U 3dUh@sdZddlZddlmZmZddlZddlmZddl m Z m Z m Z ddl mZddlmZmZmZdd lmZdd lmZmZmZd d gZd dZddZddZddZd&ddZddZddZ d'dddddddd dd!d"d!d# d$d Z!Gd%d d e e e Z"dS)(z Python implementation of the fast ICA algorithms. Reference: Tables 8.3 and 8.4 page 196 in the book: Independent Component Analysis, by Hyvarinen et al. N)IntegralReal)linalg) BaseEstimatorTransformerMixinClassNamePrefixFeaturesOutMixin)ConvergenceWarning) check_arrayas_float_arraycheck_random_state)check_is_fitted)HiddenInterval StrOptionsfasticaFastICAcCs,|tj||d|j|d|g8}|S)a Orthonormalize w wrt the first j rows of W. Parameters ---------- w : ndarray of shape (n,) Array to be orthogonalized W : ndarray of shape (p, n) Null space definition j : int < p The no of (from the first) rows of Null space W wrt which w is orthogonalized. Notes ----- Assumes that W is orthogonal w changed in place N)npr multi_dotT)wWjrB/tmp/pip-unpacked-wheel-zrfo1fqw/sklearn/decomposition/_fastica.py_gs_decorrelations(rcCsTtt||j\}}tj|t|jjdd}tj |dt ||j|gS)z@Symmetric decorrelation i.e. W <- (W * W.T) ^{-1/2} * W N)Za_minZa_max?) reighrdotrZclipfinfodtypeZtinyrsqrt)rsurrr_sym_decorrelation4sr$cCs|jd}tj||f|jd}g}t|D]} || ddf} | t| d} t|D]} |t| j ||\} } || j dd| | }t ||| |t|d}t t || d}|} ||kr`qq`| | d| || ddf<q*|t|fS)zcDeflationary FastICA using fun approx to neg-entropy function Used internally by FastICA. rr Nraxis)shaperzerosr rangecopyr!sumrrmeanrabsappendmax)Xtolgfun_argsmax_iterw_init n_componentsrn_iterrrigwtxg_wtxZw1limrrr_ica_defCs$    r>c Cst|}~t|jd}t|D]x}|t|||\} } tt| |j|| ddtjf|} ~ ~ tt t t d| |d} | }| |kr qq t dt ||dfS)zCParallel FastICA. Used internally by FastICA --main loop r&Nzij,ij->iz\FastICA did not converge. Consider increasing tolerance or the maximum number of iterations.)r$floatr)r+rrrnewaxisr1r/Zeinsumwarningswarnr ) r2r3r4r5r6r7rZp_iir;r<ZW1r=rrr_ica_parfs  ,rDcCsh|dd}||9}t||}tj|jd|jd}t|D] \}}|d|d||<q>||fS)Nalpharrr%r&r)getrtanhemptyr)r enumerater.)xr5rEgxg_xr:Zgx_irrr_logcoshs  rMcCs<t|d d}||}d|d|}||jddfS)Nrr&r')rexpr.)rJr5rOrKrLrrr_expsrPcCs|dd|djddfS)NrrNr')r.rJr5rrr_cubesrSparallelrBlogcosh-C6?svdFT) algorithmwhitenfunr5r6r3r7 whiten_solver random_state return_X_meancompute_sources return_n_iterc  Csxt||||||||| | d }|j|| d}|jdkrB|j}|j}nd}d}||j|g}| rd||| rt||j|S)aWPerform Fast Independent Component Analysis. The implementation is based on [1]_. Read more in the :ref:`User Guide `. Parameters ---------- X : array-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_components : int, 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. whiten : str or bool, default="warn" Specify the whitening strategy to use. - If 'arbitrary-variance' (default), 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. .. deprecated:: 1.1 Starting in v1.3, `whiten='unit-variance'` will be used by default. `whiten=True` is deprecated from 1.1 and will raise ValueError in 1.3. Use `whiten=arbitrary-variance` instead. 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_args : dict, 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_iter : int, default=200 Maximum number of iterations to perform. tol : float, default=1e-4 A positive scalar giving the tolerance at which the un-mixing matrix is considered to have converged. w_init : ndarray 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`. .. versionadded:: 1.2 random_state : int, 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 :term:`Glossary `. return_X_mean : bool, default=False If True, X_mean is returned too. compute_sources : bool, 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_iter : bool, default=False Whether or not to return the number of iterations. Returns ------- K : ndarray 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'. W : ndarray 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. S : ndarray of shape (n_samples, n_components) or None Estimated source matrix. X_mean : ndarray of 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.