8.5.13. sklearn.decomposition.fastica

sklearn.decomposition.fastica(X, n_components=None, algorithm='parallel', whiten=True, fun='logcosh', fun_prime='', fun_args={}, max_iter=200, tol=0.0001, w_init=None, random_state=None)

Perform Fast Independent Component Analysis.

Parameters :

X : array-like, 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, optional

Number of components to extract. If None no dimension reduction is performed.

algorithm : {‘parallel’, ‘deflation’}, optional

Apply a parallel or deflational FASTICA algorithm.

whiten: boolean, optional :

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 : string or function, optional

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 but in this case, its derivative should be provided via argument fun_prime

fun_prime : empty string (‘’) or function, optional

See fun.

fun_args: dictionary, optional :

If empty and if fun=’logcosh’, fun_args will take value {‘alpha’ : 1.0}

max_iter: int, optional :

Maximum number of iterations to perform

tol: float, optional :

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

w_init: (n_components, n_components) array, optional :

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

source_only: boolean, optional :

if True, only the sources matrix is returned

random_state: int or RandomState :

Pseudo number generator state used for random sampling.

Returns :

K: (n_components, p) array or None. :

If whiten is ‘True’, K is the pre-whitening matrix that projects data onto the first n.comp principal components. If whiten is ‘False’, K is ‘None’.

W: (n_components, n_components) array :

estimated un-mixing matrix The mixing matrix can be obtained by:

w = np.dot(W, K.T)
A = w.T * (w * w.T).I

S: (n_components, n) array :

estimated source matrix

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.`

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

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