projektAI/venv/Lib/site-packages/sklearn/cross_decomposition/_pls.py

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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 ..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
from ..utils.deprecation import deprecated
__all__ = ['PLSCanonical', 'PLSRegression', 'PLSSVD']
def _pinv2_old(a):
# Used previous scipy pinv2 that was updated in:
# https://github.com/scipy/scipy/pull/10067
# We can not set `cond` or `rcond` for pinv2 in scipy >= 1.3 to keep the
# same behavior of pinv2 for scipy < 1.3, because the condition used to
# determine the rank is dependent on the output of svd.
u, s, vh = svd(a, full_matrices=False, check_finite=False)
t = u.dtype.char.lower()
factor = {'f': 1E3, 'd': 1E6}
cond = np.max(s) * factor[t] * np.finfo(t).eps
rank = np.sum(s > cond)
u = u[:, :rank]
u /= s[:rank]
return np.transpose(np.conjugate(np.dot(u, vh[:rank])))
def _get_first_singular_vectors_power_method(X, Y, mode="A", max_iter=500,
tol=1e-06, norm_y_weights=False):
"""Return the first left and right singular vectors of X'Y.
Provides an alternative to the svd(X'Y) and uses the power method instead.
With norm_y_weights to True and in mode A, this corresponds to the
algorithm section 11.3 of the Wegelin's review, except this starts at the
"update saliences" part.
"""
eps = np.finfo(X.dtype).eps
try:
y_score = next(col for col in Y.T if np.any(np.abs(col) > eps))
except StopIteration as e:
raise StopIteration("Y residual is constant") from e
x_weights_old = 100 # init to big value for first convergence check
if mode == 'B':
# Precompute pseudo inverse matrices
# Basically: X_pinv = (X.T X)^-1 X.T
# Which requires inverting a (n_features, n_features) matrix.
# As a result, and as detailed in the Wegelin's review, CCA (i.e. mode
# B) will be unstable if n_features > n_samples or n_targets >
# n_samples
X_pinv, Y_pinv = _pinv2_old(X), _pinv2_old(Y)
for i in range(max_iter):
if mode == "B":
x_weights = np.dot(X_pinv, y_score)
else:
x_weights = np.dot(X.T, y_score) / np.dot(y_score, y_score)
x_weights /= np.sqrt(np.dot(x_weights, x_weights)) + eps
x_score = np.dot(X, x_weights)
if mode == "B":
y_weights = np.dot(Y_pinv, x_score)
else:
y_weights = np.dot(Y.T, x_score) / np.dot(x_score.T, x_score)
if norm_y_weights:
y_weights /= np.sqrt(np.dot(y_weights, y_weights)) + eps
y_score = np.dot(Y, y_weights) / (np.dot(y_weights, y_weights) + eps)
x_weights_diff = x_weights - x_weights_old
if np.dot(x_weights_diff, x_weights_diff) < tol or Y.shape[1] == 1:
break
x_weights_old = x_weights
n_iter = i + 1
if n_iter == max_iter:
warnings.warn('Maximum number of iterations reached',
ConvergenceWarning)
return x_weights, y_weights, n_iter
def _get_first_singular_vectors_svd(X, Y):
"""Return the first left and right singular vectors of X'Y.
Here the whole SVD is computed.
"""
C = np.dot(X.T, Y)
U, _, Vt = svd(C, full_matrices=False)
return U[:, 0], Vt[0, :]
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
def _svd_flip_1d(u, v):
"""Same as svd_flip but works on 1d arrays, and is inplace"""
# svd_flip would force us to convert to 2d array and would also return 2d
# arrays. We don't want that.
biggest_abs_val_idx = np.argmax(np.abs(u))
sign = np.sign(u[biggest_abs_val_idx])
u *= sign
v *= sign
class _PLS(TransformerMixin, RegressorMixin, MultiOutputMixin, BaseEstimator,
metaclass=ABCMeta):
"""Partial Least Squares (PLS)
This class implements the generic PLS algorithm.
