unbiasedsquaredphaselagindex.h File Reference

Unbiased estimator of squared Phase Lag Index between every channel pair. More...

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

Include dependency graph for unbiasedsquaredphaselagindex.h:

This graph shows which files directly or indirectly include this file:

Go to the source code of this file.

Classes
class	CONNECTIVITYLIB::UnbiasedSquaredPhaseLagIndex
	Unbiased squared Phase Lag Index estimator; removes the small-sample bias of PhaseLagIndex. More...

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

Detailed Description

Unbiased estimator of squared Phase Lag Index 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 Phase Lag Index (Stam et al. 2007) and its square are biased upward when the number of trials N is small: even uncorrelated signals produce a non-zero expected magnitude of the empirical sign average because each sign() contribution has variance 1. The unbiased squared PLI removes the diagonal contribution analytically,

USPLI_{xy}(f) = ( ( sum_n sign(Im(S_{xy}^{(n)}(f))) )^2 - N ) / ( N * (N - 1) )

which is an unbiased estimator of PLI^2 in the sense that E[USPLI] = PLI^2 for any N >= 2. Values outside the nominal [0, 1] range can occur for very small N or noise-dominated pairs; these indicate a true PLI indistinguishable from zero at the available sample size and are usually clipped to 0 for display purposes.

This estimator is the direct phase-only analogue of the squared debiased weighted PLI of Vinck et al. (2011) and is the right choice when amplitude weighting is undesirable but small-sample bias must be removed.

Definition in file unbiasedsquaredphaselagindex.h.