792 lines
26 KiB
Python
792 lines
26 KiB
Python
"""
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Python implementation of the fast ICA algorithms.
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Reference: Tables 8.3 and 8.4 page 196 in the book:
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Independent Component Analysis, by Hyvarinen et al.
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"""
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# Authors: Pierre Lafaye de Micheaux, Stefan van der Walt, Gael Varoquaux,
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# Bertrand Thirion, Alexandre Gramfort, Denis A. Engemann
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# License: BSD 3 clause
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import warnings
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from numbers import Integral, Real
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import numpy as np
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from scipy import linalg
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from ..base import BaseEstimator, TransformerMixin, ClassNamePrefixFeaturesOutMixin
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from ..exceptions import ConvergenceWarning
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from ..utils import check_array, as_float_array, check_random_state
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from ..utils.validation import check_is_fitted
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from ..utils._param_validation import Hidden, Interval, StrOptions
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__all__ = ["fastica", "FastICA"]
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def _gs_decorrelation(w, W, j):
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"""
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Orthonormalize w wrt the first j rows of W.
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Parameters
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----------
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w : ndarray of shape (n,)
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Array to be orthogonalized
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W : ndarray of shape (p, n)
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Null space definition
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j : int < p
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The no of (from the first) rows of Null space W wrt which w is
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orthogonalized.
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Notes
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-----
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Assumes that W is orthogonal
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w changed in place
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"""
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w -= np.linalg.multi_dot([w, W[:j].T, W[:j]])
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return w
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def _sym_decorrelation(W):
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"""Symmetric decorrelation
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i.e. W <- (W * W.T) ^{-1/2} * W
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"""
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s, u = linalg.eigh(np.dot(W, W.T))
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# Avoid sqrt of negative values because of rounding errors. Note that
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# np.sqrt(tiny) is larger than tiny and therefore this clipping also
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# prevents division by zero in the next step.
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s = np.clip(s, a_min=np.finfo(W.dtype).tiny, a_max=None)
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# u (resp. s) contains the eigenvectors (resp. square roots of
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# the eigenvalues) of W * W.T
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return np.linalg.multi_dot([u * (1.0 / np.sqrt(s)), u.T, W])
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def _ica_def(X, tol, g, fun_args, max_iter, w_init):
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"""Deflationary FastICA using fun approx to neg-entropy function
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Used internally by FastICA.
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"""
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n_components = w_init.shape[0]
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W = np.zeros((n_components, n_components), dtype=X.dtype)
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n_iter = []
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# j is the index of the extracted component
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for j in range(n_components):
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w = w_init[j, :].copy()
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w /= np.sqrt((w**2).sum())
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for i in range(max_iter):
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gwtx, g_wtx = g(np.dot(w.T, X), fun_args)
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w1 = (X * gwtx).mean(axis=1) - g_wtx.mean() * w
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_gs_decorrelation(w1, W, j)
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w1 /= np.sqrt((w1**2).sum())
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lim = np.abs(np.abs((w1 * w).sum()) - 1)
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w = w1
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if lim < tol:
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break
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n_iter.append(i + 1)
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W[j, :] = w
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return W, max(n_iter)
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def _ica_par(X, tol, g, fun_args, max_iter, w_init):
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"""Parallel FastICA.
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Used internally by FastICA --main loop
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"""
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W = _sym_decorrelation(w_init)
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del w_init
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p_ = float(X.shape[1])
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for ii in range(max_iter):
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gwtx, g_wtx = g(np.dot(W, X), fun_args)
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W1 = _sym_decorrelation(np.dot(gwtx, X.T) / p_ - g_wtx[:, np.newaxis] * W)
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del gwtx, g_wtx
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# builtin max, abs are faster than numpy counter parts.
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# np.einsum allows having the lowest memory footprint.
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# It is faster than np.diag(np.dot(W1, W.T)).
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lim = max(abs(abs(np.einsum("ij,ij->i", W1, W)) - 1))
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W = W1
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if lim < tol:
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break
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else:
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warnings.warn(
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"FastICA did not converge. Consider increasing "
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"tolerance or the maximum number of iterations.",
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ConvergenceWarning,
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)
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return W, ii + 1
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# Some standard non-linear functions.
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# XXX: these should be optimized, as they can be a bottleneck.
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def _logcosh(x, fun_args=None):
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alpha = fun_args.get("alpha", 1.0) # comment it out?
