orthogonal_mp_gram#

sklearn.linear_model.orthogonal_mp_gram(Gram, Xy, *, n_nonzero_coefs=None, tol=None, norms_squared=None, copy_Gram=True, copy_Xy=True, return_path=False, return_n_iter=False)[source]#

Gram Orthogonal Matching Pursuit (OMP).

Solves n_targets Orthogonal Matching Pursuit problems using only the Gram matrix X.T * X and the product X.T * y.

Read more in the User Guide.

Parameters:

Gramarray-like of shape (n_features, n_features): Gram matrix of the input data: X.T * X.
Xyarray-like of shape (n_features,) or (n_features, n_targets): Input targets multiplied by X: X.T * y.
n_nonzero_coefsint, default=None: Desired number of non-zero entries in the solution. If None (by default) this value is set to 10% of n_features.
tolfloat, default=None: Maximum squared norm of the residual. If not None, overrides n_nonzero_coefs.
norms_squaredarray-like of shape (n_targets,), default=None: Squared L2 norms of the lines of y. Required if tol is not None.
copy_Grambool, default=True: Whether the gram matrix must be copied by the algorithm. A False value is only helpful if it is already Fortran-ordered, otherwise a copy is made anyway.
copy_Xybool, default=True: Whether the covariance vector Xy must be copied by the algorithm. If False, it may be overwritten.
return_pathbool, default=False: Whether to return every value of the nonzero coefficients along the forward path. Useful for cross-validation.
return_n_iterbool, default=False: Whether or not to return the number of iterations.

Returns:

coefndarray of shape (n_features,) or (n_features, n_targets): Coefficients of the OMP solution. If return_path=True, this contains the whole coefficient path. In this case its shape is (n_features, n_features) or (n_features, n_targets, n_features) and iterating over the last axis yields coefficients in increasing order of active features.
n_iterslist or int: Number of active features across every target. Returned only if return_n_iter is set to True.

See also

OrthogonalMatchingPursuit: Orthogonal Matching Pursuit model (OMP).
orthogonal_mp: Solves n_targets Orthogonal Matching Pursuit problems.
lars_path: Compute Least Angle Regression or Lasso path using LARS algorithm.
sklearn.decomposition.sparse_encode: Generic sparse coding. Each column of the result is the solution to a Lasso problem.

Notes

Orthogonal matching pursuit was introduced in G. Mallat, Z. Zhang, Matching pursuits with time-frequency dictionaries, IEEE Transactions on Signal Processing, Vol. 41, No. 12. (December 1993), pp. 3397-3415. (https://www.di.ens.fr/~mallat/papiers/MallatPursuit93.pdf)

This implementation is based on Rubinstein, R., Zibulevsky, M. and Elad, M., Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal Matching Pursuit Technical Report - CS Technion, April 2008. https://www.cs.technion.ac.il/~ronrubin/Publications/KSVD-OMP-v2.pdf

Examples

>>> from sklearn.datasets import make_regression
>>> from sklearn.linear_model import orthogonal_mp_gram
>>> X, y = make_regression(noise=4, random_state=0)
>>> coef = orthogonal_mp_gram(X.T @ X, X.T @ y)
>>> coef.shape
(100,)
>>> X[:1,] @ coef
array([-78.68...])