1101 lines
37 KiB
Python
1101 lines
37 KiB
Python
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"""Orthogonal matching pursuit algorithms
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"""
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# Author: Vlad Niculae
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#
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# License: BSD 3 clause
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import warnings
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from math import sqrt
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from numbers import Integral, Real
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import numpy as np
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from scipy import linalg
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from scipy.linalg.lapack import get_lapack_funcs
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from ._base import LinearModel, _pre_fit, _deprecate_normalize
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from ..base import RegressorMixin, MultiOutputMixin
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from ..utils import as_float_array, check_array
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from ..utils.parallel import delayed, Parallel
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from ..utils._param_validation import Hidden, Interval, StrOptions
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from ..model_selection import check_cv
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premature = (
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"Orthogonal matching pursuit ended prematurely due to linear"
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" dependence in the dictionary. The requested precision might"
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" not have been met."
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)
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def _cholesky_omp(X, y, n_nonzero_coefs, tol=None, copy_X=True, return_path=False):
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"""Orthogonal Matching Pursuit step using the Cholesky decomposition.
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Parameters
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----------
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X : ndarray of shape (n_samples, n_features)
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Input dictionary. Columns are assumed to have unit norm.
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y : ndarray of shape (n_samples,)
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Input targets.
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n_nonzero_coefs : int
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Targeted number of non-zero elements.
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tol : float, default=None
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Targeted squared error, if not None overrides n_nonzero_coefs.
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copy_X : bool, default=True
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Whether the design matrix X must be copied by the algorithm. A false
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value is only helpful if X is already Fortran-ordered, otherwise a
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copy is made anyway.
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return_path : bool, default=False
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Whether to return every value of the nonzero coefficients along the
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forward path. Useful for cross-validation.
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Returns
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-------
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gamma : ndarray of shape (n_nonzero_coefs,)
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Non-zero elements of the solution.
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idx : ndarray of shape (n_nonzero_coefs,)
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Indices of the positions of the elements in gamma within the solution
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vector.
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coef : ndarray of shape (n_features, n_nonzero_coefs)
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The first k values of column k correspond to the coefficient value
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for the active features at that step. The lower left triangle contains
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garbage. Only returned if ``return_path=True``.
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n_active : int
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Number of active features at convergence.
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"""
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if copy_X:
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X = X.copy("F")
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else: # even if we are allowed to overwrite, still copy it if bad order
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X = np.asfortranarray(X)
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min_float = np.finfo(X.dtype).eps
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nrm2, swap = linalg.get_blas_funcs(("nrm2", "swap"), (X,))
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(potrs,) = get_lapack_funcs(("potrs",), (X,))
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alpha = np.dot(X.T, y)
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residual = y
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gamma = np.empty(0)
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n_active = 0
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indices = np.arange(X.shape[1]) # keeping track of swapping
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max_features = X.shape[1] if tol is not None else n_nonzero_coefs
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L = np.empty((max_features, max_features), dtype=X.dtype)
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if return_path:
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coefs = np.empty_like(L)
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while True:
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lam = np.argmax(np.abs(np.dot(X.T, residual)))
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if lam < n_active or alpha[lam] ** 2 < min_float:
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# atom already selected or inner product too small
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warnings.warn(premature, RuntimeWarning, stacklevel=2)
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break
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if n_active > 0:
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# Updates the Cholesky decomposition of X' X
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L[n_active, :n_active] = np.dot(X[:, :n_active].T, X[:, lam])
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linalg.solve_triangular(
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L[:n_active, :n_active],
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L[n_active, :n_active],
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trans=0,
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lower=1,
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overwrite_b=True,
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check_finite=False,
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)
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v = nrm2(L[n_active, :n_active]) ** 2
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Lkk = linalg.norm(X[:, lam]) ** 2 - v
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if Lkk <= min_float: # selected atoms are dependent
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warnings.warn(premature, RuntimeWarning, stacklevel=2)
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break
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L[n_active, n_active] = sqrt(Lkk)
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else:
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L[0, 0] = linalg.norm(X[:, lam])
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X.T[n_active], X.T[lam] = swap(X.T[n_active], X.T[lam])
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alpha[n_active], alpha[lam] = alpha[lam], alpha[n_active]
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indices[n_active], indices[lam] = indices[lam], indices[n_active]
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n_active += 1
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# solves LL'x = X'y as a composition of two triangular systems
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gamma, _ = potrs(
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L[:n_active, :n_active], alpha[:n_active], lower=True, overwrite_b=False
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)
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if return_path:
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coefs[:n_active, n_active - 1] = gamma
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residual = y - np.dot(X[:, :n_active], gamma)
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if tol is not None and nrm2(residual) ** 2 <= tol:
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break
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elif n_active == max_features:
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break
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if return_path:
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return gamma, indices[:n_active], coefs[:, :n_active], n_active
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else:
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return gamma, indices[:n_active], n_active
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def _gram_omp(
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Gram,
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Xy,
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n_nonzero_coefs,
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tol_0=None,
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tol=None,
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copy_Gram=True,
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copy_Xy=True,
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return_path=False,
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):
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"""Orthogonal Matching Pursuit step on a precomputed Gram matrix.
