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, rotation=None, 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 so-called loading matrix, the transformation of the latent variables to the observed ones, using SVD based approach. Read more in the User Guide.  New in version 0.13.   Parameters 
 
n_componentsint, default=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.  
tolfloat, defaul=1e-2 

Stopping tolerance for log-likelihood increase.  
copybool, default=True 

Whether to make a copy of X. If False, the input X gets overwritten during fitting.  
max_iterint, default=1000 

Maximum number of iterations.  
noise_variance_initndarray of shape (n_features,), default=None 

The initial guess of the noise variance for each feature. If None, it defaults to np.ones(n_features).  
svd_method{‘lapack’, ‘randomized’}, default=’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_powerint, default=3 

Number of iterations for the power method. 3 by default. Only used if svd_method equals ‘randomized’.  
rotation{‘varimax’, ‘quartimax’}, default=None 

If not None, apply the indicated rotation. Currently, varimax and quartimax are implemented. See “The varimax criterion for analytic rotation in factor analysis” H. F. Kaiser, 1958.  New in version 0.24.   
random_stateint or RandomState instance, default=0 

Only used when svd_method equals ‘randomized’. Pass an int for reproducible results across multiple function calls. See Glossary.    Attributes 
 
components_ndarray of shape (n_components, n_features) 

Components with maximum variance.  
loglike_list of shape (n_iterations,) 

The log likelihood at each iteration.  
noise_variance_ndarray of shape (n_features,) 

The estimated noise variance for each feature.  
n_iter_int 

Number of iterations run.  
mean_ndarray of shape (n_features,) 

Per-feature empirical mean, estimated from the training set.      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.    References  David Barber, Bayesian Reasoning and Machine Learning, Algorithm 21.1. Christopher M. Bishop: Pattern Recognition and Machine Learning, Chapter 12.2.4.  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 SVD based approach  
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 log-likelihood of the samples  
score_samples(X) Compute the log-likelihood of each sample  
set_params(**params) Set the parameters of this estimator.  
transform(X) Apply dimensionality reduction to X using the model.    
fit(X, y=None) [source]
 
Fit the FactorAnalysis model to X using SVD based approach  Parameters 
 
Xarray-like of shape (n_samples, n_features) 

Training data.  
yIgnored 
  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 
 
Xarray-like of shape (n_samples, n_features) 

Input samples.  
yarray-like of shape (n_samples,) or (n_samples, n_outputs), default=None 

Target values (None for unsupervised transformations).  
**fit_paramsdict 

Additional fit parameters.    Returns 
 
X_newndarray 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 
 
covndarray of shape (n_features, n_features) 

Estimated covariance of data.     
  
get_params(deep=True) [source]
 
Get parameters for this estimator.  Parameters 
 
deepbool, default=True 

If True, will return the parameters for this estimator and contained subobjects that are estimators.    Returns 
 
paramsdict 

Parameter names mapped to their values.     
  
get_precision() [source]
 
Compute data precision matrix with the FactorAnalysis model.  Returns 
 
precisionndarray of shape (n_features, n_features) 

Estimated precision of data.     
  
score(X, y=None) [source]
 
Compute the average log-likelihood of the samples  Parameters 
 
Xndarray of shape (n_samples, n_features) 

The data  
yIgnored 
  Returns 
 
llfloat 

Average log-likelihood of the samples under the current model     
  
score_samples(X) [source]
 
Compute the log-likelihood of each sample  Parameters 
 
Xndarray of shape (n_samples, n_features) 

The data    Returns 
 
llndarray of shape (n_samples,) 

Log-likelihood 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 Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.  Parameters 
 
**paramsdict 

Estimator parameters.    Returns 
 
selfestimator instance 

Estimator instance.     
  
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 
 
Xarray-like of shape (n_samples, n_features) 

Training data.    Returns 
 
X_newndarray of shape (n_samples, n_components) 

The latent variables of X.