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x *= alpha
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gx = np.tanh(x, x) # apply the tanh inplace
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g_x = np.empty(x.shape[0], dtype=x.dtype)
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# XXX compute in chunks to avoid extra allocation
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for i, gx_i in enumerate(gx): # please don't vectorize.
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g_x[i] = (alpha * (1 - gx_i**2)).mean()
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return gx, g_x
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def _exp(x, fun_args):
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exp = np.exp(-(x**2) / 2)
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gx = x * exp
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g_x = (1 - x**2) * exp
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return gx, g_x.mean(axis=-1)
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def _cube(x, fun_args):
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return x**3, (3 * x**2).mean(axis=-1)
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def fastica(
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X,
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n_components=None,
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*,
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algorithm="parallel",
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whiten="warn",
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fun="logcosh",
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fun_args=None,
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max_iter=200,
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tol=1e-04,
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w_init=None,
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whiten_solver="svd",
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random_state=None,
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return_X_mean=False,
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compute_sources=True,
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return_n_iter=False,
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):
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"""Perform Fast Independent Component Analysis.
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The implementation is based on [1]_.
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Read more in the :ref:`User Guide <ICA>`.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Training vector, where `n_samples` is the number of samples and
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`n_features` is the number of features.
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n_components : int, default=None
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Number of components to use. If None is passed, all are used.
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algorithm : {'parallel', 'deflation'}, default='parallel'
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Specify which algorithm to use for FastICA.
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whiten : str or bool, default="warn"
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Specify the whitening strategy to use.
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- If 'arbitrary-variance' (default), a whitening with variance
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arbitrary is used.
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- If 'unit-variance', the whitening matrix is rescaled to ensure that
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each recovered source has unit variance.
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- If False, the data is already considered to be whitened, and no
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whitening is performed.
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.. deprecated:: 1.1
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Starting in v1.3, `whiten='unit-variance'` will be used by default.
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`whiten=True` is deprecated from 1.1 and will raise ValueError in 1.3.
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Use `whiten=arbitrary-variance` instead.
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fun : {'logcosh', 'exp', 'cube'} or callable, default='logcosh'
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The functional form of the G function used in the
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approximation to neg-entropy. Could be either 'logcosh', 'exp',
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or 'cube'.
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You can also provide your own function. It should return a tuple
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containing the value of the function, and of its derivative, in the
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point. The derivative should be averaged along its last dimension.
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Example::
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def my_g(x):
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return x ** 3, (3 * x ** 2).mean(axis=-1)
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fun_args : dict, default=None
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Arguments to send to the functional form.
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If empty or None and if fun='logcosh', fun_args will take value
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{'alpha' : 1.0}.
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max_iter : int, default=200
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Maximum number of iterations to perform.
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tol : float, default=1e-4
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A positive scalar giving the tolerance at which the
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un-mixing matrix is considered to have converged.
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w_init : ndarray of shape (n_components, n_components), default=None
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Initial un-mixing array. If `w_init=None`, then an array of values
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drawn from a normal distribution is used.
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whiten_solver : {"eigh", "svd"}, default="svd"
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The solver to use for whitening.
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- "svd" is more stable numerically if the problem is degenerate, and
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often faster when `n_samples <= n_features`.
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- "eigh" is generally more memory efficient when
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`n_samples >= n_features`, and can be faster when
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`n_samples >= 50 * n_features`.
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.. versionadded:: 1.2
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random_state : int, RandomState instance or None, default=None
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Used to initialize ``w_init`` when not specified, with a
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normal distribution. Pass an int, for reproducible results
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across multiple function calls.
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See :term:`Glossary <random_state>`.
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return_X_mean : bool, default=False
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If True, X_mean is returned too.
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compute_sources : bool, default=True
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If False, sources are not computed, but only the rotation matrix.
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This can save memory when working with big data. Defaults to True.
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return_n_iter : bool, default=False
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Whether or not to return the number of iterations.
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Returns
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-------
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K : ndarray of shape (n_components, n_features) or None
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If whiten is 'True', K is the pre-whitening matrix that projects data
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onto the first n_components principal components. If whiten is 'False',
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K is 'None'.
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W : ndarray of shape (n_components, n_components)
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The square matrix that unmixes the data after whitening.
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The mixing matrix is the pseudo-inverse of matrix ``W K``
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if K is not None, else it is the inverse of W.
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S : ndarray of shape (n_samples, n_components) or None
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Estimated source matrix.
