796 lines
26 KiB
Python
796 lines
26 KiB
Python
"""
|
|
Python implementation of the fast ICA algorithms.
|
|
|
|
Reference: Tables 8.3 and 8.4 page 196 in the book:
|
|
Independent Component Analysis, by Hyvarinen et al.
|
|
"""
|
|
|
|
# Authors: Pierre Lafaye de Micheaux, Stefan van der Walt, Gael Varoquaux,
|
|
# Bertrand Thirion, Alexandre Gramfort, Denis A. Engemann
|
|
# License: BSD 3 clause
|
|
|
|
import warnings
|
|
from numbers import Integral, Real
|
|
|
|
import numpy as np
|
|
from scipy import linalg
|
|
|
|
from ..base import (
|
|
BaseEstimator,
|
|
ClassNamePrefixFeaturesOutMixin,
|
|
TransformerMixin,
|
|
_fit_context,
|
|
)
|
|
from ..exceptions import ConvergenceWarning
|
|
from ..utils import as_float_array, check_array, check_random_state
|
|
from ..utils._param_validation import Interval, Options, StrOptions, validate_params
|
|
from ..utils.validation import check_is_fitted
|
|
|
|
__all__ = ["fastica", "FastICA"]
|
|
|
|
|
|
def _gs_decorrelation(w, W, j):
|
|
"""
|
|
Orthonormalize w wrt the first j rows of W.
|
|
|
|
Parameters
|
|
----------
|
|
w : ndarray of shape (n,)
|
|
Array to be orthogonalized
|
|
|
|
W : ndarray of shape (p, n)
|
|
Null space definition
|
|
|
|
j : int < p
|
|
The no of (from the first) rows of Null space W wrt which w is
|
|
orthogonalized.
|
|
|
|
Notes
|
|
-----
|
|
Assumes that W is orthogonal
|
|
w changed in place
|
|
"""
|
|
w -= np.linalg.multi_dot([w, W[:j].T, W[:j]])
|
|
return w
|
|
|
|
|
|
def _sym_decorrelation(W):
|
|
"""Symmetric decorrelation
|
|
i.e. W <- (W * W.T) ^{-1/2} * W
|
|
"""
|
|
s, u = linalg.eigh(np.dot(W, W.T))
|
|
# Avoid sqrt of negative values because of rounding errors. Note that
|
|
# np.sqrt(tiny) is larger than tiny and therefore this clipping also
|
|
# prevents division by zero in the next step.
|
|
s = np.clip(s, a_min=np.finfo(W.dtype).tiny, a_max=None)
|
|
|
|
# u (resp. s) contains the eigenvectors (resp. square roots of
|
|
# the eigenvalues) of W * W.T
|
|
return np.linalg.multi_dot([u * (1.0 / np.sqrt(s)), u.T, W])
|
|
|
|
|
|
def _ica_def(X, tol, g, fun_args, max_iter, w_init):
|
|
"""Deflationary FastICA using fun approx to neg-entropy function
|
|
|
|
Used internally by FastICA.
|
|
"""
|
|
|
|
n_components = w_init.shape[0]
|
|
W = np.zeros((n_components, n_components), dtype=X.dtype)
|
|
n_iter = []
|
|
|
|
# j is the index of the extracted component
|
|
for j in range(n_components):
|
|
w = w_init[j, :].copy()
|
|
w /= np.sqrt((w**2).sum())
|
|
|
|
for i in range(max_iter):
|
|
gwtx, g_wtx = g(np.dot(w.T, X), fun_args)
|
|
|
|
w1 = (X * gwtx).mean(axis=1) - g_wtx.mean() * w
|
|
|
|
_gs_decorrelation(w1, W, j)
|
|
|
|
w1 /= np.sqrt((w1**2).sum())
|
|
|
|
lim = np.abs(np.abs((w1 * w).sum()) - 1)
|
|
w = w1
|
|
if lim < tol:
|
|
break
|
|
|
|
n_iter.append(i + 1)
|
|
W[j, :] = w
|
|
|
|
return W, max(n_iter)
|
|
|
|
|
|
def _ica_par(X, tol, g, fun_args, max_iter, w_init):
|
|
"""Parallel FastICA.
