sklearn.linear_model
.orthogonal_mp¶
- 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 <= tolRead more in the User Guide.
- Parameters:
- Xarray-like of shape (n_samples, n_features)
Input data. Columns are assumed to have unit norm.
- yndarray of shape (n_samples,) or (n_samples, n_targets)
Input targets.
- 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.
- precompute‘auto’ or bool, default=False
Whether to perform precomputations. Improves performance when n_targets or n_samples is very large.
- copy_Xbool, default=True
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_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 generates coefficients in increasing order of active features.- n_itersarray-like 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.
orthogonal_mp_gram
Solve OMP problems using Gram matrix and the product X.T * y.
lars_path
Compute Least Angle Regression or Lasso path using LARS algorithm.
sklearn.decomposition.sparse_encode
Sparse coding.
Notes
Orthogonal matching pursuit was introduced in S. 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