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.
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. 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. Example:
- def my_g(x):
return x ** 3, 3 * x ** 2
fun_args : dictionary, optional
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, 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.
random_state : int or RandomState
Pseudo number generator state used for random sampling.
return_X_mean : bool, optional
If True, X_mean is returned too.
compute_sources : bool, optional
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, optional
Whether or not to return the number of iterations.
Returns: K : array, shape (n_components, n_features) | 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 : array, shape (n_components, n_components)
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 : array, shape (n_components, n_samples) | None
Estimated source matrix
X_mean : array, 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.`
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