`` 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. References ---------- .. [1] A. Hyvarinen and E. Oja, "Fast Independent Component Analysis", Algorithms and Applications, Neural Networks, 13(4-5), 2000, pp. 411-430. r8rYrZr[r5r6r3r7r\r]r_) unit-variancearbitrary-varianceN)r_fit_transform_whiten whitening_mean_ _unmixingr0n_iter_)r2r8rYrZr[r5r6r3r7r\r]r^r_r`ZestSKX_meanZreturned_valuesrrrrs2     c seZdZUdZeedddddgeddhgeedhed d hd ged d dhege dgeeddddgee ddddgddgeddhgdgd Z e e d<d+ddd ddddddd fdd Z d,ddZd-ddZd.d d!Zd/d#d$Zd0d%d&Zed'd(Zd)d*ZZS)1ra}FastICA: a fast algorithm for Independent Component Analysis. The implementation is based on [1]_. Read more in the :ref:`User Guide `. Parameters ---------- n_components : int, 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. whiten : str or bool, default="warn" Specify the whitening strategy to use. - If 'arbitrary-variance' (default), 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. .. deprecated:: 1.1 Starting in v1.3, `whiten='unit-variance'` will be used by default. `whiten=True` is deprecated from 1.1 and will raise ValueError in 1.3. Use `whiten=arbitrary-variance` instead. 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_args : dict, 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_iter : int, default=200 Maximum number of iterations during fit. tol : float, default=1e-4 A positive scalar giving the tolerance at which the un-mixing matrix is considered to have converged. w_init : array-like 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`. .. versionadded:: 1.2 random_state : int, 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 :term:`Glossary `. Attributes ---------- components_ : ndarray of shape (n_components, n_features) The linear operator to apply to the data to get the independent sources. This is equal to the unmixing matrix when ``whiten`` is False, and equal to ``np.dot(unmixing_matrix, self.whitening_)`` when ``whiten`` is True. mixing_ : ndarray of shape (n_features, n_components) The pseudo-inverse of ``components_``. It is the linear operator that maps independent sources to the data. mean_ : ndarray of shape(n_features,) The mean over features. Only set if `self.whiten` is True. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 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. whitening_ : ndarray of shape (n_components, n_features) Only set if whiten is 'True'. This is the pre-whitening matrix that projects data onto the first `n_components` principal components. See Also -------- PCA : Principal component analysis (PCA). IncrementalPCA : Incremental principal components analysis (IPCA). KernelPCA : Kernel Principal component analysis (KPCA). MiniBatchSparsePCA : Mini-batch Sparse Principal Components Analysis. SparsePCA : Sparse Principal Components Analysis (SparsePCA). References ---------- .. [1] A. Hyvarinen and E. Oja, Independent Component Analysis: Algorithms and Applications, Neural Networks, 13(4-5), 2000, pp. 411-430. Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.decomposition import FastICA >>> X, _ = load_digits(return_X_y=True) >>> transformer = FastICA(n_components=7, ... random_state=0, ... whiten='unit-variance') >>> X_transformed = transformer.fit_transform(X) >>> X_transformed.shape (1797, 7) r&Nleft)closedrT deflationrBrdrcbooleanrUrOcubegz array-likerrXr]ra_parameter_constraintsrVrW) rYrZr[r5r6r3r7r\r]c sJt||_||_||_||_||_||_||_||_ | |_ | |_ dSN) super__init__r8rYrZr[r5r6r3r7r\r]) selfr8rYrZr[r5r6r3r7r\r] __class__rrrvs zFastICA.__init__Fcsj_jdkr$tdtd_jdkrDtjdtddd_j|jtjtjgddj }j d krpinj }t j }| d d }d |krdksntd jdkrt}n6jdkrt}n&jdkrt}ntjrfdd}|j\}} j} js | d k r d } td| d kr4t| |} | t| |kr\t| |} td| jr|jdd} || d d tjf8}jdkrt||\} } t| d d d}t| jj }| |k}t!|rtd|| |<tj"| | d| || d d |f} } n(jdkr@tj#|dddd d\} } | t$| d9} | | j d | }~ ~ t||}|t"| 9}n t%|dd}j&}|d krtj'|j(| | fd|jd }n.t'|}|j| | fkrtd!d"| | fij)||j*|d#}j+d$krt,|f|\}}nj+d%kr:t-|f|\}}~|_.