# Authors: The MNE-Python contributors.
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.
import numpy as np
from .._fiff.proj import deactivate_proj
from ..dipole import Dipole
from ..fixes import _safe_svd
from ..forward import is_fixed_orient
from ..minimum_norm.inverse import (
_check_reference,
_log_exp_var,
_prepare_forward,
combine_xyz,
)
from ..source_estimate import SourceEstimate, _BaseSourceEstimate, _make_stc
from ..utils import (
_check_depth,
_check_option,
_validate_type,
check_random_state,
logger,
sum_squared,
verbose,
warn,
)
from .mxne_optim import (
_Phi,
groups_norm2,
iterative_mixed_norm_solver,
iterative_tf_mixed_norm_solver,
mixed_norm_solver,
norm_epsilon_inf,
norm_l2inf,
tf_mixed_norm_solver,
)
def _check_ori(pick_ori, forward):
"""Check pick_ori."""
_check_option("pick_ori", pick_ori, [None, "vector"])
if pick_ori == "vector" and is_fixed_orient(forward):
raise ValueError(
'pick_ori="vector" cannot be combined with a fixed '
"orientation forward solution."
)
def _prepare_weights(forward, gain, source_weighting, weights, weights_min):
mask = None
if isinstance(weights, _BaseSourceEstimate):
weights = np.max(np.abs(weights.data), axis=1)
weights_max = np.max(weights)
if weights_min > weights_max:
raise ValueError(f"weights_min > weights_max ({weights_min} > {weights_max})")
weights_min = weights_min / weights_max
weights = weights / weights_max
n_dip_per_pos = 1 if is_fixed_orient(forward) else 3
weights = np.ravel(np.tile(weights, [n_dip_per_pos, 1]).T)
if len(weights) != gain.shape[1]:
raise ValueError(
"weights do not have the correct dimension "
f" ({len(weights)} != {gain.shape[1]})"
)
if len(source_weighting.shape) == 1:
source_weighting *= weights
else:
source_weighting *= weights[:, None]
gain *= weights[None, :]
if weights_min is not None:
mask = weights > weights_min
gain = gain[:, mask]
n_sources = np.sum(mask) // n_dip_per_pos
logger.info(f"Reducing source space to {n_sources} sources")
return gain, source_weighting, mask
def _prepare_gain(
forward, info, noise_cov, pca, depth, loose, rank, weights=None, weights_min=None
):
depth = _check_depth(depth, "depth_sparse")
forward, gain_info, gain, _, _, source_weighting, _, _, whitener = _prepare_forward(
forward, info, noise_cov, "auto", loose, rank, pca, use_cps=True, **depth
)
if weights is None:
mask = None
else:
gain, source_weighting, mask = _prepare_weights(
forward, gain, source_weighting, weights, weights_min
)
return forward, gain, gain_info, whitener, source_weighting, mask
def _reapply_source_weighting(X, source_weighting, active_set):
X *= source_weighting[active_set][:, None]
return X
def _compute_residual(forward, evoked, X, active_set, info):
# OK, picking based on row_names is safe
sel = [forward["sol"]["row_names"].index(c) for c in info["ch_names"]]
residual = evoked.copy().pick(info["ch_names"])
r_tmp = residual.copy()
r_tmp.data = np.dot(forward["sol"]["data"][sel, :][:, active_set], X)
# Take care of proj
active_projs = list()
non_active_projs = list()
for p in evoked.info["projs"]:
if p["active"]:
active_projs.append(p)
else:
non_active_projs.append(p)
if len(active_projs) > 0:
with r_tmp.info._unlock():
r_tmp.info["projs"] = deactivate_proj(
active_projs, copy=True, verbose=False
)
r_tmp.apply_proj(verbose=False)
r_tmp.add_proj(non_active_projs, remove_existing=False, verbose=False)
residual.data -= r_tmp.data
return residual
@verbose
def _make_sparse_stc(
X,
active_set,
forward,
tmin,
tstep,
active_is_idx=False,
pick_ori=None,
verbose=None,
):
source_nn = forward["source_nn"]
vector = False
if not is_fixed_orient(forward):
if pick_ori != "vector":
logger.info("combining the current components...")
