Base Class#

The BaseSolver class is inherited by all solvers. It implements regularization with various methods (generalized cross-validation, L-Curve and product method). Furthermore, it specifies the number of regularization parameters (n_reg_params) and the range of parameters to test.

class invert.solvers.base.BaseSolver(regularisation_method='GCV', n_reg_params=24, prep_leadfield=True, use_last_alpha=False, rank='auto', reduce_rank=False, plot_reg=False, verbose=0)#

Parameters

regularisation_method (str) –

Can be either
”GCV” -> generalized cross validation “L” -> L-Curve method using triangle method “Product” -> Minimal product method
n_reg_params (int) – The number of regularisation parameters to try. The higher, the more accurate the regularisation and the slower the computations.
prep_leadfield (bool) – If True -> Apply common average referencing and normalisation of the leadfield columns.
reduce_rank (bool) – Whether to reduce the rank of the M/EEG data
rank (str/int) –
Can be either int -> select only the <rank> largest eigenvectors of the data “auto” -> automatically select the optimal rank using the L-curve method and

an eigenvalue drop-off criterion
plot_reg (bool) – Plot the regularization parameters.

apply_inverse_operator(mne_obj) → mne.source_estimate.SourceEstimate#

Apply the inverse operator

Parameters: mne_obj ([mne.Evoked, mne.Epochs, mne.io.Raw]) – The MNE data object.
Returns: stc – The mne SourceEstimate object.
Return type: mne.SourceEstimate

static calc_area_tri(AB, AC, CB)#: Calculates area of a triangle given the length of each side.

static delete_from_list(a, idc)#: Delete elements of list at idc.

static euclidean_distance(A, B)#: Euclidean Distance between two points (A -> B).

static filter_norms(r_vals, l2_norms)#

Filter l2_norms where they are not monotonically decreasing.

Parameters

r_vals ([list, numpy.ndarray]) – List or array of r-values
l2_norms ([list, numpy.ndarray]) – List or array of l2_norms

Returns

bad_idc – List where indices are increasing

Return type

list

find_corner(r_vals, l2_norms)#

Find the corner of the l-curve given by plotting regularization levels (r_vals) against norms of the inverse solutions (l2_norms).

Parameters

r_vals (list) – Levels of regularization
l2_norms (list) – L2 norms of the inverse solutions per level of regularization.

Returns

idx – Index at which the L-Curve has its corner.

Return type

int

get_alphas(reference=None)#

Create list of regularization parameters (alphas) based on the largest eigenvalue of the leadfield or some reference matrix.

Parameters: reference ([None, numpy.ndarray]) – If None: use leadfield to calculate regularization parameters, else use reference matrix (e.g., M/EEG covariance matrix).
Returns: alphas – List of regularization parameters (alphas)
Return type: list

make_inverse_operator(forward: mne.forward.forward.Forward, *args, alpha='auto', **kwargs)#

Base function to create the inverse operator based on the forward: model.

Parameters

forward (mne.Forward) – The mne Forward model object.
alpha (["auto", float]) – If “auto”: Try out multiple regularization parameters and choose the optimal one, otherwise use the float.

Return type

None

prepare_forward()#: Prepare leadfield for calculating inverse solutions by applying common average referencing and unit norm scaling.

regularise_gcv(M, plot=False)#

Find optimally regularized inverse solution using the generalized cross-validation method [1].

Parameters

M (numpy.ndarray) – The M/EEG data matrix (n_channels, n_timepoints)

Returns

source_mat (numpy.ndarray) – The inverse solution (dipoles x time points)
optimum_idx (int) – The index of the selected (optimal) regularization parameter

References

[1] Grech, R., Cassar, T., Muscat, J., Camilleri, K. P., Fabri, S. G., Zervakis, M., … & Vanrumste, B. (2008). Review on solving the inverse problem in EEG source analysis. Journal of neuroengineering and rehabilitation, 5(1), 1-33.

regularise_lcurve(M, plot=False)#

Find optimally regularized inverse solution using the L-Curve method [1].

Parameters

M (numpy.ndarray) – The M/EEG data matrix (n_channels, n_timepoints)

Returns

source_mat (numpy.ndarray) – The inverse solution (dipoles x time points)
optimum_idx (int) – The index of the selected (optimal) regularization parameter

References

regularise_product(M, plot=False)#

Find optimally regularized inverse solution using the product method [1].

Parameters

M (numpy.ndarray) – The M/EEG data matrix (n_channels, n_timepoints)

Returns

source_mat (numpy.ndarray) – The inverse solution (dipoles x time points)
optimum_idx (int) – The index of the selected (optimal) regularization parameter

References

save(path)#

Saves the solver object.

pathstr: The path to save the solver.

Returns: self – Function returns itself.
Return type: BaseSolver

source_to_object(source_mat)#

Converts the source_mat matrix to the mne.SourceEstimate object.

Parameters: source_mat (numpy.ndarray) – Source matrix (dipoles, time points)-
Returns: stc
Return type: mne.SourceEstimate

unpack_data_obj(mne_obj, pick_types=None)#

Unpacks the mne data object and returns the data.

Parameters: mne_obj ([mne.Evoked, mne.EvokedArray, mne.Epochs, mne.EpochsArray, mne.Raw]) –
Returns: data – The M/EEG data matrix.
Return type: numpy.ndarray

class invert.solvers.base.InverseOperator(inverse_operator, solver_name)#

This class holds the inverse operator, which may be a simple numpy.ndarray matrix or some object like an esinet.net()

Parameters: operator (inverse) –

apply(M)#

Apply the precomputed inverse operator to the data matrix M. :param M: The M/EEG data matrix (n_channels, n_timepoints) :type M: numpy.ndarray

Returns: J – The source estimate matrix (n_sources, n_timepoints)
Return type: numpy.ndarray

has_multiple_operators()#: Check if there are multiple inverse_operators.

invertmeeg - A high-level M/EEG Python library for EEG inverse solutions

Solvers