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X_mean : ndarray of shape (n_features,)
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The mean over features. Returned only if return_X_mean is True.
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n_iter : int
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If the algorithm is "deflation", n_iter is the
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maximum number of iterations run across all components. Else
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they are just the number of iterations taken to converge. This is
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returned only when return_n_iter is set to `True`.
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Notes
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-----
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The data matrix X is considered to be a linear combination of
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non-Gaussian (independent) components i.e. X = AS where columns of S
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contain the independent components and A is a linear mixing
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matrix. In short ICA attempts to `un-mix' the data by estimating an
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un-mixing matrix W where ``S = W K X.``
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While FastICA was proposed to estimate as many sources
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as features, it is possible to estimate less by setting
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n_components < n_features. It this case K is not a square matrix
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and the estimated A is the pseudo-inverse of ``W K``.
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This implementation was originally made for data of shape
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[n_features, n_samples]. Now the input is transposed
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before the algorithm is applied. This makes it slightly
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faster for Fortran-ordered input.
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References
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----------
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.. [1] A. Hyvarinen and E. Oja, "Fast Independent Component Analysis",
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Algorithms and Applications, Neural Networks, 13(4-5), 2000,
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pp. 411-430.
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"""
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est = FastICA(
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n_components=n_components,
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algorithm=algorithm,
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whiten=whiten,
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fun=fun,
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fun_args=fun_args,
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max_iter=max_iter,
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tol=tol,
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w_init=w_init,
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whiten_solver=whiten_solver,
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random_state=random_state,
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)
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S = est._fit_transform(X, compute_sources=compute_sources)
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if est._whiten in ["unit-variance", "arbitrary-variance"]:
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K = est.whitening_
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X_mean = est.mean_
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else:
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K = None
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X_mean = None
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returned_values = [K, est._unmixing, S]
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if return_X_mean:
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returned_values.append(X_mean)
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if return_n_iter:
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returned_values.append(est.n_iter_)
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return returned_values
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class FastICA(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator):
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"""FastICA: a fast algorithm for Independent Component Analysis.
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The implementation is based on [1]_.
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Read more in the :ref:`User Guide <ICA>`.
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Parameters
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----------
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n_components : int, default=None
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Number of components to use. If None is passed, all are used.
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algorithm : {'parallel', 'deflation'}, default='parallel'
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Specify which algorithm to use for FastICA.
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whiten : str or bool, default="warn"
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Specify the whitening strategy to use.
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- If 'arbitrary-variance' (default), a whitening with variance
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arbitrary is used.
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- If 'unit-variance', the whitening matrix is rescaled to ensure that
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each recovered source has unit variance.
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- If False, the data is already considered to be whitened, and no
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whitening is performed.
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.. deprecated:: 1.1
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Starting in v1.3, `whiten='unit-variance'` will be used by default.
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`whiten=True` is deprecated from 1.1 and will raise ValueError in 1.3.
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Use `whiten=arbitrary-variance` instead.
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fun : {'logcosh', 'exp', 'cube'} or callable, default='logcosh'
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The functional form of the G function used in the
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approximation to neg-entropy. Could be either 'logcosh', 'exp',
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or 'cube'.
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You can also provide your own function. It should return a tuple
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containing the value of the function, and of its derivative, in the
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point. The derivative should be averaged along its last dimension.
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Example::
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def my_g(x):
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return x ** 3, (3 * x ** 2).mean(axis=-1)
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fun_args : dict, default=None
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Arguments to send to the functional form.
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If empty or None and if fun='logcosh', fun_args will take value
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{'alpha' : 1.0}.
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max_iter : int, default=200
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Maximum number of iterations during fit.
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tol : float, default=1e-4
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A positive scalar giving the tolerance at which the
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un-mixing matrix is considered to have converged.
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w_init : array-like of shape (n_components, n_components), default=None
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Initial un-mixing array. If `w_init=None`, then an array of values
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drawn from a normal distribution is used.
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whiten_solver : {"eigh", "svd"}, default="svd"
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The solver to use for whitening.
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- "svd" is more stable numerically if the problem is degenerate, and
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often faster when `n_samples <= n_features`.
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- "eigh" is generally more memory efficient when
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`n_samples >= n_features`, and can be faster when
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`n_samples >= 50 * n_features`.
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.. versionadded:: 1.2
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random_state : int, RandomState instance or None, default=None
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Used to initialize ``w_init`` when not specified, with a
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normal distribution. Pass an int, for reproducible results
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across multiple function calls.
