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, 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 socalled
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 aftertransform
. If None, n_components is set to the number of features. tolfloat, defaul=1e2
Stopping tolerance for loglikelihood 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 foriterated_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,)
Perfeature 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 nonGaussian 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.
Compute data covariance with the FactorAnalysis model.
get_params
([deep])Get parameters for this estimator.
Compute data precision matrix with the FactorAnalysis model.
score
(X[, y])Compute the average loglikelihood of the samples
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.

fit
(X, y=None)[source]¶ Fit the FactorAnalysis model to X using SVD based approach
 Parameters
 Xarraylike 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
andy
with optional parametersfit_params
and returns a transformed version ofX
. Parameters
 Xarraylike of shape (n_samples, n_features)
Input samples.
 yarraylike 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 loglikelihood of the samples
 Parameters
 Xndarray of shape (n_samples, n_features)
The data
 yIgnored
 Returns
 llfloat
Average loglikelihood of the samples under the current model

score_samples
(X)[source]¶ Compute the loglikelihood of each sample
 Parameters
 Xndarray of shape (n_samples, n_features)
The data
 Returns
 llndarray of 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
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
 Xarraylike of shape (n_samples, n_features)
Training data.
 Returns
 X_newndarray of shape (n_samples, n_components)
The latent variables of X.