ó ‡ˆ\c@sÙdZddlZddlmZmZddlZddlmZddl m Z m Z ddl m Z ddlmZmZdd lmZmZmZdd lmZdd lmZd e e fd „ƒYZdS(s§Factor Analysis. A latent linear variable model. FactorAnalysis is similar to probabilistic PCA implemented by PCA.score While PCA assumes Gaussian noise with the same variance for each feature, the FactorAnalysis model assumes different variances for each of them. This implementation is based on David Barber's Book, Bayesian Reasoning and Machine Learning, http://www.cs.ucl.ac.uk/staff/d.barber/brml, Algorithm 21.1 iÿÿÿÿN(tsqrttlog(tlinalgi(t BaseEstimatortTransformerMixin(txrange(t check_arraytcheck_random_state(t fast_logdettrandomized_svdt squared_norm(tcheck_is_fitted(tConvergenceWarningtFactorAnalysisc BskeZdZd dedd dddd„Zd d„Zd„Zd „Zd „Z d „Z d d „Z RS(s6Factor Analysis (FA) A simple linear generative model with Gaussian latent variables. The observations are assumed to be caused by a linear transformation of lower dimensional latent factors and added Gaussian noise. Without loss of generality the factors are distributed according to a Gaussian with zero mean and unit covariance. The noise is also zero mean and has an arbitrary diagonal covariance matrix. If we would restrict the model further, by assuming that the Gaussian noise is even isotropic (all diagonal entries are the same) we would obtain :class:`PPCA`. FactorAnalysis performs a maximum likelihood estimate of the so-called `loading` matrix, the transformation of the latent variables to the observed ones, using expectation-maximization (EM). Read more in the :ref:`User Guide `. Parameters ---------- n_components : int | None Dimensionality of latent space, the number of components of ``X`` that are obtained after ``transform``. If None, n_components is set to the number of features. tol : float Stopping tolerance for EM algorithm. copy : bool Whether to make a copy of X. If ``False``, the input X gets overwritten during fitting. max_iter : int Maximum number of iterations. noise_variance_init : None | array, shape=(n_features,) The initial guess of the noise variance for each feature. If None, it defaults to np.ones(n_features) svd_method : {'lapack', 'randomized'} Which SVD method to use. If 'lapack' use standard SVD from scipy.linalg, if 'randomized' use fast ``randomized_svd`` function. Defaults to 'randomized'. For most applications 'randomized' will be sufficiently precise while providing significant speed gains. Accuracy can also be improved by setting higher values for `iterated_power`. If this is not sufficient, for maximum precision you should choose 'lapack'. iterated_power : int, optional Number of iterations for the power method. 3 by default. Only used if ``svd_method`` equals 'randomized' random_state : int, RandomState instance or None, optional (default=0) If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by `np.random`. Only used when ``svd_method`` equals 'randomized'. Attributes ---------- components_ : array, [n_components, n_features] Components with maximum variance. loglike_ : list, [n_iterations] The log likelihood at each iteration. noise_variance_ : array, shape=(n_features,) The estimated noise variance for each feature. n_iter_ : int Number of iterations run. Examples -------- >>> from sklearn.datasets import load_digits >>> from sklearn.decomposition import FactorAnalysis >>> X, _ = load_digits(return_X_y=True) >>> transformer = FactorAnalysis(n_components=7, random_state=0) >>> X_transformed = transformer.fit_transform(X) >>> X_transformed.shape (1797, 7) References ---------- .. David Barber, Bayesian Reasoning and Machine Learning, Algorithm 21.1 .. Christopher M. Bishop: Pattern Recognition and Machine Learning, Chapter 12.2.4 See also -------- PCA: Principal component analysis is also a latent linear variable model which however assumes equal noise variance for each feature. This extra assumption makes probabilistic PCA faster