X = combine_xyz(X)
else:
vector = True
source_nn = np.reshape(source_nn, (-1, 3, 3))
if not active_is_idx:
active_idx = np.where(active_set)[0]
else:
active_idx = active_set
n_dip_per_pos = 1 if is_fixed_orient(forward) else 3
if n_dip_per_pos > 1:
active_idx = np.unique(active_idx // n_dip_per_pos)
src = forward["src"]
vertices = []
n_points_so_far = 0
for this_src in src:
this_n_points_so_far = n_points_so_far + len(this_src["vertno"])
this_active_idx = active_idx[
(n_points_so_far <= active_idx) & (active_idx < this_n_points_so_far)
]
this_active_idx -= n_points_so_far
this_vertno = this_src["vertno"][this_active_idx]
n_points_so_far = this_n_points_so_far
vertices.append(this_vertno)
source_nn = source_nn[active_idx]
return _make_stc(
X,
vertices,
src.kind,
tmin,
tstep,
src[0]["subject_his_id"],
vector=vector,
source_nn=source_nn,
)
def _split_gof(M, X, gain):
# parse out the variance explained using an orthogonal basis
# assuming x is estimated using elements of gain, with residual res
# along the first axis
assert M.ndim == X.ndim == gain.ndim == 2, (M.ndim, X.ndim, gain.ndim)
assert gain.shape == (M.shape[0], X.shape[0])
assert M.shape[1] == X.shape[1]
norm = (M * M.conj()).real.sum(0, keepdims=True)
norm[norm == 0] = np.inf
M_est = gain @ X
assert M.shape == M_est.shape
res = M - M_est
assert gain.shape[0] == M.shape[0], (gain.shape, M.shape)
# find an orthonormal basis for our matrices that spans the actual data
U, s, _ = np.linalg.svd(gain, full_matrices=False)
if U.shape[1] > 0:
U = U[:, s >= s[0] * 1e-6]
# the part that gets explained
fit_orth = U.T @ M
# the part that got over-explained (landed in residual)
res_orth = U.T @ res
# determine the weights by projecting each one onto this basis
w = (U.T @ gain)[:, :, np.newaxis] * X
w_norm = np.linalg.norm(w, axis=1, keepdims=True)
w_norm[w_norm == 0] = 1.0
w /= w_norm
# our weights are now unit-norm positive (will presrve power)
fit_back = np.linalg.norm(fit_orth[:, np.newaxis] * w, axis=0) ** 2
res_back = np.linalg.norm(res_orth[:, np.newaxis] * w, axis=0) ** 2
# and the resulting goodness of fits
gof_back = 100 * (fit_back - res_back) / norm
assert gof_back.shape == X.shape, (gof_back.shape, X.shape)
return gof_back
@verbose
def _make_dipoles_sparse(
X,
active_set,
forward,
tmin,
tstep,
M,
gain_active,
active_is_idx=False,
verbose=None,
):
times = tmin + tstep * np.arange(X.shape[1])
if not active_is_idx:
active_idx = np.where(active_set)[0]
else:
active_idx = active_set
# Compute the GOF split amongst the dipoles
assert M.shape == (gain_active.shape[0], len(times))
assert gain_active.shape[1] == len(active_idx) == X.shape[0]
gof_split = _split_gof(M, X, gain_active)
assert gof_split.shape == (len(active_idx), len(times))
assert X.shape[0] in (len(active_idx), 3 * len(active_idx))
n_dip_per_pos = 1 if is_fixed_orient(forward) else 3
if n_dip_per_pos > 1:
active_idx = active_idx // n_dip_per_pos
_, keep = np.unique(active_idx, return_index=True)
keep.sort() # maintain old order
active_idx = active_idx[keep]
gof_split.shape = (len(active_idx), n_dip_per_pos, len(times))
gof_split = gof_split.sum(1)
assert (gof_split < 100).all()
assert gof_split.shape == (len(active_idx), len(times))
dipoles = []
for k, i_dip in enumerate(active_idx):
i_pos = forward["source_rr"][i_dip][np.newaxis, :]
i_pos = i_pos.repeat(len(times), axis=0)
X_ = X[k * n_dip_per_pos : (k + 1) * n_dip_per_pos]
if n_dip_per_pos == 1:
amplitude = X_[0]
i_ori = forward["source_nn"][i_dip][np.newaxis, :]
i_ori = i_ori.repeat(len(times), axis=0)
else:
if forward["surf_ori"]:
X_ = np.dot(
forward["source_nn"][
i_dip * n_dip_per_pos : (i_dip + 1) * n_dip_per_pos
].T,
X_,
)
amplitude = np.linalg.norm(X_, axis=0)
i_ori = np.zeros((len(times), 3))
i_ori[amplitude > 0.0] = (
X_[:, amplitude > 0.0] / amplitude[amplitude > 0.0]
).T
dipoles.append(Dipole(times, i_pos, amplitude, i_ori, gof_split[k]))
return dipoles
@verbose
def make_stc_from_dipoles(dipoles, src, verbose=None):
"""Convert a list of spatio-temporal dipoles into a SourceEstimate.