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This function uses the Cholesky decomposition method.
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Parameters
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----------
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Gram : ndarray of shape (n_features, n_features)
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Gram matrix of the input data matrix.
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Xy : ndarray of shape (n_features,)
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Input targets.
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n_nonzero_coefs : int
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Targeted number of non-zero elements.
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tol_0 : float, default=None
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Squared norm of y, required if tol is not None.
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tol : float, default=None
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Targeted squared error, if not None overrides n_nonzero_coefs.
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copy_Gram : bool, default=True
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Whether the gram matrix must be copied by the algorithm. A false
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value is only helpful if it is already Fortran-ordered, otherwise a
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copy is made anyway.
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copy_Xy : bool, default=True
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Whether the covariance vector Xy must be copied by the algorithm.
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If False, it may be overwritten.
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return_path : bool, default=False
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Whether to return every value of the nonzero coefficients along the
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forward path. Useful for cross-validation.
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Returns
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-------
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gamma : ndarray of shape (n_nonzero_coefs,)
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Non-zero elements of the solution.
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idx : ndarray of shape (n_nonzero_coefs,)
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Indices of the positions of the elements in gamma within the solution
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vector.
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coefs : ndarray of shape (n_features, n_nonzero_coefs)
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The first k values of column k correspond to the coefficient value
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for the active features at that step. The lower left triangle contains
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garbage. Only returned if ``return_path=True``.
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n_active : int
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Number of active features at convergence.
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"""
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Gram = Gram.copy("F") if copy_Gram else np.asfortranarray(Gram)
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if copy_Xy or not Xy.flags.writeable:
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Xy = Xy.copy()
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min_float = np.finfo(Gram.dtype).eps
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nrm2, swap = linalg.get_blas_funcs(("nrm2", "swap"), (Gram,))
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(potrs,) = get_lapack_funcs(("potrs",), (Gram,))
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indices = np.arange(len(Gram)) # keeping track of swapping
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alpha = Xy
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tol_curr = tol_0
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delta = 0
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gamma = np.empty(0)
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n_active = 0
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max_features = len(Gram) if tol is not None else n_nonzero_coefs
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L = np.empty((max_features, max_features), dtype=Gram.dtype)
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L[0, 0] = 1.0
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if return_path:
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coefs = np.empty_like(L)
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while True:
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lam = np.argmax(np.abs(alpha))
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if lam < n_active or alpha[lam] ** 2 < min_float:
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# selected same atom twice, or inner product too small
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warnings.warn(premature, RuntimeWarning, stacklevel=3)
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break
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if n_active > 0:
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L[n_active, :n_active] = Gram[lam, :n_active]
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linalg.solve_triangular(
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L[:n_active, :n_active],
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L[n_active, :n_active],
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trans=0,
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lower=1,
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overwrite_b=True,
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check_finite=False,
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)
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v = nrm2(L[n_active, :n_active]) ** 2
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Lkk = Gram[lam, lam] - v
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if Lkk <= min_float: # selected atoms are dependent
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warnings.warn(premature, RuntimeWarning, stacklevel=3)
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break
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L[n_active, n_active] = sqrt(Lkk)
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else:
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L[0, 0] = sqrt(Gram[lam, lam])
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Gram[n_active], Gram[lam] = swap(Gram[n_active], Gram[lam])
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Gram.T[n_active], Gram.T[lam] = swap(Gram.T[n_active], Gram.T[lam])
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indices[n_active], indices[lam] = indices[lam], indices[n_active]
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Xy[n_active], Xy[lam] = Xy[lam], Xy[n_active]
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n_active += 1
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# solves LL'x = X'y as a composition of two triangular systems
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gamma, _ = potrs(
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L[:n_active, :n_active], Xy[:n_active], lower=True, overwrite_b=False
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)
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if return_path:
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coefs[:n_active, n_active - 1] = gamma
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beta = np.dot(Gram[:, :n_active], gamma)
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alpha = Xy - beta
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if tol is not None:
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tol_curr += delta
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delta = np.inner(gamma, beta[:n_active])
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tol_curr -= delta
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if abs(tol_curr) <= tol:
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break
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elif n_active == max_features:
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break
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if return_path:
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return gamma, indices[:n_active], coefs[:, :n_active], n_active
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else:
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return gamma, indices[:n_active], n_active
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def orthogonal_mp(
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X,
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y,
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*,
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n_nonzero_coefs=None,
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tol=None,
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precompute=False,
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copy_X=True,
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return_path=False,
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return_n_iter=False,
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):
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r"""Orthogonal Matching Pursuit (OMP).
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Solves n_targets Orthogonal Matching Pursuit problems.
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An instance of the problem has the form:
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When parametrized by the number of non-zero coefficients using
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`n_nonzero_coefs`:
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argmin ||y - X\gamma||^2 subject to ||\gamma||_0 <= n_{nonzero coefs}
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When parametrized by error using the parameter `tol`:
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argmin ||\gamma||_0 subject to ||y - X\gamma||^2 <= tol
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Read more in the :ref:`User Guide <omp>`.