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See :term:`Glossary <random_state>`.
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Attributes
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----------
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components_ : ndarray of shape (n_components, n_features)
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The linear operator to apply to the data to get the independent
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sources. This is equal to the unmixing matrix when ``whiten`` is
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False, and equal to ``np.dot(unmixing_matrix, self.whitening_)`` when
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``whiten`` is True.
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mixing_ : ndarray of shape (n_features, n_components)
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The pseudo-inverse of ``components_``. It is the linear operator
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that maps independent sources to the data.
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mean_ : ndarray of shape(n_features,)
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The mean over features. Only set if `self.whiten` is True.
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n_features_in_ : int
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Number of features seen during :term:`fit`.
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.. versionadded:: 0.24
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feature_names_in_ : ndarray of shape (`n_features_in_`,)
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Names of features seen during :term:`fit`. Defined only when `X`
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has feature names that are all strings.
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.. versionadded:: 1.0
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n_iter_ : int
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If the algorithm is "deflation", n_iter is the
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maximum number of iterations run across all components. Else
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they are just the number of iterations taken to converge.
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whitening_ : ndarray of shape (n_components, n_features)
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Only set if whiten is 'True'. This is the pre-whitening matrix
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that projects data onto the first `n_components` principal components.
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See Also
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--------
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PCA : Principal component analysis (PCA).
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IncrementalPCA : Incremental principal components analysis (IPCA).
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KernelPCA : Kernel Principal component analysis (KPCA).
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MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis.
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SparsePCA : Sparse Principal Components Analysis (SparsePCA).
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References
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----------
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.. [1] A. Hyvarinen and E. Oja, Independent Component Analysis:
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Algorithms and Applications, Neural Networks, 13(4-5), 2000,
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pp. 411-430.
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Examples
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--------
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>>> from sklearn.datasets import load_digits
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>>> from sklearn.decomposition import FastICA
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>>> X, _ = load_digits(return_X_y=True)
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>>> transformer = FastICA(n_components=7,
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... random_state=0,
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... whiten='unit-variance')
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>>> X_transformed = transformer.fit_transform(X)
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>>> X_transformed.shape
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(1797, 7)
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"""
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_parameter_constraints: dict = {
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"n_components": [Interval(Integral, 1, None, closed="left"), None],
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"algorithm": [StrOptions({"parallel", "deflation"})],
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"whiten": [
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Hidden(StrOptions({"warn"})),
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StrOptions({"arbitrary-variance", "unit-variance"}),
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"boolean",
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],
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"fun": [StrOptions({"logcosh", "exp", "cube"}), callable],
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"fun_args": [dict, None],
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"max_iter": [Interval(Integral, 1, None, closed="left")],
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"tol": [Interval(Real, 0.0, None, closed="left")],
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"w_init": ["array-like", None],
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"whiten_solver": [StrOptions({"eigh", "svd"})],
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"random_state": ["random_state"],
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}
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def __init__(
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self,
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n_components=None,
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*,
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algorithm="parallel",
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whiten="warn",
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fun="logcosh",
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fun_args=None,
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max_iter=200,
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tol=1e-4,
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w_init=None,
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whiten_solver="svd",
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random_state=None,
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):
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super().__init__()
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self.n_components = n_components
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self.algorithm = algorithm
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self.whiten = whiten
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|
self.fun = fun
|
|
self.fun_args = fun_args
|
|
self.max_iter = max_iter
|
|
self.tol = tol
|
|
self.w_init = w_init
|
|
self.whiten_solver = whiten_solver
|
|
self.random_state = random_state
|
|
|
|
def _fit_transform(self, X, compute_sources=False):
|
|
"""Fit the model.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like of shape (n_samples, n_features)
|
|
Training data, where `n_samples` is the number of samples
|
|
and `n_features` is the number of features.
|
|
|
|
compute_sources : bool, default=False
|
|
If False, sources are not computes but only the rotation matrix.
|
|
This can save memory when working with big data. Defaults to False.
|
|
|
|
Returns
|
|
-------
|
|
S : ndarray of shape (n_samples, n_components) or None
|
|
Sources matrix. `None` if `compute_sources` is `False`.