Parameters
----------
dipoles : Dipole | list of instances of Dipole
The dipoles to convert.
src : instance of SourceSpaces
The source space used to generate the forward operator.
%(verbose)s
Returns
-------
stc : SourceEstimate
The source estimate.
"""
logger.info("Converting dipoles into a SourceEstimate.")
if isinstance(dipoles, Dipole):
dipoles = [dipoles]
if not isinstance(dipoles, list):
raise ValueError(
"Dipoles must be an instance of Dipole or "
"a list of instances of Dipole. "
f"Got {type(dipoles)}!"
)
tmin = dipoles[0].times[0]
tstep = dipoles[0].times[1] - tmin
X = np.zeros((len(dipoles), len(dipoles[0].times)))
source_rr = np.concatenate([_src["rr"][_src["vertno"], :] for _src in src], axis=0)
n_lh_points = len(src[0]["vertno"])
lh_vertno = list()
rh_vertno = list()
for i in range(len(dipoles)):
if not np.all(dipoles[i].pos == dipoles[i].pos[0]):
raise ValueError(
"Only dipoles with fixed position over time are supported!"
)
X[i] = dipoles[i].amplitude
idx = np.all(source_rr == dipoles[i].pos[0], axis=1)
idx = np.where(idx)[0][0]
if idx < n_lh_points:
lh_vertno.append(src[0]["vertno"][idx])
else:
rh_vertno.append(src[1]["vertno"][idx - n_lh_points])
vertices = [np.array(lh_vertno).astype(int), np.array(rh_vertno).astype(int)]
stc = SourceEstimate(
X, vertices=vertices, tmin=tmin, tstep=tstep, subject=src._subject
)
logger.info("[done]")
return stc
@verbose
def mixed_norm(
evoked,
forward,
noise_cov,
alpha="sure",
loose="auto",
depth=0.8,
maxit=3000,
tol=1e-4,
active_set_size=10,
debias=True,
time_pca=True,
weights=None,
weights_min=0.0,
solver="auto",
n_mxne_iter=1,
return_residual=False,
return_as_dipoles=False,
dgap_freq=10,
rank=None,
pick_ori=None,
sure_alpha_grid="auto",
random_state=None,
verbose=None,
):
"""Mixed-norm estimate (MxNE) and iterative reweighted MxNE (irMxNE).
Compute L1/L2 mixed-norm solution :footcite:`GramfortEtAl2012` or L0.5/L2
:footcite:`StrohmeierEtAl2016` mixed-norm solution on evoked data.
Parameters
----------
evoked : instance of Evoked or list of instances of Evoked
Evoked data to invert.
forward : dict
Forward operator.
noise_cov : instance of Covariance
Noise covariance to compute whitener.
alpha : float | str
Regularization parameter. If float it should be in the range [0, 100):
0 means no regularization, 100 would give 0 active dipole.
If ``'sure'`` (default), the SURE method from
:footcite:`DeledalleEtAl2014` will be used.
.. versionchanged:: 0.24
The default was changed to ``'sure'``.
%(loose)s
%(depth)s
maxit : int
Maximum number of iterations.
tol : float
Tolerance parameter.
active_set_size : int | None
Size of active set increment. If None, no active set strategy is used.
debias : bool
Remove coefficient amplitude bias due to L1 penalty.
time_pca : bool or int
If True the rank of the concatenated epochs is reduced to
its true dimension. If is 'int' the rank is limited to this value.
weights : None | array | SourceEstimate
Weight for penalty in mixed_norm. Can be None, a
1d array with shape (n_sources,), or a SourceEstimate (e.g. obtained
with wMNE, dSPM, or fMRI).
weights_min : float
Do not consider in the estimation sources for which weights
is less than weights_min.
solver : 'cd' | 'bcd' | 'auto'
The algorithm to use for the optimization. 'cd' uses
coordinate descent, and 'bcd' applies block coordinate descent.
