sklearn.decomposition.fastica(X, n_components=None, *, algorithm='parallel', whiten='unit-variance', fun='logcosh', fun_args=None, max_iter=200, tol=0.0001, w_init=None, whiten_solver='svd', random_state=None, return_X_mean=False, compute_sources=True, return_n_iter=False)[source]#

Perform Fast Independent Component Analysis.

The implementation is based on [1].

Read more in the User Guide.

Xarray-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_componentsint, 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.

whitenstr 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.

Changed in version 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_argsdict, 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_iterint, default=200

Maximum number of iterations to perform.

tolfloat, default=1e-4

A positive scalar giving the tolerance at which the un-mixing matrix is considered to have converged.

w_initndarray 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.

Added in version 1.2.

random_stateint, 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 Glossary.

return_X_meanbool, default=False

If True, X_mean is returned too.

compute_sourcesbool, 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_iterbool, default=False

Whether or not to return the number of iterations.

Kndarray 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’.

Wndarray 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.

Sndarray of shape (n_samples, n_components) or None

Estimated source matrix.

X_meanndarray of shape (n_features,)

The mean over features. Returned only if return_X_mean is True.


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.


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.



A. Hyvarinen and E. Oja, “Fast Independent Component Analysis”, Algorithms and Applications, Neural Networks, 13(4-5), 2000, pp. 411-430.


>>> 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)