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Parameters
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----------
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X : ndarray of shape (n_samples, n_features)
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Input data. Columns are assumed to have unit norm.
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y : ndarray of shape (n_samples,) or (n_samples, n_targets)
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Input targets.
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n_nonzero_coefs : int, default=None
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Desired number of non-zero entries in the solution. If None (by
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default) this value is set to 10% of n_features.
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tol : float, default=None
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Maximum norm of the residual. If not None, overrides n_nonzero_coefs.
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precompute : 'auto' or bool, default=False
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Whether to perform precomputations. Improves performance when n_targets
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or n_samples is very large.
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copy_X : bool, default=True
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Whether the design matrix X must be copied by the algorithm. A false
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value is only helpful if X is already Fortran-ordered, otherwise a
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copy is made anyway.
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return_path : bool, default=False
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Whether to return every value of the nonzero coefficients along the
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forward path. Useful for cross-validation.
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return_n_iter : bool, default=False
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Whether or not to return the number of iterations.
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Returns
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-------
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coef : ndarray of shape (n_features,) or (n_features, n_targets)
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Coefficients of the OMP solution. If `return_path=True`, this contains
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the whole coefficient path. In this case its shape is
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(n_features, n_features) or (n_features, n_targets, n_features) and
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iterating over the last axis generates coefficients in increasing order
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of active features.
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n_iters : array-like or int
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Number of active features across every target. Returned only if
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`return_n_iter` is set to True.
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See Also
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--------
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OrthogonalMatchingPursuit : Orthogonal Matching Pursuit model.
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orthogonal_mp_gram : Solve OMP problems using Gram matrix and the product X.T * y.
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lars_path : Compute Least Angle Regression or Lasso path using LARS algorithm.
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sklearn.decomposition.sparse_encode : Sparse coding.
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Notes
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-----
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Orthogonal matching pursuit was introduced in S. Mallat, Z. Zhang,
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Matching pursuits with time-frequency dictionaries, IEEE Transactions on
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Signal Processing, Vol. 41, No. 12. (December 1993), pp. 3397-3415.
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(https://www.di.ens.fr/~mallat/papiers/MallatPursuit93.pdf)
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This implementation is based on Rubinstein, R., Zibulevsky, M. and Elad,
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M., Efficient Implementation of the K-SVD Algorithm using Batch Orthogonal
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Matching Pursuit Technical Report - CS Technion, April 2008.
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https://www.cs.technion.ac.il/~ronrubin/Publications/KSVD-OMP-v2.pdf
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"""
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X = check_array(X, order="F", copy=copy_X)
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copy_X = False
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if y.ndim == 1:
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y = y.reshape(-1, 1)
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y = check_array(y)
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if y.shape[1] > 1: # subsequent targets will be affected
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copy_X = True
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if n_nonzero_coefs is None and tol is None:
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# default for n_nonzero_coefs is 0.1 * n_features
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# but at least one.
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n_nonzero_coefs = max(int(0.1 * X.shape[1]), 1)
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if tol is not None and tol < 0:
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raise ValueError("Epsilon cannot be negative")
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if tol is None and n_nonzero_coefs <= 0:
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raise ValueError("The number of atoms must be positive")
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if tol is None and n_nonzero_coefs > X.shape[1]:
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raise ValueError(
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"The number of atoms cannot be more than the number of features"
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)
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if precompute == "auto":
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precompute = X.shape[0] > X.shape[1]
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if precompute:
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G = np.dot(X.T, X)
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G = np.asfortranarray(G)
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Xy = np.dot(X.T, y)
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if tol is not None:
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norms_squared = np.sum((y**2), axis=0)
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else:
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norms_squared = None
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return orthogonal_mp_gram(
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G,
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Xy,
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n_nonzero_coefs=n_nonzero_coefs,
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tol=tol,
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norms_squared=norms_squared,
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copy_Gram=copy_X,
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copy_Xy=False,
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return_path=return_path,
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)
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if return_path:
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coef = np.zeros((X.shape[1], y.shape[1], X.shape[1]))
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else:
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coef = np.zeros((X.shape[1], y.shape[1]))
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n_iters = []
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for k in range(y.shape[1]):
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||
|
out = _cholesky_omp(
|
||
|
X, y[:, k], n_nonzero_coefs, tol, copy_X=copy_X, return_path=return_path
|
||
|
)
|
||
|
if return_path:
|
||
|
_, idx, coefs, n_iter = out
|
||
|
coef = coef[:, :, : len(idx)]
|
||
|
for n_active, x in enumerate(coefs.T):
|
||
|
coef[idx[: n_active + 1], k, n_active] = x[: n_active + 1]
|
||
|
else:
|
||
|
x, idx, n_iter = out
|
||
|
coef[idx, k] = x
|
||
|
n_iters.append(n_iter)
|
||
|
|
||
|
if y.shape[1] == 1:
|
||
|
n_iters = n_iters[0]
|
||
|
|
||
|
if return_n_iter:
|
||
|
return np.squeeze(coef), n_iters
|
||
|
else:
|
||
|
return np.squeeze(coef)
|
||
|
|
||
|
|
||
|
def 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 :ref:`User Guide <omp>`.
