range(n_components)
x_rotations_ = W (P.T W)^(-1)
y_rotations_ = C (Q.T C)^(-1)
where Xk and Yk are residual matrices at iteration k.
`Slides explaining PLS
<http://www.eigenvector.com/Docs/Wise_pls_properties.pdf>`_
For each component k, find weights u, v that optimize::
max corr(Xk u, Yk v) * std(Xk u) std(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 symmetric version of the PLS
regression. But slightly different than the CCA. This is mostly used
for modeling.
This implementation provides the same results that the "plspm" package
provided in the R language (R-project), using the function plsca(X, Y).
Results are equal or collinear with the function
``pls(..., mode = "canonical")`` of the "mixOmics" package. The difference
relies in the fact that mixOmics implementation does not exactly implement
the Wold algorithm since it does not normalize y_weights to one.
Examples
--------
>>> from sklearn.cross_decomposition import PLSCanonical
>>> 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(n_components=2)
>>> plsca.fit(X, Y)
PLSCanonical()
>>> X_c, Y_c = plsca.transform(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.
Tenenhaus, M. (1998). La regression PLS: theorie et pratique. Paris:
Editions Technic.
See also
--------
CCA
PLSSVD
"""
@_deprecate_positional_args
def __init__(self, n_components=2, *, scale=True, algorithm="nipals",
max_iter=500, tol=1e-06, copy=True):
super().__init__(
n_components=n_components, scale=scale,
deflation_mode="canonical", mode="A",
norm_y_weights=True, algorithm=algorithm,
max_iter=max_iter, tol=tol, copy=copy)
class PLSSVD(TransformerMixin, BaseEstimator):
"""Partial Least Square SVD
Simply perform a svd on the crosscovariance matrix: X'Y
There are no iterative deflation here.
Read more in the :ref:`User Guide <cross_decomposition>`.
.. versionadded:: 0.8
Parameters
----------
n_components : int, default 2
Number of components to keep.
scale : boolean, default True
Whether to scale X and Y.
copy : boolean, default True
Whether to copy X and Y, or perform in-place computations.
Attributes
----------
x_weights_ : array, [p, n_components]
X block weights vectors.
y_weights_ : array, [q, n_components]
Y block weights vectors.
x_scores_ : array, [n_samples, n_components]
X scores.
y_scores_ : array, [n_samples, n_components]
Y scores.
Examples
--------
>>> import numpy as np
>>> from sklearn.cross_decomposition import PLSSVD
>>> X = np.array([[0., 0., 1.],
... [1.,0.,0.],
... [2.,2.,2.],
... [2.,5.,4.]])
>>> Y = np.array([[0.1, -0.2],
... [0.9, 1.1],
... [6.2, 5.9],
... [11.9, 12.3]])
>>> plsca = PLSSVD(n_components=2)
>>> plsca.fit(X, Y)
PLSSVD()
>>> X_c, Y_c = plsca.transform(X, Y)
>>> X_c.shape, Y_c.shape
((4, 2), (4, 2))
See also
--------
PLSCanonical
CCA
"""
@_deprecate_positional_args
def __init__(self, n_components=2, *, scale=True, copy=True):
self.n_components = n_components
self.scale = scale
self.copy = copy
def fit(self, X, Y):
"""Fit model to data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and
n_features is the number of predictors.
Y : array-like of shape (n_samples, n_targets)
Target vectors, where n_samples is the number of samples and
n_targets is the number of response variables.
"""
# copy since this will contains the centered data
check_consistent_length(X, Y)
X = self._validate_data(X, dtype=np.float64, copy=self.copy,
ensure_min_samples=2)
Y = check_array(Y, dtype=np.float64, copy=self.copy, ensure_2d=False)
if Y.ndim == 1:
Y = Y.reshape(-1, 1)
if self.n_components > max(Y.shape[1], X.shape[1]):
raise ValueError("Invalid number of components n_components=%d"
" with X of shape %s and Y of shape %s."
% (self.n_components, str(X.shape), str(Y.shape)))
# Scale (in place)
X, Y, self.x_mean_, self.y_mean_, self.x_std_, self.y_std_ = (
_center_scale_xy(X, Y, self.scale))
# svd(X'Y)
C = np.dot(X.T, Y)
# The arpack svds solver only works if the number of extracted
# components is smaller than rank(X) - 1. Hence, if we want to extract
# all the components (C.shape[1]), we have to use another one. Else,
# let's use arpacks to compute only the interesting components.
if self.n_components >= np.min(C.shape):
U, s, V = svd(C, full_matrices=False)
else:
U, s, V = svds(C, k=self.n_components)
# Deterministic output
U, V = svd_flip(U, V)
V = V.T
self.x_scores_ = np.dot(X, U)
self.y_scores_ = np.dot(Y, V)
self.x_weights_ = U
self.y_weights_ = V
return self
def transform(self, X, Y=None):
"""
Apply the dimension reduction learned on the train data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and
n_features is the number of predictors.
Y : array-like of shape (n_samples, n_targets)
Target vectors, where n_samples is the number of samples and
n_targets is the number of response variables.
"""
check_is_fitted(self)
X = check_array(X, dtype=np.float64)
Xr = (X - self.x_mean_) / self.x_std_
x_scores = np.dot(Xr, self.x_weights_)
if Y is not None:
Y = check_array(Y, ensure_2d=False, dtype=np.float64)
if Y.ndim == 1:
Y = Y.reshape(-1, 1)
Yr = (Y - self.y_mean_) / self.y_std_
y_scores = np.dot(Yr, self.y_weights_)
return x_scores, y_scores
return x_scores
def fit_transform(self, X, y=None):
"""Learn and apply the dimension reduction on the train data.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training vectors, where n_samples is the number of samples and
n_features is the number of predictors.
y : array-like of shape (n_samples, n_targets)
Target vectors, where n_samples is the number of samples and
n_targets is the number of response variables.
Returns
-------
x_scores if Y is not given, (x_scores, y_scores) otherwise.
"""
return self.fit(X, y).transform(X, y)