|
|
|
|
Used internally by FastICA --main loop
|
|
|
|
"""
|
|
W = _sym_decorrelation(w_init)
|
|
del w_init
|
|
p_ = float(X.shape[1])
|
|
for ii in range(max_iter):
|
|
gwtx, g_wtx = g(np.dot(W, X), fun_args)
|
|
W1 = _sym_decorrelation(np.dot(gwtx, X.T) / p_ - g_wtx[:, np.newaxis] * W)
|
|
del gwtx, g_wtx
|
|
# builtin max, abs are faster than numpy counter parts.
|
|
# np.einsum allows having the lowest memory footprint.
|
|
# It is faster than np.diag(np.dot(W1, W.T)).
|
|
lim = max(abs(abs(np.einsum("ij,ij->i", W1, W)) - 1))
|
|
W = W1
|
|
if lim < tol:
|
|
break
|
|
else:
|
|
warnings.warn(
|
|
(
|
|
"FastICA did not converge. Consider increasing "
|
|
"tolerance or the maximum number of iterations."
|
|
),
|
|
ConvergenceWarning,
|
|
)
|
|
|
|
return W, ii + 1
|
|
|
|
|
|
# Some standard non-linear functions.
|
|
# XXX: these should be optimized, as they can be a bottleneck.
|
|
def _logcosh(x, fun_args=None):
|
|
alpha = fun_args.get("alpha", 1.0) # comment it out?
|
|
|
|
x *= alpha
|
|
gx = np.tanh(x, x) # apply the tanh inplace
|
|
g_x = np.empty(x.shape[0], dtype=x.dtype)
|
|
# XXX compute in chunks to avoid extra allocation
|
|
for i, gx_i in enumerate(gx): # please don't vectorize.
|
|
g_x[i] = (alpha * (1 - gx_i**2)).mean()
|
|
return gx, g_x
|
|
|
|
|
|
def _exp(x, fun_args):
|
|
exp = np.exp(-(x**2) / 2)
|
|
gx = x * exp
|
|
g_x = (1 - x**2) * exp
|
|
return gx, g_x.mean(axis=-1)
|
|
|
|
|
|
def _cube(x, fun_args):
|
|
return x**3, (3 * x**2).mean(axis=-1)
|
|
|
|
|
|
@validate_params(
|
|
{
|
|
"X": ["array-like"],
|
|
"return_X_mean": ["boolean"],
|
|
"compute_sources": ["boolean"],
|
|
"return_n_iter": ["boolean"],
|
|
},
|
|
prefer_skip_nested_validation=False,
|
|
)
|
|
def fastica(
|
|
X,
|
|
n_components=None,
|
|
*,
|
|
algorithm="parallel",
|
|
whiten="unit-variance",
|
|
fun="logcosh",
|
|
fun_args=None,
|
|
max_iter=200,
|
|
tol=1e-04,
|
|
w_init=None,
|
|
whiten_solver="svd",
|
|
random_state=None,
|
|
return_X_mean=False,
|
|
compute_sources=True,
|
|
return_n_iter=False,
|
|
):
|
|
"""Perform Fast Independent Component Analysis.
|
|
|
|
The implementation is based on [1]_.
|
|
|
|
Read more in the :ref:`User Guide <ICA>`.
|
|
|
|
Parameters
|
|
----------
|
|
X : array-like of shape (n_samples, n_features)
|
|
Training vector, where `n_samples` is the number of samples and
|
|
`n_features` is the number of features.
|
|
|
|
n_components : int, default=None
|
|
Number of components to use. If None is passed, all are used.
|
|
|
|
algorithm : {'parallel', 'deflation'}, default='parallel'
|
|
Specify which algorithm to use for FastICA.
|
|
|
|
whiten : str or bool, default='unit-variance'
|
|
Specify the whitening strategy to use.
|
|
|
|
- If 'arbitrary-variance', a whitening with variance
|
|
arbitrary is used.
|
|
- If 'unit-variance', the whitening matrix is rescaled to ensure that
|
|
each recovered source has unit variance.
|
|
- If False, the data is already considered to be whitened, and no
|
|
whitening is performed.
|
|
|
|
.. versionchanged:: 1.3
|
|
The default value of `whiten` changed to 'unit-variance' in 1.3.
|
|
|
|
fun : {'logcosh', 'exp', 'cube'} or callable, default='logcosh'
|
|
The functional form of the G function used in the
|
|
approximation to neg-entropy. Could be either 'logcosh', 'exp',
|
|
or 'cube'.