|
||
|
|
||
|
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 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
|
||
|
"""
|
||
|
Gram = check_array(Gram, order="F", copy=copy_Gram)
|
||
|
Xy = np.asarray(Xy)
|
||
|
if Xy.ndim > 1 and Xy.shape[1] > 1:
|
||
|
# or subsequent target will be affected
|
||
|
copy_Gram = True
|
||
|
if Xy.ndim == 1:
|
||
|
Xy = Xy[:, np.newaxis]
|
||
|
if tol is not None:
|
||
|
norms_squared = [norms_squared]
|
||
|
if copy_Xy or not Xy.flags.writeable:
|
||
|
# Make the copy once instead of many times in _gram_omp itself.
|
||
|
Xy = Xy.copy()
|
||
|
|
||
|
if n_nonzero_coefs is None and tol is None:
|
||
|
n_nonzero_coefs = int(0.1 * len(Gram))
|
||
|
if tol is not None and norms_squared is None:
|
||
|
raise ValueError(
|
||
|
"Gram OMP needs the precomputed norms in order "
|
||
|
"to evaluate the error sum of squares."
|
||
|
)
|
||
|
if tol is not None and tol < 0:
|
||
|
raise ValueError("Epsilon cannot be negative")
|
||
|
if tol is None and n_nonzero_coefs <= 0:
|
||
|
raise ValueError("The number of atoms must be positive")
|
||
|
if tol is None and n_nonzero_coefs > len(Gram):
|
||
|
raise ValueError(
|
||
|
"The number of atoms cannot be more than the number of features"
|
||
|
)
|
||
|
|
||
|
if return_path:
|
||
|
coef = np.zeros((len(Gram), Xy.shape[1], len(Gram)), dtype=Gram.dtype)
|
||
|
else:
|
||
|
coef = np.zeros((len(Gram), Xy.shape[1]), dtype=Gram.dtype)
|
||
|
|
||
|
n_iters = []
|
||
|
for k in range(Xy.shape[1]):
|
||
|
out = _gram_omp(
|
||
|
Gram,
|
||
|
Xy[:, k],
|
||
|
n_nonzero_coefs,
|
||
|
norms_squared[k] if tol is not None else None,
|
||
|
tol,
|
||
|
copy_Gram=copy_Gram,
|
||
|
copy_Xy=False,
|
||
|
return_path=return_path,
|
||
|
)
|
||
|
if return_path:
|
||
|
_, idx, coefs, n_iter = out
|
||
|
coef = coef[:, :, : len(idx)]
|
||
|
for n_active, x in enumerate(coefs.T):
|
||
|
coef[idx[: n_active + 1], k, n_active] = x[: n_active + 1]
|
||
|
else:
|
||
|
x, idx, n_iter = out
|
||
|
coef[idx, k] = x
|
||
|
n_iters.append(n_iter)
|
||
|
|
||
|
if Xy.shape[1] == 1:
|
||
|
n_iters = n_iters[0]
|
||
|
|
||
|
if return_n_iter:
|
||
|
return np.squeeze(coef), n_iters
|
||
|
else:
|
||
|
return np.squeeze(coef)
|
||
|
|
||
|
|
||
|
class OrthogonalMatchingPursuit(MultiOutputMixin, RegressorMixin, LinearModel):
|
||
|
"""Orthogonal Matching Pursuit model (OMP).
|
||
|
|
||
|
Read more in the :ref:`User Guide <omp>`.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
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 norm of the residual. If not None, overrides n_nonzero_coefs.
|
||
|
|
||
|
fit_intercept : bool, default=True
|
||
|
Whether to calculate the intercept for this model. If set
|
||
|
to false, no intercept will be used in calculations
|
||
|
(i.e. data is expected to be centered).
|
||
|
|
||
|
normalize : bool, default=False
|
||
|
This parameter is ignored when ``fit_intercept`` is set to False.
|
||
|
If True, the regressors X will be normalized before regression by
|
||
|
subtracting the mean and dividing by the l2-norm.
|
||
|
If you wish to standardize, please use
|
||
|
:class:`~sklearn.preprocessing.StandardScaler` before calling ``fit``
|
||
|
on an estimator with ``normalize=False``.
|
||
|
|
||
|
.. versionchanged:: 1.2
|
||
|
default changed from True to False in 1.2.
|
||
|
|
||
|
.. deprecated:: 1.2
|
||
|
``normalize`` was deprecated in version 1.2 and will be removed in 1.4.
|
||
|
|
||
|
precompute : 'auto' or bool, default='auto'
|
||
|
Whether to use a precomputed Gram and Xy matrix to speed up
|
||
|
calculations. Improves performance when :term:`n_targets` or
|
||
|
:term:`n_samples` is very large. Note that if you already have such
|
||
|
matrices, you can pass them directly to the fit method.
