debiasedsquaredweightedphaselagindex.h File Reference

Debiased squared Weighted Phase Lag Index (Vinck et al., 2011) between every channel pair. More...

#include "../connectivity_global.h"
#include "abstractmetric.h"
#include "../connectivitysettings.h"
#include <QSharedPointer>
#include <QMutex>
#include <Eigen/Core>

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Classes
class	CONNECTIVITYLIB::DebiasedSquaredWeightedPhaseLagIndex
	Debiased squared Weighted Phase Lag Index (Vinck et al. 2011); low-bias volume-conduction-robust estimator. More...

Namespaces
namespace	CONNECTIVITYLIB
	Functional connectivity metrics (coherence, PLV, cross-correlation, etc.).

Detailed Description

Debiased squared Weighted Phase Lag Index (Vinck et al., 2011) between every channel pair.

SPDX-License-Identifier: BSD-3-Clause Copyright (c) 2018-2026 MNE-CPP Authors

Author

Daniel Strohmeier danie.nosp@m.l.st.nosp@m.rohme.nosp@m.ier@.nosp@m.gmail.nosp@m..com; Lorenz Esch loren.nosp@m.z.es.nosp@m.ch@tu.nosp@m.-ilm.nosp@m.enau..nosp@m.de; Juan GPC jgarc.nosp@m.iapr.nosp@m.ieto@.nosp@m.mgh..nosp@m.harva.nosp@m.rd.e.nosp@m.du; Gabriel Motta gabri.nosp@m.elbe.nosp@m.nmott.nosp@m.a@gm.nosp@m.ail.c.nosp@m.om; Christoph Dinh chris.nosp@m.toph.nosp@m..dinh.nosp@m.@mne.nosp@m.-cpp..nosp@m.org

Since

0.1.0

Date

April 2018

The plain WeightedPhaseLagIndex is still positively biased for small numbers of trials N because the squared expectation in the numerator picks up a diagonal variance term. Vinck, Oostenveld, van Wingerden, Battaglia and Pennartz (NeuroImage 2011) derived the analytic correction

dwPLI_{xy}(f) = ( ( sum_n Im(S_{xy}^{(n)}) )^2 - sum_n Im(S_{xy}^{(n)})^2 ) / ( ( sum_n |Im(S_{xy}^{(n)})| )^2 - sum_n Im(S_{xy}^{(n)})^2 )

whose expectation equals wPLI^2 even for very small trial counts. This is the recommended PLI-family estimator whenever the trial count is low (single-subject epoched MEG/EEG, sliding-window time-resolved connectivity, sub-second tapered segments) and is the volume-conduction- robust counterpart of magnitude-squared coherence.

The dwPLI is bounded in [0, 1] for any N once the analytic bias is subtracted, and inherits the zero-lag rejection property of the PLI family - any pair of channels driven by the same source with constant gains has Im(S_{xy}) = 0 sample-by-sample and therefore dwPLI = 0 by construction.

Definition in file debiasedsquaredweightedphaselagindex.h.