|
|
You can also provide your own function. It should return a tuple
|
|
containing the value of the function, and of its derivative, in the
|
|
point. The derivative should be averaged along its last dimension.
|
|
Example::
|
|
|
|
def my_g(x):
|
|
return x ** 3, (3 * x ** 2).mean(axis=-1)
|
|
|
|
fun_args : dict, default=None
|
|
Arguments to send to the functional form.
|
|
If empty or None and if fun='logcosh', fun_args will take value
|
|
{'alpha' : 1.0}.
|
|
|
|
max_iter : int, default=200
|
|
Maximum number of iterations to perform.
|
|
|
|
tol : float, default=1e-4
|
|
A positive scalar giving the tolerance at which the
|
|
un-mixing matrix is considered to have converged.
|
|
|
|
w_init : ndarray of shape (n_components, n_components), default=None
|
|
Initial un-mixing array. If `w_init=None`, then an array of values
|
|
drawn from a normal distribution is used.
|
|
|
|
whiten_solver : {"eigh", "svd"}, default="svd"
|
|
The solver to use for whitening.
|
|
|
|
- "svd" is more stable numerically if the problem is degenerate, and
|
|
often faster when `n_samples <= n_features`.
|
|
|
|
- "eigh" is generally more memory efficient when
|
|
`n_samples >= n_features`, and can be faster when
|
|
`n_samples >= 50 * n_features`.
|
|
|
|
.. versionadded:: 1.2
|
|
|
|
random_state : int, RandomState instance or None, default=None
|
|
Used to initialize ``w_init`` when not specified, with a
|
|
normal distribution. Pass an int, for reproducible results
|
|
across multiple function calls.
|
|
See :term:`Glossary <random_state>`.
|
|
|
|
return_X_mean : bool, default=False
|
|
If True, X_mean is returned too.
|
|
|
|
compute_sources : bool, default=True
|
|
If False, sources are not computed, but only the rotation matrix.
|
|
This can save memory when working with big data. Defaults to True.
|
|
|
|
return_n_iter : bool, default=False
|
|
Whether or not to return the number of iterations.
|
|
|
|
Returns
|
|
-------
|
|
K : ndarray of shape (n_components, n_features) or None
|
|
If whiten is 'True', K is the pre-whitening matrix that projects data
|
|
onto the first n_components principal components. If whiten is 'False',
|
|
K is 'None'.
|
|
|
|
W : ndarray of shape (n_components, n_components)
|
|
The square matrix that unmixes the data after whitening.
|
|
The mixing matrix is the pseudo-inverse of matrix ``W K``
|
|
if K is not None, else it is the inverse of W.
|
|
|
|
S : ndarray of shape (n_samples, n_components) or None
|
|
Estimated source matrix.
|
|
|
|
X_mean : ndarray of shape (n_features,)
|
|
The mean over features. Returned only if return_X_mean is True.
|
|
|
|
n_iter : int
|
|
If the algorithm is "deflation", n_iter is the
|
|
maximum number of iterations run across all components. Else
|
|
they are just the number of iterations taken to converge. This is
|
|
returned only when return_n_iter is set to `True`.
|
|
|
|
Notes
|
|
-----
|
|
The data matrix X is considered to be a linear combination of
|
|
non-Gaussian (independent) components i.e. X = AS where columns of S
|
|
contain the independent components and A is a linear mixing
|
|
matrix. In short ICA attempts to `un-mix' the data by estimating an
|
|
un-mixing matrix W where ``S = W K X.``
|
|
While FastICA was proposed to estimate as many sources
|
|
as features, it is possible to estimate less by setting
|
|
n_components < n_features. It this case K is not a square matrix
|
|
and the estimated A is the pseudo-inverse of ``W K``.
|
|
|
|
This implementation was originally made for data of shape
|
|
[n_features, n_samples]. Now the input is transposed
|
|
before the algorithm is applied. This makes it slightly
|
|
faster for Fortran-ordered input.
|
|
|
|
References
|
|
----------
|
|
.. [1] A. Hyvarinen and E. Oja, "Fast Independent Component Analysis",
|
|
Algorithms and Applications, Neural Networks, 13(4-5), 2000,
|
|
pp. 411-430.
