# mne.connectivity.spectral_connectivity¶

mne.connectivity.spectral_connectivity(data, method='coh', indices=None, sfreq=6.283185307179586, mode='multitaper', fmin=None, fmax=inf, fskip=0, faverage=False, tmin=None, tmax=None, mt_bandwidth=None, mt_adaptive=False, mt_low_bias=True, cwt_freqs=None, cwt_n_cycles=7, block_size=1000, n_jobs=1, cwt_frequencies=None, verbose=None)[source]

Compute frequency- and time-frequency-domain connectivity measures.

The connectivity method(s) are specified using the “method” parameter. All methods are based on estimates of the cross- and power spectral densities (CSD/PSD) Sxy and Sxx, Syy.

The spectral densities can be estimated using a multitaper method with digital prolate spheroidal sequence (DPSS) windows, a discrete Fourier transform with Hanning windows, or a continuous wavelet transform using Morlet wavelets. The spectral estimation mode is specified using the “mode” parameter.

By default, the connectivity between all signals is computed (only connections corresponding to the lower-triangular part of the connectivity matrix). If one is only interested in the connectivity between some signals, the “indices” parameter can be used. For example, to compute the connectivity between the signal with index 0 and signals “2, 3, 4” (a total of 3 connections) one can use the following:

indices = (np.array([0, 0, 0]),    # row indices
np.array([2, 3, 4]))    # col indices

con_flat = spectral_connectivity(data, method='coh',
indices=indices, ...)


In this case con_flat.shape = (3, n_freqs). The connectivity scores are in the same order as defined indices.

Supported Connectivity Measures

The connectivity method(s) is specified using the “method” parameter. The following methods are supported (note: E[] denotes average over epochs). Multiple measures can be computed at once by using a list/tuple, e.g., ['coh', 'pli'] to compute coherence and PLI.

‘coh’ : Coherence given by:

         | E[Sxy] |
C = ---------------------
sqrt(E[Sxx] * E[Syy])


‘cohy’ : Coherency given by:

           E[Sxy]
C = ---------------------
sqrt(E[Sxx] * E[Syy])


‘imcoh’ : Imaginary coherence [R8488] given by:

          Im(E[Sxy])
C = ----------------------
sqrt(E[Sxx] * E[Syy])


‘plv’ : Phase-Locking Value (PLV) [R8588] given by:

PLV = |E[Sxy/|Sxy|]|


‘ppc’ : Pairwise Phase Consistency (PPC), an unbiased estimator of squared PLV [R8688].

‘pli’ : Phase Lag Index (PLI) [R8788] given by:

PLI = |E[sign(Im(Sxy))]|


‘pli2_unbiased’ : Unbiased estimator of squared PLI [R8888].

‘wpli’ : Weighted Phase Lag Index (WPLI) [R8888] given by:

          |E[Im(Sxy)]|
WPLI = ------------------
E[|Im(Sxy)|]


‘wpli2_debiased’ : Debiased estimator of squared WPLI [R8888].

Parameters: data : array-like, shape=(n_epochs, n_signals, n_times) | Epochs The data from which to compute connectivity. Note that it is also possible to combine multiple signals by providing a list of tuples, e.g., data = [(arr_0, stc_0), (arr_1, stc_1), (arr_2, stc_2)], corresponds to 3 epochs, and arr_* could be an array with the same number of time points as stc_*. The array-like object can also be a list/generator of array, shape =(n_signals, n_times), or a list/generator of SourceEstimate or VolSourceEstimate objects. method : string | list of string Connectivity measure(s) to compute. indices : tuple of arrays | None Two arrays with indices of connections for which to compute connectivity. If None, all connections are computed. sfreq : float The sampling frequency. mode : str Spectrum estimation mode can be either: ‘multitaper’, ‘fourier’, or ‘cwt_morlet’. fmin : float | tuple of floats The lower frequency of interest. Multiple bands are defined using a tuple, e.g., (8., 20.) for two bands with 8Hz and 20Hz lower freq. If None the frequency corresponding to an epoch length of 5 cycles is used. fmax : float | tuple of floats The upper frequency of interest. Multiple bands are dedined using a tuple, e.g. (13., 30.) for two band with 13Hz and 30Hz upper freq. fskip : int Omit every “(fskip + 1)-th” frequency bin to decimate in frequency domain. faverage : boolean Average connectivity scores for each frequency band. If True, the output freqs will be a list with arrays of the frequencies that were averaged. tmin : float | None Time to start connectivity estimation. Note: when “data” is an array, the first sample is assumed to be at time 0. For other types (Epochs, etc.), the time information contained in the object is used to compute the time indices. tmax : float | None Time to end connectivity estimation. Note: when “data” is an array, the first sample is assumed to be at time 0. For other types (Epochs, etc.), the time information contained in the object is used to compute the time indices. mt_bandwidth : float | None The bandwidth of the multitaper windowing function in Hz. Only used in ‘multitaper’ mode. mt_adaptive : bool Use adaptive weights to combine the tapered spectra into PSD. Only used in ‘multitaper’ mode. mt_low_bias : bool Only use tapers with more than 90% spectral concentration within bandwidth. Only used in ‘multitaper’ mode. cwt_freqs : array Array of frequencies of interest. Only used in ‘cwt_morlet’ mode. cwt_n_cycles: float | array of float Number of cycles. Fixed number or one per frequency. Only used in ‘cwt_morlet’ mode. block_size : int How many connections to compute at once (higher numbers are faster but require more memory). n_jobs : int How many epochs to process in parallel. verbose : bool, str, int, or None If not None, override default verbose level (see mne.verbose() and Logging documentation for more). con : array | list of arrays Computed connectivity measure(s). The shape of each array is either (n_signals, n_signals, n_freqs) mode: ‘multitaper’ or ‘fourier’ (n_signals, n_signals, n_freqs, n_times) mode: ‘cwt_morlet’ when “indices” is None, or (n_con, n_freqs) mode: ‘multitaper’ or ‘fourier’ (n_con, n_freqs, n_times) mode: ‘cwt_morlet’ when “indices” is specified and “n_con = len(indices[0])”. freqs : array Frequency points at which the connectivity was computed. times : array Time points for which the connectivity was computed. n_epochs : int Number of epochs used for computation. n_tapers : int The number of DPSS tapers used. Only defined in ‘multitaper’ mode. Otherwise None is returned.

References

 [R8488] (1, 2) Nolte et al. “Identifying true brain interaction from EEG data using the imaginary part of coherency” Clinical neurophysiology, vol. 115, no. 10, pp. 2292-2307, Oct. 2004.
 [R8588] (1, 2) Lachaux et al. “Measuring phase synchrony in brain signals” Human brain mapping, vol. 8, no. 4, pp. 194-208, Jan. 1999.
 [R8688] (1, 2) Vinck et al. “The pairwise phase consistency: a bias-free measure of rhythmic neuronal synchronization” NeuroImage, vol. 51, no. 1, pp. 112-122, May 2010.
 [R8788] (1, 2) Stam et al. “Phase lag index: assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources” Human brain mapping, vol. 28, no. 11, pp. 1178-1193, Nov. 2007.
 [R8888] (1, 2, 3, 4) Vinck et al. “An improved index of phase-synchronization for electro-physiological data in the presence of volume-conduction, noise and sample-size bias” NeuroImage, vol. 55, no. 4, pp. 1548-1565, Apr. 2011.