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# `sklearn.linear_model`.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)

  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:
    Gram ndarray of shape (n_features, n_features)

      Gram matrix of the input data: X.T * X.

    Xy ndarray of shape (n_features,) or (n_features, n_targets)

      Input targets multiplied by X: X.T * y.

    n_nonzero_coefs int, default=None

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

    tol float, default=None

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

    norms_squared array-like of shape (n_targets,), default=None

      Squared L2 norms of the lines of y. Required if tol is not None.

    copy_Gram bool, 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_Xy bool, default=True

      Whether the covariance vector Xy must be copied by the algorithm. If False, it may be overwritten.

    return_path bool, default=False

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

    return_n_iter bool, default=False

      Whether or not to return the number of iterations.

  Returns:
    coef ndarray 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_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 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