|
||
|
|
||
|
Attributes
|
||
|
----------
|
||
|
coef_ : ndarray of shape (n_features,) or (n_targets, n_features)
|
||
|
Parameter vector (w in the formula).
|
||
|
|
||
|
intercept_ : float or ndarray of shape (n_targets,)
|
||
|
Independent term in decision function.
|
||
|
|
||
|
n_iter_ : int or array-like
|
||
|
Number of active features across every target.
|
||
|
|
||
|
n_nonzero_coefs_ : int
|
||
|
The number of non-zero coefficients in the solution. If
|
||
|
`n_nonzero_coefs` is None and `tol` is None this value is either set
|
||
|
to 10% of `n_features` or 1, whichever is greater.
|
||
|
|
||
|
n_features_in_ : int
|
||
|
Number of features seen during :term:`fit`.
|
||
|
|
||
|
.. versionadded:: 0.24
|
||
|
|
||
|
feature_names_in_ : ndarray of shape (`n_features_in_`,)
|
||
|
Names of features seen during :term:`fit`. Defined only when `X`
|
||
|
has feature names that are all strings.
|
||
|
|
||
|
.. versionadded:: 1.0
|
||
|
|
||
|
See Also
|
||
|
--------
|
||
|
orthogonal_mp : Solves n_targets Orthogonal Matching Pursuit problems.
|
||
|
orthogonal_mp_gram : Solves n_targets Orthogonal Matching Pursuit
|
||
|
problems using only the Gram matrix X.T * X and the product X.T * y.
|
||
|
lars_path : Compute Least Angle Regression or Lasso path using LARS algorithm.
|
||
|
Lars : Least Angle Regression model a.k.a. LAR.
|
||
|
LassoLars : Lasso model fit with Least Angle Regression a.k.a. Lars.
|
||
|
sklearn.decomposition.sparse_encode : Generic sparse coding.
|
||
|
Each column of the result is the solution to a Lasso problem.
|
||
|
OrthogonalMatchingPursuitCV : Cross-validated
|
||
|
Orthogonal Matching Pursuit model (OMP).
|
||
|
|
||
|
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.linear_model import OrthogonalMatchingPursuit
|
||
|
>>> from sklearn.datasets import make_regression
|
||
|
>>> X, y = make_regression(noise=4, random_state=0)
|
||
|
>>> reg = OrthogonalMatchingPursuit().fit(X, y)
|
||
|
>>> reg.score(X, y)
|
||
|
0.9991...
|
||
|
>>> reg.predict(X[:1,])
|
||
|
array([-78.3854...])
|
||
|
"""
|
||
|
|
||
|
_parameter_constraints: dict = {
|
||
|
"n_nonzero_coefs": [Interval(Integral, 1, None, closed="left"), None],
|
||
|
"tol": [Interval(Real, 0, None, closed="left"), None],
|
||
|
"fit_intercept": ["boolean"],
|
||
|
"normalize": ["boolean", Hidden(StrOptions({"deprecated"}))],
|
||
|
"precompute": [StrOptions({"auto"}), "boolean"],
|
||
|
}
|
||
|
|
||
|
def __init__(
|
||
|
self,
|
||
|
*,
|
||
|
n_nonzero_coefs=None,
|
||
|
tol=None,
|
||
|
fit_intercept=True,
|
||
|
normalize="deprecated",
|
||
|
precompute="auto",
|
||
|
):
|
||
|
self.n_nonzero_coefs = n_nonzero_coefs
|
||
|
self.tol = tol
|
||
|
self.fit_intercept = fit_intercept
|
||
|
self.normalize = normalize
|
||
|
self.precompute = precompute
|
||
|
|
||
|
def fit(self, X, y):
|
||
|
"""Fit the model using X, y as training data.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
X : array-like of shape (n_samples, n_features)
|
||
|
Training data.
|
||
|
|
||
|
y : array-like of shape (n_samples,) or (n_samples, n_targets)
|
||
|
Target values. Will be cast to X's dtype if necessary.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
self : object
|
||
|
Returns an instance of self.
|
||
|
"""
|
||
|
self._validate_params()
|
||
|
|
||
|
_normalize = _deprecate_normalize(
|
||
|
self.normalize, estimator_name=self.__class__.__name__
|
||
|
)
|
||
|
|
||
|
X, y = self._validate_data(X, y, multi_output=True, y_numeric=True)
|
||
|
n_features = X.shape[1]
|
||
|
|
||
|
X, y, X_offset, y_offset, X_scale, Gram, Xy = _pre_fit(
|
||
|
X, y, None, self.precompute, _normalize, self.fit_intercept, copy=True
|
||
|
)
|
||
|
|
||
|
if y.ndim == 1:
|
||
|
y = y[:, np.newaxis]
|
||
|
|
||
|
if self.n_nonzero_coefs is None and self.tol is None:
|
||
|
# default for n_nonzero_coefs is 0.1 * n_features
|
||
|
# but at least one.
|
||
|
self.n_nonzero_coefs_ = max(int(0.1 * n_features), 1)
|
||
|
else:
|
||
|
self.n_nonzero_coefs_ = self.n_nonzero_coefs
|
||
|
|
||
|
if Gram is False:
|
||
|
coef_, self.n_iter_ = orthogonal_mp(
|
||
|
X,
|
||
|
y,
|
||
|
n_nonzero_coefs=self.n_nonzero_coefs_,
|
||
|
tol=self.tol,
|
||
|
precompute=False,
|
||
|
copy_X=True,
|
||
|
return_n_iter=True,
|
||
|
)
|
||
|
else:
|
||
|
norms_sq = np.sum(y**2, axis=0) if self.tol is not None else None
|
||
|
|
||
|
coef_, self.n_iter_ = orthogonal_mp_gram(
|
||
|
Gram,
|
||
|
Xy=Xy,
|
||
|
n_nonzero_coefs=self.n_nonzero_coefs_,
|
||
|
tol=self.tol,
|
||
|
norms_squared=norms_sq,
|
||
|
copy_Gram=True,
|
||
|
copy_Xy=True,
|
||
|
return_n_iter=True,
|
||
|
)
|
||
|
self.coef_ = coef_.T
|
||
|
self._set_intercept(X_offset, y_offset, X_scale)
|
||
|
return self
|
||
|
|
||
|
|
||
|
def _omp_path_residues(
|
||
|
X_train,
|
||
|
y_train,
|
||
|
X_test,
|
||
|
y_test,
|
||
|
copy=True,
|
||
|
fit_intercept=True,
|
||
|
normalize=False,
|
||
|
max_iter=100,
|
||
|
):
|
||
|
"""Compute the residues on left-out data for a full LARS path.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
X_train : ndarray of shape (n_samples, n_features)
|
||
|
The data to fit the LARS on.
|
||
|
|
||
|
y_train : ndarray of shape (n_samples)
|
||
|
The target variable to fit LARS on.
|
||
|
|
||
|
X_test : ndarray of shape (n_samples, n_features)
|
||
|
The data to compute the residues on.
|
||
|
|
||
|
y_test : ndarray of shape (n_samples)
|
||
|
The target variable to compute the residues on.
|
||
|
|
||
|
copy : bool, default=True
|
||
|
Whether X_train, X_test, y_train and y_test should be copied. If
|
||
|
False, they may be overwritten.
|
||
|
|
||
|
fit_intercept : bool, default=True
|
||
|
Whether to calculate the intercept for this model. If set
|
||
|
to false, no intercept will be used in calculations
|
||
|
(i.e. data is expected to be centered).
|
||
|
|
||
|
normalize : bool, default=False
|
||
|
This parameter is ignored when ``fit_intercept`` is set to False.
|
||
|
If True, the regressors X will be normalized before regression by
|
||
|
subtracting the mean and dividing by the l2-norm.
|
||
|
If you wish to standardize, please use
|
||
|
:class:`~sklearn.preprocessing.StandardScaler` before calling ``fit``
|
||
|
on an estimator with ``normalize=False``.
|
||
|
|
||
|
.. versionchanged:: 1.2
|
||
|
default changed from True to False in 1.2.
|
||
|
|
||
|
.. deprecated:: 1.2
|
||
|
``normalize`` was deprecated in version 1.2 and will be removed in 1.4.
|
||
|
|
||
|
max_iter : int, default=100
|
||
|
Maximum numbers of iterations to perform, therefore maximum features
|
||
|
to include. 100 by default.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
residues : ndarray of shape (n_samples, max_features)
|
||
|
Residues of the prediction on the test data.
|
||
|
"""
|
||
|
|
||
|
if copy:
|
||
|
X_train = X_train.copy()
|
||
|
y_train = y_train.copy()
|
||
|
X_test = X_test.copy()
|
||
|
y_test = y_test.copy()
|
||
|
|
||
|
if fit_intercept:
|
||
|
X_mean = X_train.mean(axis=0)
|
||
|
X_train -= X_mean
|
||
|
X_test -= X_mean
|
||
|
y_mean = y_train.mean(axis=0)
|
||
|
y_train = as_float_array(y_train, copy=False)
|
||
|
y_train -= y_mean
|
||
|
y_test = as_float_array(y_test, copy=False)
|
||
|
y_test -= y_mean
|
||
|
|
||
|
if normalize:
|
||
|
norms = np.sqrt(np.sum(X_train**2, axis=0))
|
||
|
nonzeros = np.flatnonzero(norms)
|
||
|
X_train[:, nonzeros] /= norms[nonzeros]
|
||
|
|
||
|
coefs = orthogonal_mp(
|
||
|
X_train,
|
||
|
y_train,
|
||
|
n_nonzero_coefs=max_iter,
|
||
|
tol=None,
|
||
|
precompute=False,
|
||
|
copy_X=False,
|
||
|
return_path=True,
|
||
|
)
|
||
|
if coefs.ndim == 1:
|
||
|
coefs = coefs[:, np.newaxis]
|
||
|
if normalize:
|
||
|
coefs[nonzeros] /= norms[nonzeros][:, np.newaxis]
|
||
|
|
||
|
return np.dot(coefs.T, X_test.T) - y_test
|
||
|
|
||
|
|
||
|
class OrthogonalMatchingPursuitCV(RegressorMixin, LinearModel):
|
||
|
"""Cross-validated Orthogonal Matching Pursuit model (OMP).