'cd' is only available for fixed orientation.
n_mxne_iter : int
The number of MxNE iterations. If > 1, iterative reweighting
is applied.
return_residual : bool
If True, the residual is returned as an Evoked instance.
return_as_dipoles : bool
If True, the sources are returned as a list of Dipole instances.
dgap_freq : int or np.inf
The duality gap is evaluated every dgap_freq iterations. Ignored if
solver is 'cd'.
%(rank_none)s
.. versionadded:: 0.18
%(pick_ori)s
sure_alpha_grid : array | str
If ``'auto'`` (default), the SURE is evaluated along 15 uniformly
distributed alphas between alpha_max and 0.1 * alpha_max. If array, the
grid is directly specified. Ignored if alpha is not "sure".
.. versionadded:: 0.24
random_state : int | None
The random state used in a random number generator for delta and
epsilon used for the SURE computation. Defaults to None.
.. versionadded:: 0.24
%(verbose)s
Returns
-------
stc : SourceEstimate | list of SourceEstimate
Source time courses for each evoked data passed as input.
residual : instance of Evoked
The residual a.k.a. data not explained by the sources.
Only returned if return_residual is True.
See Also
--------
tf_mixed_norm
References
----------
.. footbibliography::
"""
_validate_type(alpha, ("numeric", str), "alpha")
if isinstance(alpha, str):
_check_option("alpha", alpha, ("sure",))
elif not 0.0 <= alpha < 100:
raise ValueError(
f'If not equal to "sure" alpha must be in [0, 100). Got alpha = {alpha}'
)
if n_mxne_iter < 1:
raise ValueError(
"MxNE has to be computed at least 1 time. "
f"Requires n_mxne_iter >= 1, got {n_mxne_iter}"
)
if dgap_freq <= 0.0:
raise ValueError(
f"dgap_freq must be a positive integer. Got dgap_freq = {dgap_freq}"
)
if not (
isinstance(sure_alpha_grid, np.ndarray | list) or sure_alpha_grid == "auto"
):
raise ValueError(
'If not equal to "auto" sure_alpha_grid must be an '
f"array. Got {type(sure_alpha_grid)}"
)
if (isinstance(sure_alpha_grid, str) and sure_alpha_grid != "auto") and (
isinstance(alpha, str) and alpha != "sure"
):
raise Exception(
"If sure_alpha_grid is manually specified, alpha must "
f'be "sure". Got {alpha}'
)
pca = True
if not isinstance(evoked, list):
evoked = [evoked]
_check_reference(evoked[0])
all_ch_names = evoked[0].ch_names
if not all(all_ch_names == evoked[i].ch_names for i in range(1, len(evoked))):
raise Exception("All the datasets must have the same good channels.")
forward, gain, gain_info, whitener, source_weighting, mask = _prepare_gain(
forward,
evoked[0].info,
noise_cov,
pca,
depth,
loose,
rank,
weights,
weights_min,
)
_check_ori(pick_ori, forward)
sel = [all_ch_names.index(name) for name in gain_info["ch_names"]]
M = np.concatenate([e.data[sel] for e in evoked], axis=1)
# Whiten data
logger.info("Whitening data matrix.")