as it can be computed in closed form. FastICA: Independent component analysis, a latent variable model with non-Gaussian latent variables. g{®Gáz„?ièt randomizediic Csk||_||_||_||_|dkrCtd|ƒ‚n||_||_||_||_dS(NtlapackRsASVD method %s is not supported. Please consider the documentation(RR( t n_componentstcopyttoltmax_itert ValueErrort svd_methodtnoise_variance_inittiterated_powert random_state( tselfRRRRRRRR((sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pyt__init__Šs         cst|dˆjdtjƒ}|j\}}ˆj‰ˆdkrK|‰ntj|ddƒˆ_|ˆj8}t |ƒ}|t dtj ƒˆ}tj |ddƒ}ˆj dkrÖtj|d|jƒ}nItˆj ƒ|kr tdtˆj ƒ|fƒ‚ntjˆj ƒ}g} tj } d} ˆjdkrV‡fd †} nIˆjd krŒtˆjƒ‰‡‡‡fd †} ntd ˆjƒ‚xJtˆjƒD]!} tj |ƒ| }| |||ƒ\}}}|d C}tj tj|ddƒƒdd…tjf|}~||9}|tjtj |ƒƒ}||tjtj |ƒƒ7}|| d9}| j|ƒ|| ˆjkr¡Pn|} tj|tj|d ddƒ| ƒ}q¯Wtjdddt ƒ|ˆ_!|ˆ_"| ˆ_#| dˆ_$ˆS(sîFit the FactorAnalysis model to X using EM Parameters ---------- X : array-like, shape (n_samples, n_features) Training data. y : Ignored Returns ------- self Rtdtypetaxisig@sInoise_variance_init dimension does not with number of features : %d != %dgê-™—q=Rcs=tj|dtƒ\}}}|ˆ |ˆ t|ˆƒfS(Nt full_matrices(RtsvdtFalseR (tXt_tstV(R(sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pytmy_svdÆsRcsDt|ˆdˆdˆjƒ\}}}||t|ƒt|ƒfS(NRtn_iter(R RR (R R!R"R#(RRR(sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pyR$Ís sASVD method %s is not supported. Please consider the documentationigð?gNs FactorAnalysis did not converge.s You might wants& to increase the number of iterations.i(%RRtnptfloat64tshapeRtNonetmeantmean_RRtpitvarRtonesRtlenRtarraytinfRRRRRtmaximumtnewaxistsumtappendRtwarningstwarnR t components_tnoise_variance_tloglike_tn_iter_(RR tyt n_samplest n_featurestnsqrttllconstR-tpsitlogliketold_lltSMALLR$titsqrt_psiR"R#t unexp_vartWtll((RRRsDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pytfitšsd        6   -    cCsžt|dƒt|ƒ}tjt|jƒƒ}||j}|j|j}tj |tj ||jj ƒƒ}tj ||j ƒ}tj ||ƒ}|S(s¥Apply dimensionality reduction to X using the model. Compute the expected mean of the latent variables. See Barber, 21.2.33 (or Bishop, 12.66). Parameters ---------- X : array-like, shape (n_samples, n_features) Training data. Returns ------- X_new : array-like, shape (n_samples, n_components) The latent variables of X. R8( R RR&teyeR/R8R+R9RtinvtdottT(RR tIht X_transformedtWpsitcov_zttmp((sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pyt transformös   %cCsUt|dƒtj|jj|jƒ}|jddt|ƒd…c|j7<|S(sCompute data covariance with the FactorAnalysis model. ``cov = components_.T * components_ + diag(noise_variance)`` Returns ------- cov : array, shape (n_features, n_features) Estimated covariance of data. R8Ni(R R&RMR8RNtflatR/R9(Rtcov((sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pytget_covariances )cCsIt|dƒ|jjd}|jdkr@tjd|jƒS|j|krbtj|j ƒƒS|j}tj ||j|j ƒ}|j ddt |ƒd…cd7R8t precision((sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pyt get_precision$s  &  !-cCs†t|dƒ||j}|jƒ}|jd}d|tj||ƒjddƒ}|d|tdtjƒt |ƒ8}|S(s)Compute the log-likelihood of each sample Parameters ---------- X : array, shape (n_samples, n_features) The data Returns ------- ll : array, shape (n_samples,) Log-likelihood of each sample under the current model R8igà¿Rgà?g@( R R+RZR(R&RMR4RR,R(RR tXrRYR>tlog_like((sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pyt score_samplesAs    &cCstj|j|ƒƒS(s:Compute the average log-likelihood of the samples Parameters ---------- X : array, shape (n_samples, n_features) The data y : Ignored Returns ------- ll : float Average log-likelihood of the samples under the current model (R&R*R](RR R<((sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pytscoreXsN( t__name__t __module__t__doc__R)tTrueRRJRTRWRZR]R^(((sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pyR $se  \    (RaR6tmathRRtnumpyR&tscipyRtbaseRRtexternals.six.movesRtutilsRRt utils.extmathRR R tutils.validationR t exceptionsR R (((sDlib/python2.7/site-packages/sklearn/decomposition/factor_analysis.pyts