Main ref: Wegelin, a survey of Partial Least Squares (PLS) methods,
with emphasis on the two-block case
https://www.stat.washington.edu/research/reports/2000/tr371.pdf
"""
@abstractmethod
def __init__(self, n_components=2, *, scale=True,
deflation_mode="regression",
mode="A", algorithm="nipals", max_iter=500, tol=1e-06,
copy=True):
self.n_components = n_components
self.deflation_mode = deflation_mode
self.mode = mode
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,) or (n_samples, n_targets)
Target vectors, where `n_samples` is the number of samples and
`n_targets` is the number of response variables.
"""
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]
n_components = self.n_components
if self.deflation_mode == 'regression':
# With PLSRegression n_components is bounded by the rank of (X.T X)
# see Wegelin page 25
rank_upper_bound = p
if not 1 <= n_components <= rank_upper_bound:
# TODO: raise an error in 1.1
warnings.warn(
f"As of version 0.24, n_components({n_components}) should "
f"be in [1, n_features]."
f"n_components={rank_upper_bound} will be used instead. "
f"In version 1.1 (renaming of 0.26), an error will be "
f"raised.",
FutureWarning
)
n_components = rank_upper_bound
else:
# With CCA and PLSCanonical, n_components is bounded by the rank of
# X and the rank of Y: see Wegelin page 12
rank_upper_bound = min(n, p, q)
if not 1 <= self.n_components <= rank_upper_bound:
# TODO: raise an error in 1.1
warnings.warn(
f"As of version 0.24, n_components({n_components}) should "
f"be in [1, min(n_features, n_samples, n_targets)] = "
f"[1, {rank_upper_bound}]. "
f"n_components={rank_upper_bound} will be used instead. "
f"In version 1.1 (renaming of 0.26), an error will be "
f"raised.",
FutureWarning
)
n_components = rank_upper_bound
if self.algorithm not in ("svd", "nipals"):
raise ValueError("algorithm should be 'svd' or 'nipals', got "
f"{self.algorithm}.")
self._norm_y_weights = (self.deflation_mode == 'canonical') # 1.1
norm_y_weights = self._norm_y_weights
# Scale (in place)
Xk, Yk, self._x_mean, self._y_mean, self._x_std, self._y_std = (
_center_scale_xy(X, Y, self.scale))
self.x_weights_ = np.zeros((p, n_components)) # U
self.y_weights_ = np.zeros((q, n_components)) # V
self._x_scores = np.zeros((n, n_components)) # Xi
self._y_scores = np.zeros((n, n_components)) # Omega
self.x_loadings_ = np.zeros((p, n_components)) # Gamma
self.y_loadings_ = np.zeros((q, n_components)) # Delta
self.n_iter_ = []
# This whole thing corresponds to the algorithm in section 4.1 of the
# review from Wegelin. See above for a notation mapping from code to
# paper.
Y_eps = np.finfo(Yk.dtype).eps
for k in range(n_components):