|
||
|
|
||
|
See glossary entry for :term:`cross-validation estimator`.
|
||
|
|
||
|
Read more in the :ref:`User Guide <omp>`.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
copy : bool, 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.
|
||
|
|
||
|
fit_intercept : bool, default=True
|
||
|
Whether to calculate the intercept for this model. If set
|
||
|
to false, no intercept will be used in calculations
|
||
|
(i.e. data is expected to be centered).
|
||
|
|
||
|
normalize : bool, default=False
|
||
|
This parameter is ignored when ``fit_intercept`` is set to False.
|
||
|
If True, the regressors X will be normalized before regression by
|
||
|
subtracting the mean and dividing by the l2-norm.
|
||
|
If you wish to standardize, please use
|
||
|
:class:`~sklearn.preprocessing.StandardScaler` before calling ``fit``
|
||
|
on an estimator with ``normalize=False``.
|
||
|
|
||
|
.. versionchanged:: 1.2
|
||
|
default changed from True to False in 1.2.
|
||
|
|
||
|
.. deprecated:: 1.2
|
||
|
``normalize`` was deprecated in version 1.2 and will be removed in 1.4.
|
||
|
|
||
|
max_iter : int, default=None
|
||
|
Maximum numbers of iterations to perform, therefore maximum features
|
||
|
to include. 10% of ``n_features`` but at least 5 if available.
|
||
|
|
||
|
cv : int, cross-validation generator or iterable, default=None
|
||
|
Determines the cross-validation splitting strategy.
|
||
|
Possible inputs for cv are:
|
||
|
|
||
|
- None, to use the default 5-fold cross-validation,
|
||
|
- integer, to specify the number of folds.
|
||
|
- :term:`CV splitter`,
|
||
|
- An iterable yielding (train, test) splits as arrays of indices.
|
||
|
|
||
|
For integer/None inputs, :class:`KFold` is used.
|
||
|
|
||
|
Refer :ref:`User Guide <cross_validation>` for the various
|
||
|
cross-validation strategies that can be used here.
|
||
|
|
||
|
.. versionchanged:: 0.22
|
||
|
``cv`` default value if None changed from 3-fold to 5-fold.
|
||
|
|
||
|
n_jobs : int, default=None
|
||
|
Number of CPUs to use during the cross validation.
|
||
|
``None`` means 1 unless in a :obj:`joblib.parallel_backend` context.
|
||
|
``-1`` means using all processors. See :term:`Glossary <n_jobs>`
|
||
|
for more details.
|
||
|
|
||
|
verbose : bool or int, default=False
|
||
|
Sets the verbosity amount.
|
||
|
|
||
|
Attributes
|
||
|
----------
|
||
|
intercept_ : float or ndarray of shape (n_targets,)
|
||
|
Independent term in decision function.
|
||
|
|
||
|
coef_ : ndarray of shape (n_features,) or (n_targets, n_features)
|
||
|
Parameter vector (w in the problem formulation).
|
||
|
|
||
|
n_nonzero_coefs_ : int
|
||
|
Estimated number of non-zero coefficients giving the best mean squared
|
||
|
error over the cross-validation folds.
|
||
|
|
||
|
n_iter_ : int or array-like
|
||
|
Number of active features across every target for the model refit with
|
||
|
the best hyperparameters got by cross-validating across all folds.
|
||
|
|
||
|
n_features_in_ : int
|
||
|
Number of features seen during :term:`fit`.
|
||
|
|
||
|
.. versionadded:: 0.24
|
||
|
|
||
|
feature_names_in_ : ndarray of shape (`n_features_in_`,)
|
||
|
Names of features seen during :term:`fit`. Defined only when `X`
|
||
|
has feature names that are all strings.
|
||
|
|
||
|
.. versionadded:: 1.0
|
||
|
|
||
|
See Also
|
||
|
--------
|
||
|
orthogonal_mp : Solves n_targets Orthogonal Matching Pursuit problems.
|
||
|
orthogonal_mp_gram : Solves n_targets Orthogonal Matching Pursuit
|
||
|
problems using only the Gram matrix X.T * X and the product X.T * y.
|
||
|
lars_path : Compute Least Angle Regression or Lasso path using LARS algorithm.
|
||
|
Lars : Least Angle Regression model a.k.a. LAR.
|
||
|
LassoLars : Lasso model fit with Least Angle Regression a.k.a. Lars.
|
||
|
OrthogonalMatchingPursuit : Orthogonal Matching Pursuit model (OMP).
|
||
|
LarsCV : Cross-validated Least Angle Regression model.
|
||
|
LassoLarsCV : Cross-validated Lasso model fit with Least Angle Regression.
|
||
|
sklearn.decomposition.sparse_encode : Generic sparse coding.