M = np.dot(whitener, M)
if time_pca:
U, s, Vh = _safe_svd(M, full_matrices=False)
if not isinstance(time_pca, bool) and isinstance(time_pca, int):
U = U[:, :time_pca]
s = s[:time_pca]
Vh = Vh[:time_pca]
M = U * s
# Scaling to make setting of tol and alpha easy
tol *= sum_squared(M)
n_dip_per_pos = 1 if is_fixed_orient(forward) else 3
alpha_max = norm_l2inf(np.dot(gain.T, M), n_dip_per_pos, copy=False)
alpha_max *= 0.01
gain /= alpha_max
source_weighting /= alpha_max
# Alpha selected automatically by SURE minimization
if alpha == "sure":
alpha_grid = sure_alpha_grid
if isinstance(sure_alpha_grid, str) and sure_alpha_grid == "auto":
alpha_grid = np.geomspace(100, 10, num=15)
X, active_set, best_alpha_ = _compute_mxne_sure(
M,
gain,
alpha_grid,
sigma=1,
random_state=random_state,
n_mxne_iter=n_mxne_iter,
maxit=maxit,
tol=tol,
n_orient=n_dip_per_pos,
active_set_size=active_set_size,
debias=debias,
solver=solver,
dgap_freq=dgap_freq,
verbose=verbose,
)
logger.info(f"Selected alpha: {best_alpha_}")
else:
if n_mxne_iter == 1:
X, active_set, E = mixed_norm_solver(
M,
gain,
alpha,
maxit=maxit,
tol=tol,
active_set_size=active_set_size,
n_orient=n_dip_per_pos,
debias=debias,
solver=solver,
dgap_freq=dgap_freq,
verbose=verbose,
)
else:
X, active_set, E = iterative_mixed_norm_solver(
M,
gain,
alpha,
n_mxne_iter,
maxit=maxit,
tol=tol,
n_orient=n_dip_per_pos,
active_set_size=active_set_size,
debias=debias,
solver=solver,
dgap_freq=dgap_freq,
verbose=verbose,
)
if time_pca:
X = np.dot(X, Vh)
M = np.dot(M, Vh)
gain_active = gain[:, active_set]
if mask is not None:
active_set_tmp = np.zeros(len(mask), dtype=bool)
active_set_tmp[mask] = active_set
active_set = active_set_tmp
del active_set_tmp
if active_set.sum() == 0:
warn("No active dipoles found. alpha is too big.")
M_estimate = np.zeros_like(M)
else:
# Reapply weights to have correct unit
X = _reapply_source_weighting(X, source_weighting, active_set)
source_weighting[source_weighting == 0] = 1 # zeros
gain_active /= source_weighting[active_set]
del source_weighting
M_estimate = np.dot(gain_active, X)
outs = list()
residual = list()
cnt = 0
for e in evoked:
tmin = e.times[0]
tstep = 1.0 / e.info["sfreq"]
Xe = X[:, cnt : (cnt + len(e.times))]
if return_as_dipoles:
out = _make_dipoles_sparse(
Xe,
active_set,
forward,
tmin,
tstep,
M[:, cnt : (cnt + len(e.times))],
gain_active,
)
else:
out = _make_sparse_stc(
Xe, active_set, forward, tmin, tstep, pick_ori=pick_ori
)
outs.append(out)
cnt += len(e.times)
if return_residual:
residual.append(_compute_residual(forward, e, Xe, active_set, gain_info))
_log_exp_var(M, M_estimate, prefix="")
logger.info("[done]")
if len(outs) == 1:
out = outs[0]
if return_residual:
residual = residual[0]
else:
out = outs
if return_residual:
out = out, residual
return out
def _window_evoked(evoked, size):
"""Window evoked (size in seconds)."""
if isinstance(size, float | int):
lsize = rsize = float(size)
else:
lsize, rsize = size
evoked = evoked.copy()
sfreq = float(evoked.info["sfreq"])
lsize = int(lsize * sfreq)
rsize = int(rsize * sfreq)
lhann = np.hanning(lsize * 2)[:lsize]
rhann = np.hanning(rsize * 2)[-rsize:]
window = np.r_[lhann, np.ones(len(evoked.times) - lsize - rsize), rhann]
evoked.data *= window[None, :]
return evoked
@verbose
def tf_mixed_norm(
evoked,
forward,
noise_cov,
loose="auto",
depth=0.8,
maxit=3000,
tol=1e-4,
weights=None,
weights_min=0.0,
pca=True,
debias=True,
wsize=64,
tstep=4,
window=0.02,
return_residual=False,
return_as_dipoles=False,
alpha=None,
l1_ratio=None,
dgap_freq=10,
rank=None,
pick_ori=None,
n_tfmxne_iter=1,
verbose=None,
):
"""Time-Frequency Mixed-norm estimate (TF-MxNE).
Compute L1/L2 + L1 mixed-norm solution on time-frequency
dictionary. Works with evoked data
:footcite:`GramfortEtAl2013b,GramfortEtAl2011`.