# Find first left and right singular vectors of the X.T.dot(Y)
# cross-covariance matrix.
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
try:
x_weights, y_weights, n_iter_ = \
_get_first_singular_vectors_power_method(
Xk, Yk, mode=self.mode, max_iter=self.max_iter,
tol=self.tol, norm_y_weights=norm_y_weights)
except StopIteration as e:
if str(e) != "Y residual is constant":
raise
warnings.warn(f"Y residual is constant at iteration {k}")
break
self.n_iter_.append(n_iter_)
elif self.algorithm == "svd":
x_weights, y_weights = _get_first_singular_vectors_svd(Xk, Yk)
# inplace sign flip for consistency across solvers and archs
_svd_flip_1d(x_weights, y_weights)
# compute scores, i.e. the projections of X and Y
x_scores = np.dot(Xk, x_weights)
if norm_y_weights:
y_ss = 1
else:
y_ss = np.dot(y_weights, y_weights)
y_scores = np.dot(Yk, y_weights) / y_ss
# Deflation: subtract rank-one approx to obtain Xk+1 and Yk+1
x_loadings = np.dot(x_scores, Xk) / np.dot(x_scores, x_scores)
Xk -= np.outer(x_scores, x_loadings)
if self.deflation_mode == "canonical":
# regress Yk on y_score
y_loadings = np.dot(y_scores, Yk) / np.dot(y_scores, y_scores)
Yk -= np.outer(y_scores, y_loadings)
if self.deflation_mode == "regression":
# regress Yk on x_score
y_loadings = np.dot(x_scores, Yk) / np.dot(x_scores, x_scores)
Yk -= np.outer(x_scores, y_loadings)
self.x_weights_[:, k] = x_weights
self.y_weights_[:, k] = y_weights
self._x_scores[:, k] = x_scores
self._y_scores[:, k] = y_scores
self.x_loadings_[:, k] = x_loadings
self.y_loadings_[:, k] = y_loadings
# X was approximated as Xi . Gamma.T + X_(R+1)
# Xi . Gamma.T is a sum of n_components rank-1 matrices. X_(R+1) is
# whatever is left to fully reconstruct X, and can be 0 if X is of rank
# n_components.
# Similiarly, Y was approximated as Omega . Delta.T + Y_(R+1)
# Compute transformation matrices (rotations_). See User Guide.
self.x_rotations_ = np.dot(
self.x_weights_,
pinv2(np.dot(self.x_loadings_.T, self.x_weights_),
check_finite=False))
self.y_rotations_ = np.dot(
self.y_weights_, pinv2(np.dot(self.y_loadings_.T, self.y_weights_),
check_finite=False))
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.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Samples to transform.
Y : array-like of shape (n_samples, n_targets), default=None
Target vectors.
copy : bool, 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):
"""Predict targets of given samples.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Samples.
copy : bool, default=True
Whether to copy `X` and `Y`, or perform in-place normalization.
Notes
-----
This call requires the estimation of a matrix of shape
`(n_features, n_targets)`, 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), default=None
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)
# mypy error: Decorated property not supported
@deprecated( # type: ignore
"Attribute norm_y_weights was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26).")
@property
def norm_y_weights(self):
return self._norm_y_weights
@deprecated( # type: ignore
"Attribute x_mean_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26).")
@property
def x_mean_(self):
return self._x_mean
@deprecated( # type: ignore
"Attribute y_mean_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26).")
@property
def y_mean_(self):
return self._y_mean
@deprecated( # type: ignore
"Attribute x_std_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26).")
@property
def x_std_(self):
return self._x_std
@deprecated( # type: ignore
"Attribute y_std_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26).")
@property
def y_std_(self):
return self._y_std
@property
def x_scores_(self):
# TODO: raise error in 1.1 instead
if not isinstance(self, PLSRegression):
pass
warnings.warn(
"Attribute x_scores_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26). Use "
"est.transform(X) on the training data instead.",
FutureWarning
)
return self._x_scores
@property
def y_scores_(self):
# TODO: raise error in 1.1 instead
if not isinstance(self, PLSRegression):
warnings.warn(
"Attribute y_scores_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26). Use "
"est.transform(X) on the training data instead.",
FutureWarning
)
return self._y_scores
def _more_tags(self):
return {'poor_score': True,
'requires_y': False}
class PLSRegression(_PLS):
"""PLS regression
PLSRegression is also known as PLS2 or PLS1, depending on the number of
targets.
Read more in the :ref:`User Guide <cross_decomposition>`.
.. versionadded:: 0.8
Parameters
----------
n_components : int, default=2
Number of components to keep. Should be in `[1, min(n_samples,
n_features, n_targets)]`.
scale : bool, default=True
Whether to scale `X` and `Y`.
max_iter : int, default=500
The maximum number of iterations of the power method when
`algorithm='nipals'`. Ignored otherwise.
tol : float, default=1e-06
The tolerance used as convergence criteria in the power method: the
algorithm stops whenever the squared norm of `u_i - u_{i-1}` is less
than `tol`, where `u` corresponds to the left singular vector.
copy : bool, default=True
Whether to copy `X` and `Y` in fit before applying centering, and
potentially scaling. If False, these operations will be done inplace,
modifying both arrays.