|rvjrftj/|||gj }nt||j }nd }jrjd&kr|stj/|||gj }tj0|ddd'}||}||j }t||_1| _2|_3n|_1tj4j1dd(_5|_6|S))adFit the model. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where `n_samples` is the number of samples and `n_features` is the number of features. compute_sources : bool, default=False If False, sources are not computes but only the rotation matrix. This can save memory when working with big data. Defaults to False. Returns ------- S : ndarray of shape (n_samples, n_components) or None Sources matrix. `None` if `compute_sources` is `False`. rBzAStarting in v1.3, whiten='unit-variance' will be used by default.rdTzStarting in v1.3, whiten=True should be specified as whiten='arbitrary-variance' (its current behaviour). This behavior is deprecated in 1.1 and will raise ValueError in 1.3.r) stacklevel)r,r Zensure_min_samplesNrErr&zalpha must be in [1,2]rUrOrrcsj|f|Srt)r[rRrwrrr4@sz!FastICA._fit_transform..gz(Ignoring n_components with whiten=False.z/n_components is too large: it will be set to %srNr'rzfThere are some small singular values, using whiten_solver = 'svd' might lead to more accurate results.)outrXF)Z full_matrices check_finiter)r,)sizer%z/w_init has invalid shape -- should be %(shape)sr))r3r4r5r6r7rTrprc)r(Zkeepdims)r})7rZrfrArB FutureWarning_validate_datarfloat64float32rr5r r]rF ValueErrorr[rMrPrScallabler)r8minr.r@r\rrrZargsortrr epsanyr!rXsignr r7Zasarraynormalr3r6rYrDr>rjrZstd components_rhrgZpinvmixing_ri)rwr2r_ZXTr5r]rEr4Z n_featuresZ n_samplesr8rmdr#Z sort_indicesrZdegenerate_idxrlZX1r7kwargsrr9rkZS_stdrr{rre s                            zFastICA._fit_transformcCs||j|ddS)a5Fit the model and recover the sources from X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where `n_samples` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- X_new : ndarray of shape (n_samples, n_components) Estimated sources obtained by transforming the data with the estimated unmixing matrix. TrbZ_validate_paramsrerwr2yrrr fit_transformszFastICA.fit_transformcCs||j|dd|S)aFit the model to X. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data, where `n_samples` is the number of samples and `n_features` is the number of features. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Returns the instance itself. Frbrrrrrfitsz FastICA.fitTcCsHt||j||o|jtjtjgdd}|jr8||j8}t||jj S)a_Recover the sources from X (apply the unmixing matrix). Parameters ---------- X : array-like of shape (n_samples, n_features) Data to transform, where `n_samples` is the number of samples and `n_features` is the number of features. copy : bool, default=True If False, data passed to fit can be overwritten. Defaults to True. Returns ------- X_new : ndarray of shape (n_samples, n_components) Estimated sources obtained by transforming the data with the estimated unmixing matrix. F)r,r reset) r rrfrrrrhrrrrwr2r,rrr transforms  zFastICA.transformcCsHt|t||o|jtjtjgd}t||jj}|jrD||j 7}|S)a1Transform the sources back to the mixed data (apply mixing matrix). Parameters ---------- X : array-like of shape (n_samples, n_components) Sources, where `n_samples` is the number of samples and `n_components` is the number of components. copy : bool, default=True If False, data passed to fit are overwritten. Defaults to True. Returns ------- X_new : ndarray of shape (n_samples, n_features) Reconstructed data obtained with the mixing matrix. )r,r ) r r rfrrrrrrrhrrrrinverse_transforms  zFastICA.inverse_transformcCs |jjdS)z&Number of transformed output features.r)rr)r{rrr_n_features_outszFastICA._n_features_outcCsdtjtjgiS)NZpreserves_dtype)rrrr{rrr _more_tagsszFastICA._more_tags)N)F)N)N)T)T)__name__ __module__ __qualname____doc__rrrrrdictrrs__annotations__rvrerrrrpropertyrr __classcell__rrrxrrTsJ       (     )N)N)#rrAZnumbersrrZnumpyrZscipyrbaserrr exceptionsr utilsr r r Zutils.validationr Zutils._param_validationrrr__all__rr$r>rDrMrPrSrrrrrrsD    #  8