sklearn.decomposition.FactorAnalysis

class sklearn.decomposition.FactorAnalysis(n_components=None, tol=0.01, copy=True, max_iter=1000, verbose=0, noise_variance_init=None)

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 expectation-maximization (EM).

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.

verbose : int | bool

Print verbose output.

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)

See also

PCA

Principal component analysis, a similar non-probabilistic model model that can be computed in closed form.

ProbabilisticPCA

probabilistic PCA.

FastICA

Independent component analysis, a latent variable model with non-Gaussian latent variables.

References

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.

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.
score(X[, y])	Compute score of X under FactorAnalysis model.
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, verbose=0, noise_variance_init=None)

fit(X, y=None)

Fit the FactorAnalysis model to X using EM

Parameters :

X : array-like, shape (n_samples, n_features)

Training data.

Returns :

self :

fit_transform(X, y=None, **fit_params)

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()

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)

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.

score(X, y=None)

Compute score of X under FactorAnalysis model.

Parameters :

X: array of shape(n_samples, n_features) :

The data to test

Returns :

ll: array of shape (n_samples), :

log-likelihood of each row of X under the current model

set_params(**params)

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). The former have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Returns :self :

transform(X)

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.