Attributes
----------
x_weights_ : ndarray of shape (n_features, n_components)
The left singular vectors of the cross-covariance matrices of each
iteration.
y_weights_ : ndarray of shape (n_targets, n_components)
The right singular vectors of the cross-covariance matrices of each
iteration.
x_loadings_ : ndarray of shape (n_features, n_components)
The loadings of `X`.
y_loadings_ : ndarray of shape (n_targets, n_components)
The loadings of `Y`.
x_scores_ : ndarray of shape (n_samples, n_components)
The transformed training samples.
y_scores_ : ndarray of shape (n_samples, n_components)
The transformed training targets.
x_rotations_ : ndarray of shape (n_features, n_components)
The projection matrix used to transform `X`.
y_rotations_ : ndarray of shape (n_features, n_components)
The projection matrix used to transform `Y`.
coef_ : ndarray of shape (n_features, n_targets)
The coefficients of the linear model such that `Y` is approximated as
`Y = X @ coef_`.
n_iter_ : list of shape (n_components,)
Number of iterations of the power method, for each
component.
n_features_in_ : int
Number of features seen during :term:`fit`.
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)
"""
# 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)
@_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",
algorithm='nipals', max_iter=max_iter,
tol=tol, copy=copy)
class PLSCanonical(_PLS):
"""Partial Least Squares transformer and regressor.
Read more in the :ref:`User Guide <cross_decomposition>`.
.. versionadded:: 0.8
Parameters
----------
n_components : int, default=2
Number of components to keep. Should be in `[1, min(n_samples,
n_features, n_targets)]`.
scale : bool, default=True
Whether to scale `X` and `Y`.
algorithm : {'nipals', 'svd'}, default='nipals'
The algorithm used to estimate the first singular vectors of the
cross-covariance matrix. 'nipals' uses the power method while 'svd'
will compute the whole SVD.
max_iter : int, default=500
the maximum number of iterations of the power method when
`algorithm='nipals'`. Ignored otherwise.
tol : float, default=1e-06
The tolerance used as convergence criteria in the power method: the
algorithm stops whenever the squared norm of `u_i - u_{i-1}` is less
than `tol`, where `u` corresponds to the left singular vector.
copy : bool, default=True
Whether to copy `X` and `Y` in fit before applying centering, and
potentially scaling. If False, these operations will be done inplace,
modifying both arrays.
Attributes
----------
x_weights_ : ndarray of shape (n_features, n_components)
The left singular vectors of the cross-covariance matrices of each
iteration.
y_weights_ : ndarray of shape (n_targets, n_components)
The right singular vectors of the cross-covariance matrices of each
iteration.
x_loadings_ : ndarray of shape (n_features, n_components)
The loadings of `X`.
y_loadings_ : ndarray of shape (n_targets, n_components)
The loadings of `Y`.
x_scores_ : ndarray of shape (n_samples, n_components)
The transformed training samples.
.. deprecated:: 0.24
`x_scores_` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26). You can just call `transform` on the training
data instead.
y_scores_ : ndarray of shape (n_samples, n_components)
The transformed training targets.
.. deprecated:: 0.24
`y_scores_` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26). You can just call `transform` on the training
data instead.
x_rotations_ : ndarray of shape (n_features, n_components)
The projection matrix used to transform `X`.
y_rotations_ : ndarray of shape (n_features, n_components)
The projection matrix used to transform `Y`.
coef_ : ndarray of shape (n_features, n_targets)
The coefficients of the linear model such that `Y` is approximated as
`Y = X @ coef_`.
n_iter_ : list of shape (n_components,)
Number of iterations of the power method, for each
component. Empty if `algorithm='svd'`.
n_features_in_ : int
Number of features seen during :term:`fit`.
