""" 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 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 `. .. 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 `_ 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 `. .. 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 `_ 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 `. .. 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)