Parameters
----------
evoked : instance of Evoked
Evoked data to invert.
forward : dict
Forward operator.
noise_cov : instance of Covariance
Noise covariance to compute whitener.
%(loose)s
%(depth)s
maxit : int
Maximum number of iterations.
tol : float
Tolerance parameter.
weights : None | array | SourceEstimate
Weight for penalty in mixed_norm. Can be None or
1d array of length n_sources or a SourceEstimate e.g. obtained
with wMNE or dSPM or fMRI.
weights_min : float
Do not consider in the estimation sources for which weights
is less than weights_min.
pca : bool
If True the rank of the data is reduced to true dimension.
debias : bool
Remove coefficient amplitude bias due to L1 penalty.
wsize : int or array-like
Length of the STFT window in samples (must be a multiple of 4).
If an array is passed, multiple TF dictionaries are used (each having
its own wsize and tstep) and each entry of wsize must be a multiple
of 4. See :footcite:`BekhtiEtAl2016`.
tstep : int or array-like
Step between successive windows in samples (must be a multiple of 2,
a divider of wsize and smaller than wsize/2) (default: wsize/2).
If an array is passed, multiple TF dictionaries are used (each having
its own wsize and tstep), and each entry of tstep must be a multiple
of 2 and divide the corresponding entry of wsize. See
:footcite:`BekhtiEtAl2016`.
window : float or (float, float)
Length of time window used to take care of edge artifacts in seconds.
It can be one float or float if the values are different for left
and right window length.
return_residual : bool
If True, the residual is returned as an Evoked instance.
return_as_dipoles : bool
If True, the sources are returned as a list of Dipole instances.
alpha : float in [0, 100) or None
Overall regularization parameter.
If alpha and l1_ratio are not None, alpha_space and alpha_time are
overridden by alpha * alpha_max * (1. - l1_ratio) and alpha * alpha_max
* l1_ratio. 0 means no regularization, 100 would give 0 active dipole.
l1_ratio : float in [0, 1] or None
Proportion of temporal regularization.
If l1_ratio and alpha are not None, alpha_space and alpha_time are
overridden by alpha * alpha_max * (1. - l1_ratio) and alpha * alpha_max
* l1_ratio. 0 means no time regularization a.k.a. MxNE.
dgap_freq : int or np.inf
The duality gap is evaluated every dgap_freq iterations.
%(rank_none)s
.. versionadded:: 0.18
%(pick_ori)s
n_tfmxne_iter : int
Number of TF-MxNE iterations. If > 1, iterative reweighting is applied.
%(verbose)s
Returns
-------
stc : instance of SourceEstimate
Source time courses.
residual : instance of Evoked
The residual a.k.a. data not explained by the sources.
Only returned if return_residual is True.
See Also
--------
mixed_norm
References
----------
.. footbibliography::
"""
_check_reference(evoked)
all_ch_names = evoked.ch_names
info = evoked.info
if not (0.0 <= alpha < 100.0):
raise ValueError(f"alpha must be in [0, 100). Got alpha = {alpha}")
if not (0.0 <= l1_ratio <= 1.0):
raise ValueError(f"l1_ratio must be in range [0, 1]. Got l1_ratio = {l1_ratio}")
alpha_space = alpha * (1.0 - l1_ratio)
alpha_time = alpha * l1_ratio
if n_tfmxne_iter < 1:
raise ValueError(
"TF-MxNE has to be computed at least 1 time. "
f"Requires n_tfmxne_iter >= 1, got {n_tfmxne_iter}"
)
if dgap_freq <= 0.0:
raise ValueError(
f"dgap_freq must be a positive integer. Got dgap_freq = {dgap_freq}"
)
tstep = np.atleast_1d(tstep)
wsize = np.atleast_1d(wsize)
if len(tstep) != len(wsize):
raise ValueError(
"The same number of window sizes and steps must be "
f"passed. Got tstep = {tstep} and wsize = {wsize}"
)
forward, gain, gain_info, whitener, source_weighting, mask = _prepare_gain(
forward, evoked.info, noise_cov, pca, depth, loose, rank, weights, weights_min
)
_check_ori(pick_ori, forward)
n_dip_per_pos = 1 if is_fixed_orient(forward) else 3
if window is not None:
evoked = _window_evoked(evoked, window)
sel = [all_ch_names.index(name) for name in gain_info["ch_names"]]
M = evoked.data[sel]
# Whiten data
logger.info("Whitening data matrix.")