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)
See Also
--------
CCA
PLSSVD
"""
# 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.
@_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",
algorithm=algorithm,
max_iter=max_iter, tol=tol, copy=copy)
class CCA(_PLS):
"""Canonical Correlation Analysis, also known as "Mode B" PLS.
Read more in the :ref:`User Guide <cross_decomposition>`.
Parameters
----------
n_components : int, default=2
Number of components to keep. Should be in `[1, min(n_samples,
n_features, n_targets)]`.
scale : bool, default=True
Whether to scale `X` and `Y`.
max_iter : int, default=500
the maximum number of iterations of the power method.
tol : float, default=1e-06
The tolerance used as convergence criteria in the power method: the
algorithm stops whenever the squared norm of `u_i - u_{i-1}` is less
than `tol`, where `u` corresponds to the left singular vector.
copy : bool, default=True
Whether to copy `X` and `Y` in fit before applying centering, and
potentially scaling. If False, these operations will be done inplace,
modifying both arrays.
Attributes
----------
x_weights_ : ndarray of shape (n_features, n_components)
The left singular vectors of the cross-covariance matrices of each
iteration.
y_weights_ : ndarray of shape (n_targets, n_components)
The right singular vectors of the cross-covariance matrices of each
iteration.
x_loadings_ : ndarray of shape (n_features, n_components)
The loadings of `X`.
y_loadings_ : ndarray of shape (n_targets, n_components)
The loadings of `Y`.
x_scores_ : ndarray of shape (n_samples, n_components)
The transformed training samples.
.. deprecated:: 0.24
`x_scores_` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26). You can just call `transform` on the training
data instead.
y_scores_ : ndarray of shape (n_samples, n_components)
The transformed training targets.
.. deprecated:: 0.24
`y_scores_` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26). You can just call `transform` on the training
data instead.
x_rotations_ : ndarray of shape (n_features, n_components)
The projection matrix used to transform `X`.
y_rotations_ : ndarray of shape (n_features, n_components)
The projection matrix used to transform `Y`.
coef_ : ndarray of shape (n_features, n_targets)
The coefficients of the linear model such that `Y` is approximated as
`Y = X @ coef_`.
n_iter_ : list of shape (n_components,)
Number of iterations of the power method, for each
component.
n_features_in_ : int
Number of features seen during :term:`fit`.
Examples
--------
>>> from sklearn.cross_decomposition import CCA
>>> X = [[0., 0., 1.], [1.,0.,0.], [2.,2.,2.], [3.,5.,4.]]
>>> Y = [[0.1, -0.2], [0.9, 1.1], [6.2, 5.9], [11.9, 12.3]]
>>> cca = CCA(n_components=1)
>>> cca.fit(X, Y)
CCA(n_components=1)
>>> X_c, Y_c = cca.transform(X, Y)
See Also
--------
PLSCanonical
PLSSVD
"""
@_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="canonical", mode="B",
algorithm="nipals", max_iter=max_iter, tol=tol,
copy=copy)
class PLSSVD(TransformerMixin, BaseEstimator):
"""Partial Least Square SVD.
This transformer simply performs a SVD on the crosscovariance matrix X'Y.
It is able to project both the training data `X` and the targets `Y`. The
training data X is projected on the left singular vectors, while the
targets are projected on the right singular vectors.
Read more in the :ref:`User Guide <cross_decomposition>`.
.. versionadded:: 0.8
Parameters
----------
n_components : int, default=2
The number of components to keep. Should be in `[1,
min(n_samples, n_features, n_targets)]`.
scale : bool, default=True
Whether to scale `X` and `Y`.
copy : bool, default=True
Whether to copy `X` and `Y` in fit before applying centering, and
potentially scaling. If False, these operations will be done inplace,
modifying both arrays.
Attributes
----------
x_weights_ : ndarray of shape (n_features, n_components)
The left singular vectors of the SVD of the cross-covariance matrix.
