FactorAnalysis

#include <Skigen/Decomposition>

template <typename Scalar = double>
class Skigen::FactorAnalysis(n_components=0, max_iter=1000, tol=1e-3)

Factor Analysis estimator.

Estimates a covariance model of the form:

$$\Sigma = W W^\top + \mathrm{diag}(\psi)$$

where $W$ is the loading matrix (n_features × n_components) and $\psi$ are the per-feature noise variances.

Uses the Expectation-Maximization (EM) algorithm:

Mirrors sklearn.decomposition.FactorAnalysis.

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Parameters:

• n_components : int, default=0 Number of latent factors (0 = auto).

• max_iter : int, default=1000 Maximum EM iterations.

• tol : Scalar, default=1e-3 Convergence tolerance on log-likelihood change.

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Attributes:

• components : MatrixType Loading matrix W of shape (n_features, n_components).

• noise_variance : VectorType Per-feature noise variances ψ of length n_features.

• covariance : MatrixType Estimated covariance matrix (n_features × n_features).

• log_likelihood : Scalar Final log-likelihood of the fitted model.

• n_iter : int Number of EM iterations performed.

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Methods

SKIGEN_PARAMS()

Fit the factor analysis model via EM.

Parameters:

• X Data matrix of shape (n_samples, n_features).

Returns:

• result Reference to the fitted estimator (*this).

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score(X)

Return the Gaussian log-likelihood of X under the fitted model.

Parameters:

• X : MatrixType Data matrix of shape (n_samples, n_features).

Returns:

• result : Scalar Average log-likelihood per sample.

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