M = np.dot(whitener, M)
n_steps = np.ceil(M.shape[1] / tstep.astype(float)).astype(int)
n_freqs = wsize // 2 + 1
n_coefs = n_steps * n_freqs
phi = _Phi(wsize, tstep, n_coefs, evoked.data.shape[1])
# Scaling to make setting of tol and alpha easy
tol *= sum_squared(M)
alpha_max = norm_epsilon_inf(gain, M, phi, l1_ratio, n_dip_per_pos)
alpha_max *= 0.01
gain /= alpha_max
source_weighting /= alpha_max
if n_tfmxne_iter == 1:
X, active_set, E = tf_mixed_norm_solver(
M,
gain,
alpha_space,
alpha_time,
wsize=wsize,
tstep=tstep,
maxit=maxit,
tol=tol,
verbose=verbose,
n_orient=n_dip_per_pos,
dgap_freq=dgap_freq,
debias=debias,
)
else:
X, active_set, E = iterative_tf_mixed_norm_solver(
M,
gain,
alpha_space,
alpha_time,
wsize=wsize,
tstep=tstep,
n_tfmxne_iter=n_tfmxne_iter,
maxit=maxit,
tol=tol,
verbose=verbose,
n_orient=n_dip_per_pos,
dgap_freq=dgap_freq,
debias=debias,
)
if active_set.sum() == 0:
raise Exception("No active dipoles found. alpha_space/alpha_time are too big.")
# Compute estimated whitened sensor data for each dipole (dip, ch, time)
gain_active = gain[:, active_set]
if mask is not None:
active_set_tmp = np.zeros(len(mask), dtype=bool)
active_set_tmp[mask] = active_set
active_set = active_set_tmp
del active_set_tmp
X = _reapply_source_weighting(X, source_weighting, active_set)
gain_active /= source_weighting[active_set]
if return_residual:
residual = _compute_residual(forward, evoked, X, active_set, gain_info)
if return_as_dipoles:
out = _make_dipoles_sparse(
X, active_set, forward, evoked.times[0], 1.0 / info["sfreq"], M, gain_active
)
else:
out = _make_sparse_stc(
X,
active_set,
forward,
evoked.times[0],
1.0 / info["sfreq"],
pick_ori=pick_ori,
)
logger.info("[done]")
if return_residual:
out = out, residual
return out
@verbose
def _compute_mxne_sure(
M,
gain,
alpha_grid,
sigma,
n_mxne_iter,
maxit,
tol,
n_orient,
active_set_size,
debias,
solver,
dgap_freq,
random_state,
verbose,
):
"""Stein Unbiased Risk Estimator (SURE).
Implements the finite-difference Monte-Carlo approximation
of the SURE for Multi-Task LASSO.
See reference :footcite:`DeledalleEtAl2014`.
Parameters
----------
M : array, shape (n_sensors, n_times)
The data.
gain : array, shape (n_sensors, n_dipoles)
The gain matrix a.k.a. lead field.
alpha_grid : array, shape (n_alphas,)
The grid of alphas used to evaluate the SURE.
sigma : float
The true or estimated noise level in the data. Usually 1 if the data
has been previously whitened using MNE whitener.
n_mxne_iter : int
The number of MxNE iterations. If > 1, iterative reweighting is
applied.
maxit : int
Maximum number of iterations.
tol : float
Tolerance parameter.
n_orient : int
The number of orientation (1 : fixed or 3 : free or loose).
active_set_size : int
Size of active set increase at each iteration.
debias : bool
Debias source estimates.
solver : 'cd' | 'bcd' | 'auto'
The algorithm to use for the optimization.
dgap_freq : int or np.inf
The duality gap is evaluated every dgap_freq iterations.
random_state : int | None
The random state used in a random number generator for delta and
epsilon used for the SURE computation.
Returns
-------
X : array, shape (n_active, n_times)
Coefficient matrix.
active_set : array, shape (n_dipoles,)
Array of indices of non-zero coefficients.
best_alpha_ : float
Alpha that minimizes the SURE.