Used to project `X` in `transform`.
y_weights_ : ndarray of (n_targets, n_components)
The right singular vectors of the SVD of the cross-covariance matrix.
Used to project `X` in `transform`.
x_scores_ : ndarray of shape (n_samples, n_components)
The transformed training samples.
.. deprecated:: 0.24
`x_scores_` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26). You can just call `transform` on the training
data instead.
y_scores_ : ndarray of shape (n_samples, n_components)
The transformed training targets.
.. deprecated:: 0.24
`y_scores_` is deprecated in 0.24 and will be removed in 1.1
(renaming of 0.26). You can just call `transform` on the training
data instead.
n_features_in_ : int
Number of features seen during :term:`fit`.
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]])
>>> pls = PLSSVD(n_components=2).fit(X, Y)
>>> X_c, Y_c = pls.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 samples.
Y : array-like of shape (n_samples,) or (n_samples, n_targets)
Targets.
"""
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)
# we'll compute the SVD of the cross-covariance matrix = X.T.dot(Y)
# This matrix rank is at most min(n_samples, n_features, n_targets) so
# n_components cannot be bigger than that.
n_components = self.n_components
rank_upper_bound = min(X.shape[0], X.shape[1], Y.shape[1])
if not 1 <= n_components <= rank_upper_bound:
# TODO: raise an error in 1.1
warnings.warn(
f"As of version 0.24, n_components({n_components}) should be "
f"in [1, min(n_features, n_samples, n_targets)] = "
f"[1, {rank_upper_bound}]. "
f"n_components={rank_upper_bound} will be used instead. "
f"In version 1.1 (renaming of 0.26), an error will be raised.",
FutureWarning
)
n_components = rank_upper_bound
X, Y, self._x_mean, self._y_mean, self._x_std, self._y_std = (
_center_scale_xy(X, Y, self.scale))
# Compute SVD of cross-covariance matrix
C = np.dot(X.T, Y)
U, s, Vt = svd(C, full_matrices=False)
U = U[:, :n_components]
Vt = Vt[:n_components]
U, Vt = svd_flip(U, Vt)
V = Vt.T
self._x_scores = np.dot(X, U) # TODO: remove in 1.1
self._y_scores = np.dot(Y, V) # TODO: remove in 1.1
self.x_weights_ = U
self.y_weights_ = V
return self
# mypy error: Decorated property not supported
@deprecated( # type: ignore
"Attribute x_scores_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26). Use est.transform(X) on "
"the training data instead."
)
@property
def x_scores_(self):
return self._x_scores
# mypy error: Decorated property not supported
@deprecated( # type: ignore
"Attribute y_scores_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26). Use est.transform(X, Y) "
"on the training data instead."
)
@property
def y_scores_(self):
return self._y_scores
@deprecated( # type: ignore
"Attribute x_mean_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26).")
@property
def x_mean_(self):
return self._x_mean
@deprecated( # type: ignore
"Attribute y_mean_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26).")
@property
def y_mean_(self):
return self._y_mean
@deprecated( # type: ignore
"Attribute x_std_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26).")
@property
def x_std_(self):
return self._x_std
@deprecated( # type: ignore
"Attribute y_std_ was deprecated in version 0.24 and "
"will be removed in 1.1 (renaming of 0.26).")
@property
def y_std_(self):
return self._y_std
def transform(self, X, Y=None):
"""
Apply the dimensionality reduction.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Samples to be transformed.
Y : array-like of shape (n_samples,) or (n_samples, n_targets), \
default=None
Targets.
Returns
-------
out : array-like or tuple of array-like
The transformed data `X_tranformed` if `Y` is not None,
`(X_transformed, Y_transformed)` otherwise.
"""
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 dimensionality reduction.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training samples.
y : array-like of shape (n_samples,) or (n_samples, n_targets), \
default=None
Targets.
Returns
-------
out : array-like or tuple of array-like
The transformed data `X_tranformed` if `Y` is not None,
`(X_transformed, Y_transformed)` otherwise.
"""
return self.fit(X, y).transform(X, y)