# sklearn.decomposition.fastica¶

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

Perform Fast Independent Component Analysis.

Read more in the User Guide.

Parameters
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 extract. If None no dimension reduction is performed.

algorithm{‘parallel’, ‘deflation’}, default=’parallel’

Apply a parallel or deflational FASTICA algorithm.

whitenbool, default=True

If True perform an initial whitening of the data. If False, the data is assumed to have already been preprocessed: it should be centered, normed and white. Otherwise you will get incorrect results. In this case the parameter n_components will be ignored.

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, np.mean(3 * x ** 2, 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-04

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 of dimension (n.comp,n.comp). If None (default) then an array of normal r.v.’s is used.

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.

Returns
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.

n_iterint

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.

Implemented using FastICA: A. Hyvarinen and E. Oja, Independent Component Analysis: Algorithms and Applications, Neural Networks, 13(4-5), 2000, pp. 411-430