sklearn.linear_model.orthogonal_mp(X, y, n_nonzero_coefs=None, tol=None, precompute=False, copy_X=True, return_path=False, return_n_iter=False)[source]

Orthogonal Matching Pursuit (OMP)

Solves n_targets Orthogonal Matching Pursuit problems. An instance of the problem has the form:

When parametrized by the number of non-zero coefficients using n_nonzero_coefs: argmin ||y - Xgamma||^2 subject to ||gamma||_0 <= n_{nonzero coefs}

When parametrized by error using the parameter tol: argmin ||gamma||_0 subject to ||y - Xgamma||^2 <= tol

Read more in the User Guide.


X : array, shape (n_samples, n_features)

Input data. Columns are assumed to have unit norm.

y : array, shape (n_samples,) or (n_samples, n_targets)

Input targets

n_nonzero_coefs : int

Desired number of non-zero entries in the solution. If None (by default) this value is set to 10% of n_features.

tol : float

Maximum norm of the residual. If not None, overrides n_nonzero_coefs.

precompute : {True, False, ‘auto’},

Whether to perform precomputations. Improves performance when n_targets or n_samples is very large.

copy_X : bool, optional

Whether the design matrix X must be copied by the algorithm. A false value is only helpful if X is already Fortran-ordered, otherwise a copy is made anyway.

return_path : bool, optional. Default: False

Whether to return every value of the nonzero coefficients along the forward path. Useful for cross-validation.

return_n_iter : bool, optional default False

Whether or not to return the number of iterations.


coef : array, 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_iters : array-like or int

Number of active features across every target. Returned only if return_n_iter is set to True.

See also

OrthogonalMatchingPursuit, orthogonal_mp_gram, lars_path, decomposition.sparse_encode


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. (

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.