## 2 Related Work  
Different functional-connectivity estimation methods have been proposed in the last few years and developed based on different domains integrating signal processing and information theory. The functional-connectivity metrics infer different synchronizations and broadly divide into amplitude, spectral, and phase synchronizations. Although each estimation method has unique properties, they each quantify functional dependence on pairwise signals [22]. Let \(s(t)\) be the EEG signal, where \(t\) is the number of time samples, and \(z(t)\) be the corresponding analytical signal computed from the Hilbert transform [23]. \[z(t)=s(t)+\widetilde{s}(t)=A(t)e^{i\phi(t)} \tag{1}\]  
where \(\widetilde{s}(t)\) is the Hilbert transform of the signal, \(\phi(t)\) is the instantaneous phase of the signal, and \(A(t)\) is the instantaneous amplitude of the signal. \[\phi(t)=\arctan\frac{\widetilde{s}(t)}{s(t)} \tag{2}\]  
\[A(t)=|z(t)|=\sqrt{\left(s(t)\right)^{2}+\left(\widetilde{s}(t)\right)^{2}} \tag{3}\]  
We estimate the functional connectivity of each frequency band using amplitude, spectral, and phase synchronization methods. Amplitude Coupling:  
Leakage-corrected amplitude envelope correlation (AEC-c): Let \(s_{1},s_{2}\) be two EEG signals (from two EEG channels), and their complex-valued (Hilbert transform) time-frequency representations (power envelopes) are \(S_{1}(t,f),S_{2}(t,f)\). The amplitude envelope correlation is obtained by calculating the Pearson correlation of the bandpass-filtered orthogonalized signals [24]. \[S_{2\perp S_{1}}(t,f)=\Im\left[S_{2}(t,f)\frac{S_{1}(t,f)^{*}}{|S_{1}(t,f)|}\right] \tag{4}\]  
where \(\Im\) denotes the imaginary operator, \({}^{*}\) denotes the complex conjugate, and \(\perp\) denotes the orthogonality. We perform orthogonalization in both directions and compute the Pearson correlation between two orthogonalized signals simultaneously. The average of the orthogonalized correlations is the connectivity measure. The orthogonalization of the signals corrects the spatial leakage. \[C_{\perp}(X,Y)=\frac{Corr\left(|S_{1}|,|S_{2\perp S_{1}}|\right)+Corr\left(|S_ {2}|,|S_{1\perp S_{2}}|\right)}{2} \tag{5}\]  
Spectral Coherence:  
We consider coherence and imaginary coherence as spectral coupling metrics because they capture power spectra of the signals [25]. Coherence (_Coh_): The coherency [25] between two EEG signals, \(S_{1}\) and \(S_{2}\), is defined as  
\[C=\frac{\left\langle z_{1}(t)z_{2}^{*}(t)\right\rangle}{\sqrt{\left\langle z_{ 1}{}^{2}\right\rangle\left\langle z_{2}{}^{2}\right\rangle}}=\frac{\left\langle A _{1}A_{2}e^{i\Delta\varnothing}\right\rangle}{\left\langle A_{1}{}^{2}\right \rangle\left\langle A_{2}{}^{2}\right\rangle} \tag{6}\]  
where \(\Delta\varnothing=\varnothing_{1}-\varnothing_{2}\) is the phase difference, and \(*\) and \(\left\langle\ \right\rangle\) denote the complex conjugation. Coherence is the absolute value of coherency defined as follows:  
\[Coh=\left|\frac{\left\langle A_{1}A_{2}e^{i\Delta\varnothing}\right\rangle}{ \left\langle A_{1}{}^{2}\right\rangle\left\langle A_{2}{}^{2}\right\rangle}\right| \tag{7}\]Coherence is affected by spatial leakage. Therefore, the imaginary part of coherence is used to reduce the spatial leakage. Imaginary part of coherency (_ImCoh_): Spatial leakage in the coherence metric is corrected in _ImCoh_, resulting in zero phase-lag linear interaction. \[ImCoh=\frac{\left\langle A_{1}A_{2}\text{sin}\Delta\varnothing\right\rangle}{ \sqrt{\left\langle A_{1}{}^{2}\right\rangle\left\langle A_{2}{}^{2}\right\rangle}} \tag{8}\]  
Phase Synchronization:  
All phase estimation measures assess the phase synchrony between two EEG signals in each frequency band obtained from the instantaneous phase of the signal [26].