|
|
"""
|
|
self._whiten = self.whiten
|
|
|
|
if self._whiten == "warn":
|
|
warnings.warn(
|
|
"Starting in v1.3, whiten='unit-variance' will be used by default.",
|
|
FutureWarning,
|
|
)
|
|
self._whiten = "arbitrary-variance"
|
|
|
|
if self._whiten is True:
|
|
warnings.warn(
|
|
"Starting in v1.3, whiten=True should be specified as "
|
|
"whiten='arbitrary-variance' (its current behaviour). This "
|
|
"behavior is deprecated in 1.1 and will raise ValueError in 1.3.",
|
|
FutureWarning,
|
|
stacklevel=2,
|
|
)
|
|
self._whiten = "arbitrary-variance"
|
|
|
|
XT = self._validate_data(
|
|
X, copy=self._whiten, dtype=[np.float64, np.float32], ensure_min_samples=2
|
|
).T
|
|
fun_args = {} if self.fun_args is None else self.fun_args
|
|
random_state = check_random_state(self.random_state)
|
|
|
|
alpha = fun_args.get("alpha", 1.0)
|
|
if not 1 <= alpha <= 2:
|
|
raise ValueError("alpha must be in [1,2]")
|
|
|
|
if self.fun == "logcosh":
|
|
g = _logcosh
|
|
elif self.fun == "exp":
|
|
g = _exp
|
|
elif self.fun == "cube":
|
|
g = _cube
|
|
elif callable(self.fun):
|
|
|
|
def g(x, fun_args):
|
|
return self.fun(x, **fun_args)
|
|
|
|
n_features, n_samples = XT.shape
|
|
n_components = self.n_components
|
|
if not self._whiten and n_components is not None:
|
|
n_components = None
|
|
warnings.warn("Ignoring n_components with whiten=False.")
|
|
|
|
if n_components is None:
|
|
n_components = min(n_samples, n_features)
|
|
if n_components > min(n_samples, n_features):
|
|
n_components = min(n_samples, n_features)
|
|
warnings.warn(
|
|
"n_components is too large: it will be set to %s" % n_components
|
|
)
|
|
|
|
if self._whiten:
|
|
# Centering the features of X
|
|
X_mean = XT.mean(axis=-1)
|
|
XT -= X_mean[:, np.newaxis]
|
|
|
|
# Whitening and preprocessing by PCA
|
|
if self.whiten_solver == "eigh":
|
|
# Faster when num_samples >> n_features
|
|
d, u = linalg.eigh(XT.dot(X))
|
|
sort_indices = np.argsort(d)[::-1]
|
|
eps = np.finfo(d.dtype).eps
|
|
degenerate_idx = d < eps
|
|
if np.any(degenerate_idx):
|
|
warnings.warn(
|
|
"There are some small singular values, using "
|
|
"whiten_solver = 'svd' might lead to more "
|
|
"accurate results."
|
|
)
|
|
d[degenerate_idx] = eps # For numerical issues
|
|
np.sqrt(d, out=d)
|
|
d, u = d[sort_indices], u[:, sort_indices]
|
|
elif self.whiten_solver == "svd":
|
|
u, d = linalg.svd(XT, full_matrices=False, check_finite=False)[:2]
|
|
|
|
# Give consistent eigenvectors for both svd solvers
|
|
u *= np.sign(u[0])
|
|
|
|
K = (u / d).T[:n_components] # see (6.33) p.140
|
|
del u, d
|
|
X1 = np.dot(K, XT)
|
|
# see (13.6) p.267 Here X1 is white and data
|
|
# in X has been projected onto a subspace by PCA
|
|
X1 *= np.sqrt(n_samples)
|
|
else:
|
|
# X must be casted to floats to avoid typing issues with numpy
|
|
# 2.0 and the line below
|
|
X1 = as_float_array(XT, copy=False) # copy has been taken care of
|
|
|
|
w_init = self.w_init
|
|
if w_init is None:
|
|
w_init = np.asarray(
|
|
random_state.normal(size=(n_components, n_components)), dtype=X1.dtype
|
|
)
|
|
|
|
else:
|
|
w_init = np.asarray(w_init)
|
|
if w_init.shape != (n_components, n_components):
|
|
raise ValueError(
|
|
"w_init has invalid shape -- should be %(shape)s"
|
|
% {"shape": (n_components, n_components)}
|
|
)
|
|
|
|
kwargs = {
|
|
"tol": self.tol,
|
|
"g": g,
|
|
"fun_args": fun_args,
|
|
"max_iter": self.max_iter,
|
|
"w_init": w_init,
|
|
}
|
|
|
|
if self.algorithm == "parallel":
|
|
W, n_iter = _ica_par(X1, **kwargs)
|
|
elif self.algorithm == "deflation":
|
|
W, n_iter = _ica_def(X1, **kwargs)
|
|
del X1
|
|
|
|
