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Factor Analysis (FA) This node has been automatically generated by wrapping the ``sklearn.decomposition.factor_analysis.FactorAnalysis`` class from the ``sklearn`` library. The wrapped instance can be accessed through the ``scikits_alg`` attribute. 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 socalled `loading` matrix, the transformation of the latent variables to the observed ones, using expectationmaximization (EM). Read more in the :ref:`User Guide <FA>`. **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 or RandomState Pseudo number generator state used for random sampling. Only used if ``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. **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 nonGaussian latent variables.














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Factor Analysis (FA) This node has been automatically generated by wrapping the ``sklearn.decomposition.factor_analysis.FactorAnalysis`` class from the ``sklearn`` library. The wrapped instance can be accessed through the ``scikits_alg`` attribute. 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 socalled `loading` matrix, the transformation of the latent variables to the observed ones, using expectationmaximization (EM). Read more in the :ref:`User Guide <FA>`. **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 or RandomState Pseudo number generator state used for random sampling. Only used if ``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. **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 nonGaussian latent variables.




Apply dimensionality reduction to X using the model. This node has been automatically generated by wrapping the sklearn.decomposition.factor_analysis.FactorAnalysis class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Compute the expected mean of the latent variables. See Barber, 21.2.33 (or Bishop, 12.66). Parameters
Returns



Fit the FactorAnalysis model to X using EM This node has been automatically generated by wrapping the sklearn.decomposition.factor_analysis.FactorAnalysis class from the sklearn library. The wrapped instance can be accessed through the scikits_alg attribute. Parameters
Returns self

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