References
----------
.. footbibliography::
"""
def g(w):
return np.sqrt(np.sqrt(groups_norm2(w.copy(), n_orient)))
def gprime(w):
return 2.0 * np.repeat(g(w), n_orient).ravel()
def _run_solver(alpha, M, n_mxne_iter, as_init=None, X_init=None, w_init=None):
if n_mxne_iter == 1:
X, active_set, _ = mixed_norm_solver(
M,
gain,
alpha,
maxit=maxit,
tol=tol,
active_set_size=active_set_size,
n_orient=n_orient,
debias=debias,
solver=solver,
dgap_freq=dgap_freq,
active_set_init=as_init,
X_init=X_init,
verbose=False,
)
else:
X, active_set, _ = iterative_mixed_norm_solver(
M,
gain,
alpha,
n_mxne_iter,
maxit=maxit,
tol=tol,
n_orient=n_orient,
active_set_size=active_set_size,
debias=debias,
solver=solver,
dgap_freq=dgap_freq,
weight_init=w_init,
verbose=False,
)
return X, active_set
def _fit_on_grid(gain, M, eps, delta):
coefs_grid_1_0 = np.zeros((len(alpha_grid), gain.shape[1], M.shape[1]))
coefs_grid_2_0 = np.zeros((len(alpha_grid), gain.shape[1], M.shape[1]))
active_sets, active_sets_eps = [], []
M_eps = M + eps * delta
# warm start - first iteration (leverages convexity)
logger.info("Warm starting...")
for j, alpha in enumerate(alpha_grid):
logger.info(f"alpha: {alpha}")
X, a_set = _run_solver(alpha, M, 1)
X_eps, a_set_eps = _run_solver(alpha, M_eps, 1)
coefs_grid_1_0[j][a_set, :] = X
coefs_grid_2_0[j][a_set_eps, :] = X_eps
active_sets.append(a_set)
active_sets_eps.append(a_set_eps)
# next iterations
if n_mxne_iter == 1:
return coefs_grid_1_0, coefs_grid_2_0, active_sets
else:
coefs_grid_1 = coefs_grid_1_0.copy()
coefs_grid_2 = coefs_grid_2_0.copy()
logger.info("Fitting SURE on grid.")
for j, alpha in enumerate(alpha_grid):
logger.info(f"alpha: {alpha}")
if active_sets[j].sum() > 0:
w = gprime(coefs_grid_1[j])
X, a_set = _run_solver(alpha, M, n_mxne_iter - 1, w_init=w)
coefs_grid_1[j][a_set, :] = X
active_sets[j] = a_set
if active_sets_eps[j].sum() > 0:
w_eps = gprime(coefs_grid_2[j])
X_eps, a_set_eps = _run_solver(
alpha, M_eps, n_mxne_iter - 1, w_init=w_eps
)
coefs_grid_2[j][a_set_eps, :] = X_eps
active_sets_eps[j] = a_set_eps
return coefs_grid_1, coefs_grid_2, active_sets
def _compute_sure_val(coef1, coef2, gain, M, sigma, delta, eps):
n_sensors, n_times = gain.shape[0], M.shape[1]
dof = (gain @ (coef2 - coef1) * delta).sum() / eps
df_term = np.linalg.norm(M - gain @ coef1) ** 2
sure = df_term - n_sensors * n_times * sigma**2
sure += 2 * dof * sigma**2
return sure
sure_path = np.empty(len(alpha_grid))
rng = check_random_state(random_state)
# See Deledalle et al. 20214 Sec. 5.1
eps = 2 * sigma / (M.shape[0] ** 0.3)
delta = rng.randn(*M.shape)
coefs_grid_1, coefs_grid_2, active_sets = _fit_on_grid(gain, M, eps, delta)
logger.info("Computing SURE values on grid.")
for i, (coef1, coef2) in enumerate(zip(coefs_grid_1, coefs_grid_2)):
sure_path[i] = _compute_sure_val(coef1, coef2, gain, M, sigma, delta, eps)
if verbose:
logger.info(f"alpha {alpha_grid[i]} :: sure {sure_path[i]}")
best_alpha_ = alpha_grid[np.argmin(sure_path)]
X = coefs_grid_1[np.argmin(sure_path)]
active_set = active_sets[np.argmin(sure_path)]
X = X[active_set, :]
return X, active_set, best_alpha_
Datasets
Models