|
||
|
Each column of the result is the solution to a Lasso problem.
|
||
|
|
||
|
Notes
|
||
|
-----
|
||
|
In `fit`, once the optimal number of non-zero coefficients is found through
|
||
|
cross-validation, the model is fit again using the entire training set.
|
||
|
|
||
|
Examples
|
||
|
--------
|
||
|
>>> from sklearn.linear_model import OrthogonalMatchingPursuitCV
|
||
|
>>> from sklearn.datasets import make_regression
|
||
|
>>> X, y = make_regression(n_features=100, n_informative=10,
|
||
|
... noise=4, random_state=0)
|
||
|
>>> reg = OrthogonalMatchingPursuitCV(cv=5).fit(X, y)
|
||
|
>>> reg.score(X, y)
|
||
|
0.9991...
|
||
|
>>> reg.n_nonzero_coefs_
|
||
|
10
|
||
|
>>> reg.predict(X[:1,])
|
||
|
array([-78.3854...])
|
||
|
"""
|
||
|
|
||
|
_parameter_constraints: dict = {
|
||
|
"copy": ["boolean"],
|
||
|
"fit_intercept": ["boolean"],
|
||
|
"normalize": ["boolean", Hidden(StrOptions({"deprecated"}))],
|
||
|
"max_iter": [Interval(Integral, 0, None, closed="left"), None],
|
||
|
"cv": ["cv_object"],
|
||
|
"n_jobs": [Integral, None],
|
||
|
"verbose": ["verbose"],
|
||
|
}
|
||
|
|
||
|
def __init__(
|
||
|
self,
|
||
|
*,
|
||
|
copy=True,
|
||
|
fit_intercept=True,
|
||
|
normalize="deprecated",
|
||
|
max_iter=None,
|
||
|
cv=None,
|
||
|
n_jobs=None,
|
||
|
verbose=False,
|
||
|
):
|
||
|
self.copy = copy
|
||
|
self.fit_intercept = fit_intercept
|
||
|
self.normalize = normalize
|
||
|
self.max_iter = max_iter
|
||
|
self.cv = cv
|
||
|
self.n_jobs = n_jobs
|
||
|
self.verbose = verbose
|
||
|
|
||
|
def fit(self, X, y):
|
||
|
"""Fit the model using X, y as training data.
|
||
|
|
||
|
Parameters
|
||
|
----------
|
||
|
X : array-like of shape (n_samples, n_features)
|
||
|
Training data.
|
||
|
|
||
|
y : array-like of shape (n_samples,)
|
||
|
Target values. Will be cast to X's dtype if necessary.
|
||
|
|
||
|
Returns
|
||
|
-------
|
||
|
self : object
|
||
|
Returns an instance of self.
|
||
|
"""
|
||
|
self._validate_params()
|
||
|
|
||
|
_normalize = _deprecate_normalize(
|
||
|
self.normalize, estimator_name=self.__class__.__name__
|
||
|
)
|
||
|
|
||
|
X, y = self._validate_data(X, y, y_numeric=True, ensure_min_features=2)
|
||
|
X = as_float_array(X, copy=False, force_all_finite=False)
|
||
|
cv = check_cv(self.cv, classifier=False)
|
||
|
max_iter = (
|
||
|
min(max(int(0.1 * X.shape[1]), 5), X.shape[1])
|
||
|
if not self.max_iter
|
||
|
else self.max_iter
|
||
|
)
|
||
|
cv_paths = Parallel(n_jobs=self.n_jobs, verbose=self.verbose)(
|
||
|
delayed(_omp_path_residues)(
|
||
|
X[train],
|
||
|
y[train],
|
||
|
X[test],
|
||
|
y[test],
|
||
|
self.copy,
|
||
|
self.fit_intercept,
|
||
|
_normalize,
|
||
|
max_iter,
|
||
|
)
|
||
|
for train, test in cv.split(X)
|
||
|
)
|
||
|
|
||
|
min_early_stop = min(fold.shape[0] for fold in cv_paths)
|
||
|
mse_folds = np.array(
|
||
|
[(fold[:min_early_stop] ** 2).mean(axis=1) for fold in cv_paths]
|
||
|
)
|
||
|
best_n_nonzero_coefs = np.argmin(mse_folds.mean(axis=0)) + 1
|
||
|
self.n_nonzero_coefs_ = best_n_nonzero_coefs
|
||
|
omp = OrthogonalMatchingPursuit(
|
||
|
n_nonzero_coefs=best_n_nonzero_coefs,
|
||
|
fit_intercept=self.fit_intercept,
|
||
|
normalize=_normalize,
|
||
|
)
|
||
|
|
||
|
# avoid duplicating warning for deprecated normalize
|
||
|
with warnings.catch_warnings():
|
||
|
warnings.filterwarnings("ignore", category=FutureWarning)
|
||
|
omp.fit(X, y)
|
||
|
|
||
|
self.coef_ = omp.coef_
|
||
|
self.intercept_ = omp.intercept_
|
||
|
self.n_iter_ = omp.n_iter_
|
||
|
return self
|