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.
The implementation is based on [1].
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 andn_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 ofW 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.