""" The :mod:`sklearn.pls` module implements Partial Least Squares (PLS). """ # Author: Edouard Duchesnay # 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 _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 y_score = next(col for col in Y.T if np.any(np.abs(col) > eps)) 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 = pinv2(X, check_finite=False, cond=10*eps) Y_pinv = pinv2(Y, check_finite=False, cond=10*eps) 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 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) 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 `. .. 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. 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. Empty if `algorithm='svd'`. 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 `. .. 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'`. 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 `. 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. 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 `. .. 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. 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)