self.n_iter_ = n_iter
|
|
|
|
if compute_sources:
|
|
if self._whiten:
|
|
S = np.linalg.multi_dot([W, K, XT]).T
|
|
else:
|
|
S = np.dot(W, XT).T
|
|
else:
|
|
S = None
|
|
|
|
if self._whiten:
|
|
if self._whiten == "unit-variance":
|
|
if not compute_sources:
|
|
S = np.linalg.multi_dot([W, K, XT]).T
|
|
S_std = np.std(S, axis=0, keepdims=True)
|
|
S /= S_std
|
|
W /= S_std.T
|
|
|
|
self.components_ = np.dot(W, K)
|
|
self.mean_ = X_mean
|
|
self.whitening_ = K
|
|
else:
|
|
self.components_ = W
|
|
|
|
self.mixing_ = linalg.pinv(self.components_, check_finite=False)
|
|
self._unmixing = W
|
|
|
|
return S
|
|
|
|
def fit_transform(self, X, y=None):
|
|
"""Fit the model and recover the sources from X.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like of shape (n_samples, n_features)
|
|
Training data, where `n_samples` is the number of samples
|
|
and `n_features` is the number of features.
|
|
|
|
y : Ignored
|
|
Not used, present for API consistency by convention.
|
|
|
|
Returns
|
|
-------
|
|
X_new : ndarray of shape (n_samples, n_components)
|
|
Estimated sources obtained by transforming the data with the
|
|
estimated unmixing matrix.
|
|
"""
|
|
self._validate_params()
|
|
|
|
return self._fit_transform(X, compute_sources=True)
|
|
|
|
def fit(self, X, y=None):
|
|
"""Fit the model to X.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like of shape (n_samples, n_features)
|
|
Training data, where `n_samples` is the number of samples
|
|
and `n_features` is the number of features.
|
|
|
|
y : Ignored
|
|
Not used, present for API consistency by convention.
|
|
|
|
Returns
|
|
-------
|
|
self : object
|
|
Returns the instance itself.
|
|
"""
|
|
self._validate_params()
|
|
|
|
self._fit_transform(X, compute_sources=False)
|
|
return self
|
|
|
|
def transform(self, X, copy=True):
|
|
"""Recover the sources from X (apply the unmixing matrix).
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like of shape (n_samples, n_features)
|
|
Data to transform, where `n_samples` is the number of samples
|
|
and `n_features` is the number of features.
|
|
|
|
copy : bool, default=True
|
|
If False, data passed to fit can be overwritten. Defaults to True.
|
|
|
|
Returns
|
|
-------
|
|
X_new : ndarray of shape (n_samples, n_components)
|
|
Estimated sources obtained by transforming the data with the
|
|
estimated unmixing matrix.
|
|
"""
|
|
check_is_fitted(self)
|
|
|
|
X = self._validate_data(
|
|
X, copy=(copy and self._whiten), dtype=[np.float64, np.float32], reset=False
|
|
)
|
|
if self._whiten:
|
|
X -= self.mean_
|
|
|
|
return np.dot(X, self.components_.T)
|
|
|
|
def inverse_transform(self, X, copy=True):
|
|
"""Transform the sources back to the mixed data (apply mixing matrix).
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like of shape (n_samples, n_components)
|
|
Sources, where `n_samples` is the number of samples
|
|
and `n_components` is the number of components.
|
|
copy : bool, default=True
|
|
If False, data passed to fit are overwritten. Defaults to True.
|
|
|
|
Returns
|
|
-------
|
|
X_new : ndarray of shape (n_samples, n_features)
|
|
Reconstructed data obtained with the mixing matrix.
|
|
"""
|
|
check_is_fitted(self)
|
|
|
|
X = check_array(X, copy=(copy and self._whiten), dtype=[np.float64, np.float32])
|
|
X = np.dot(X, self.mixing_.T)
|
|
if self._whiten:
|
|
X += self.mean_
|
|
|
|
return X
|
|
|
|
@property
|
|
def _n_features_out(self):
|
|
"""Number of transformed output features."""
|
|
return self.components_.shape[0]
|
|
|
|
def _more_tags(self):
|
|
return {"preserves_dtype": [np.float32, np.float64]}
|