|
|
|
|
Examples
|
|
--------
|
|
>>> from sklearn.datasets import load_digits
|
|
>>> from sklearn.decomposition import fastica
|
|
>>> X, _ = load_digits(return_X_y=True)
|
|
>>> K, W, S = fastica(X, n_components=7, random_state=0, whiten='unit-variance')
|
|
>>> K.shape
|
|
(7, 64)
|
|
>>> W.shape
|
|
(7, 7)
|
|
>>> S.shape
|
|
(1797, 7)
|
|
"""
|
|
est = FastICA(
|
|
n_components=n_components,
|
|
algorithm=algorithm,
|
|
whiten=whiten,
|
|
fun=fun,
|
|
fun_args=fun_args,
|
|
max_iter=max_iter,
|
|
tol=tol,
|
|
w_init=w_init,
|
|
whiten_solver=whiten_solver,
|
|
random_state=random_state,
|
|
)
|
|
est._validate_params()
|
|
S = est._fit_transform(X, compute_sources=compute_sources)
|
|
|
|
if est.whiten in ["unit-variance", "arbitrary-variance"]:
|
|
K = est.whitening_
|
|
X_mean = est.mean_
|
|
else:
|
|
K = None
|
|
X_mean = None
|
|
|
|
returned_values = [K, est._unmixing, S]
|
|
if return_X_mean:
|
|
returned_values.append(X_mean)
|
|
if return_n_iter:
|
|
returned_values.append(est.n_iter_)
|
|
|
|
return returned_values
|
|
|
|
|
|
class FastICA(ClassNamePrefixFeaturesOutMixin, TransformerMixin, BaseEstimator):
|
|
"""FastICA: a fast algorithm for Independent Component Analysis.
|
|
|
|
The implementation is based on [1]_.
|
|
|
|
Read more in the :ref:`User Guide <ICA>`.
|
|
|
|
Parameters
|
|
----------
|
|
n_components : int, default=None
|
|
Number of components to use. If None is passed, all are used.
|
|
|
|
algorithm : {'parallel', 'deflation'}, default='parallel'
|
|
Specify which algorithm to use for FastICA.
|
|
|
|
whiten : str or bool, default='unit-variance'
|
|
Specify the whitening strategy to use.
|
|
|
|
- If 'arbitrary-variance', a whitening with variance
|
|
arbitrary is used.
|
|
- If 'unit-variance', the whitening matrix is rescaled to ensure that
|
|
each recovered source has unit variance.
|
|
- If False, the data is already considered to be whitened, and no
|
|
whitening is performed.
|
|
|
|
.. versionchanged:: 1.3
|
|
The default value of `whiten` changed to 'unit-variance' in 1.3.
|
|
|
|
fun : {'logcosh', 'exp', 'cube'} or callable, default='logcosh'
|
|
The functional form of the G function used in the
|
|
approximation to neg-entropy. Could be either 'logcosh', 'exp',
|
|
or 'cube'.
|
|
You can also provide your own function. It should return a tuple
|
|
containing the value of the function, and of its derivative, in the
|
|
point. The derivative should be averaged along its last dimension.
|
|
Example::
|
|
|
|
def my_g(x):
|
|
return x ** 3, (3 * x ** 2).mean(axis=-1)
|
|
|
|
fun_args : dict, default=None
|
|
Arguments to send to the functional form.
|
|
If empty or None and if fun='logcosh', fun_args will take value
|
|
{'alpha' : 1.0}.
|
|
|
|
max_iter : int, default=200
|
|
Maximum number of iterations during fit.
|
|
|
|
tol : float, default=1e-4
|
|
A positive scalar giving the tolerance at which the
|
|
un-mixing matrix is considered to have converged.
|
|
|
|
w_init : array-like of shape (n_components, n_components), default=None
|
|
Initial un-mixing array. If `w_init=None`, then an array of values
|
|
drawn from a normal distribution is used.
|
|
|
|
whiten_solver : {"eigh", "svd"}, default="svd"
|
|
The solver to use for whitening.
|
|
|
|
- "svd" is more stable numerically if the problem is degenerate, and
|
|
often faster when `n_samples <= n_features`.
|
|
|
|
- "eigh" is generally more memory efficient when
|
|
`n_samples >= n_features`, and can be faster when
|
|
`n_samples >= 50 * n_features`.
|
|
|
|
.. versionadded:: 1.2
|
|
|
|
random_state : int, RandomState instance or None, default=None
|
|
Used to initialize ``w_init`` when not specified, with a
|
|
normal distribution. Pass an int, for reproducible results
|
|
across multiple function calls.
