sklearn.decomposition
.FactorAnalysis¶

class
sklearn.decomposition.
FactorAnalysis
(n_components=None, tol=0.01, copy=True, max_iter=1000, noise_variance_init=None, svd_method=’randomized’, iterated_power=3, random_state=0)[source]¶ Factor 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
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 User Guide.
Parameters:  n_components : int  None
Dimensionality of latent space, the number of components of
X
that are obtained aftertransform
. 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.
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.
References
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)
Methods
fit
(X[, y])Fit the FactorAnalysis model to X using EM fit_transform
(X[, y])Fit to data, then transform it. get_covariance
()Compute data covariance with the FactorAnalysis model. get_params
([deep])Get parameters for this estimator. get_precision
()Compute data precision matrix with the FactorAnalysis model. score
(X[, y])Compute the average loglikelihood of the samples score_samples
(X)Compute the loglikelihood of each sample set_params
(**params)Set the parameters of this estimator. transform
(X)Apply dimensionality reduction to X using the model. 
__init__
(n_components=None, tol=0.01, copy=True, max_iter=1000, noise_variance_init=None, svd_method=’randomized’, iterated_power=3, random_state=0)[source]¶

fit
(X, y=None)[source]¶ Fit the FactorAnalysis model to X using EM
Parameters:  X : arraylike, shape (n_samples, n_features)
Training data.
 y : Ignored
Returns:  self

fit_transform
(X, y=None, **fit_params)[source]¶ Fit to data, then transform it.
Fits transformer to X and y with optional parameters fit_params and returns a transformed version of X.
Parameters:  X : numpy array of shape [n_samples, n_features]
Training set.
 y : numpy array of shape [n_samples]
Target values.
Returns:  X_new : numpy array of shape [n_samples, n_features_new]
Transformed array.

get_covariance
()[source]¶ Compute 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.

get_params
(deep=True)[source]¶ Get parameters for this estimator.
Parameters:  deep : boolean, optional
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:  params : mapping of string to any
Parameter names mapped to their values.

get_precision
()[source]¶ Compute data precision matrix with the FactorAnalysis model.
Returns:  precision : array, shape (n_features, n_features)
Estimated precision of data.

score
(X, y=None)[source]¶ Compute the average loglikelihood of the samples
Parameters:  X : array, shape (n_samples, n_features)
The data
 y : Ignored
Returns:  ll : float
Average loglikelihood of the samples under the current model

score_samples
(X)[source]¶ Compute the loglikelihood of each sample
Parameters:  X : array, shape (n_samples, n_features)
The data
Returns:  ll : array, shape (n_samples,)
Loglikelihood of each sample under the current model

set_params
(**params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form
<component>__<parameter>
so that it’s possible to update each component of a nested object.Returns:  self

transform
(X)[source]¶ 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 : arraylike, shape (n_samples, n_features)
Training data.
Returns:  X_new : arraylike, shape (n_samples, n_components)
The latent variables of X.