pyeeg.solvers.SVDSolver

class pyeeg.solvers.SVDSolver(verbose=False, truncated=False, use_full_svd=False)

Linear regression using the singular value decomposition (SVD).

Solves the regularized normal equations (XᵀX + lambda I + M) beta = Xᵀy via SVD. By default the SVD is computed on the small normal matrix XᵀX (n_features, n_features), which is much faster for tall matrices (n_samples >> n_features) and gives identical results to factorizing the tall design matrix X directly.

Parameters:

• verbose (bool, optional) – Whether to print progress information. Default is False.

• truncated (bool, optional) – If True, alpha is reinterpreted as the fraction of total variance to keep (between 0 and 1). Instead of Tikhonov regularization (which shrinks all components), truncated SVD keeps the top-k components explaining alpha of the variance and discards the rest entirely. Incompatible with M (quadratic regularizer). Default is False.

• use_full_svd (bool, optional) – If True, SVD the tall design matrix X (n_samples, n_features) for higher numerical precision. If False (default), SVD the small normal matrix XᵀX (n_features, n_features) which is much faster for tall matrices (n_samples >> n_features) and gives identical results. Default is False.

Notes

A warning is shown in the case where n_features > n_samples; if so the user should rather use partial regression.

Methods

SVDSolver.solve(X, y[, alpha, M])

Solve the SVD regression and return the coefficients.