|
|
See :term:`Glossary <random_state>`.
|
|
|
|
Attributes
|
|
----------
|
|
components_ : ndarray of shape (n_components, n_features)
|
|
The linear operator to apply to the data to get the independent
|
|
sources. This is equal to the unmixing matrix when ``whiten`` is
|
|
False, and equal to ``np.dot(unmixing_matrix, self.whitening_)`` when
|
|
``whiten`` is True.
|
|
|
|
mixing_ : ndarray of shape (n_features, n_components)
|
|
The pseudo-inverse of ``components_``. It is the linear operator
|
|
that maps independent sources to the data.
|
|
|
|
mean_ : ndarray of shape(n_features,)
|
|
The mean over features. Only set if `self.whiten` is True.
|
|
|
|
n_features_in_ : int
|
|
Number of features seen during :term:`fit`.
|
|
|
|
.. versionadded:: 0.24
|
|
|
|
feature_names_in_ : ndarray of shape (`n_features_in_`,)
|
|
Names of features seen during :term:`fit`. Defined only when `X`
|
|
has feature names that are all strings.
|
|
|
|
.. versionadded:: 1.0
|
|
|
|
n_iter_ : int
|
|
If the algorithm is "deflation", n_iter is the
|
|
maximum number of iterations run across all components. Else
|
|
they are just the number of iterations taken to converge.
|
|
|
|
whitening_ : ndarray of shape (n_components, n_features)
|
|
Only set if whiten is 'True'. This is the pre-whitening matrix
|
|
that projects data onto the first `n_components` principal components.
|
|
|
|
See Also
|
|
--------
|
|
PCA : Principal component analysis (PCA).
|
|
IncrementalPCA : Incremental principal components analysis (IPCA).
|
|
KernelPCA : Kernel Principal component analysis (KPCA).
|
|
MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis.
|
|
SparsePCA : Sparse Principal Components Analysis (SparsePCA).
|
|
|
|
References
|
|
----------
|
|
.. [1] A. Hyvarinen and E. Oja, Independent Component Analysis:
|
|
Algorithms and Applications, Neural Networks, 13(4-5), 2000,
|
|
pp. 411-430.
|
|
|
|
Examples
|
|
--------
|
|
>>> from sklearn.datasets import load_digits
|
|
>>> from sklearn.decomposition import FastICA
|
|
>>> X, _ = load_digits(return_X_y=True)
|
|
>>> transformer = FastICA(n_components=7,
|
|
... random_state=0,
|
|
... whiten='unit-variance')
|
|
>>> X_transformed = transformer.fit_transform(X)
|
|
>>> X_transformed.shape
|
|
(1797, 7)
|
|
"""
|
|
|
|
_parameter_constraints: dict = {
|
|
"n_components": [Interval(Integral, 1, None, closed="left"), None],
|
|
"algorithm": [StrOptions({"parallel", "deflation"})],
|
|
"whiten": [
|
|
StrOptions({"arbitrary-variance", "unit-variance"}),
|
|
Options(bool, {False}),
|
|
],
|
|
"fun": [StrOptions({"logcosh", "exp", "cube"}), callable],
|
|
"fun_args": [dict, None],
|
|
"max_iter": [Interval(Integral, 1, None, closed="left")],
|
|
"tol": [Interval(Real, 0.0, None, closed="left")],
|
|
"w_init": ["array-like", None],
|
|
"whiten_solver": [StrOptions({"eigh", "svd"})],
|
|
"random_state": ["random_state"],
|
|
}
|
|
|
|
def __init__(
|
|
self,
|
|
n_components=None,
|
|
*,
|
|
algorithm="parallel",
|
|
whiten="unit-variance",
|
|
fun="logcosh",
|
|
fun_args=None,
|
|
max_iter=200,
|
|
tol=1e-4,
|
|
w_init=None,
|
|
whiten_solver="svd",
|
|
random_state=None,
|
|
):
|
|
super().__init__()
|
|
self.n_components = n_components
|
|
self.algorithm = algorithm
|
|
self.whiten = whiten
|
|
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`.
|
|
"""
|
|
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
|
|
|
|
@_fit_context(prefer_skip_nested_validation=True)
|
|
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.
|
|
"""
|
|
return self._fit_transform(X, compute_sources=True)
|
|
|
|
@_fit_context(prefer_skip_nested_validation=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._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]}
|