mne_connectivity.spectral_connectivity_epochs#

mne_connectivity.spectral_connectivity_epochs(data, names=None, method='coh', indices=None, sfreq=None, 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, gc_n_lags=40, rank=None, block_size=1000, n_jobs=1, 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.

Parameters:

dataarray_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.
nameslist | np.ndarray | None: The names of the nodes of the dataset used to compute connectivity. If ‘None’ (default), then names will be a list of integers from 0 to n_nodes. If a list of names, then it must be equal in length to n_nodes.
methodstr | list of str: Connectivity measure(s) to compute. These can be ['coh', 'cohy', 'imcoh', 'mic', 'mim', 'plv', 'ciplv', 'ppc', 'pli', 'dpli', 'wpli', 'wpli2_debiased', 'gc', 'gc_tr']. Multivariate methods (['mic', 'mim', 'gc', 'gc_tr]) cannot be called with the other methods.
indicestuple of array | None: Two arrays with indices of connections for which to compute connectivity. If a bivariate method is called, each array for the seeds and targets should contain the channel indices for each bivariate connection. If a multivariate method is called, each array for the seeds and targets should consist of nested arrays containing the channel indices for each multivariate connection. If None, connections between all channels are computed, unless a Granger causality method is called, in which case an error is raised.
sfreqfloat: The sampling frequency. Required if data is not Epochs.
modestr: Spectrum estimation mode can be either: ‘multitaper’, ‘fourier’, or ‘cwt_morlet’.
fminfloat | tuple of float: 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.
fmaxfloat | tuple of float: 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.
fskipint: Omit every “(fskip + 1)-th” frequency bin to decimate in frequency domain.
faveragebool: Average connectivity scores for each frequency band. If True, the output freqs will be a list with arrays of the frequencies that were averaged.
tminfloat | 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.
tmaxfloat | 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_bandwidthfloat | None: The bandwidth of the multitaper windowing function in Hz. Only used in ‘multitaper’ mode.
mt_adaptivebool: Use adaptive weights to combine the tapered spectra into PSD. Only used in ‘multitaper’ mode.
mt_low_biasbool: Only use tapers with more than 90 percent spectral concentration within bandwidth. Only used in ‘multitaper’ mode.
cwt_freqsarray: Array of frequencies of interest. Only used in ‘cwt_morlet’ mode.
cwt_n_cyclesfloat | array of float: Number of cycles. Fixed number or one per frequency. Only used in ‘cwt_morlet’ mode.
gc_n_lagsint: Number of lags to use for the vector autoregressive model when computing Granger causality. Higher values increase computational cost, but reduce the degree of spectral smoothing in the results. Only used if method contains any of ['gc', 'gc_tr'].
ranktuple of array | None: Two arrays with the rank to project the seed and target data to, respectively, using singular value decomposition. If None, the rank of the data is computed and projected to. Only used if method contains any of ['mic', 'mim', 'gc', 'gc_tr'].
block_sizeint: How many connections to compute at once (higher numbers are faster but require more memory).
n_jobsint: How many samples to process in parallel.
verbosebool, str, int, or None: If not None, override default verbose level (see mne.verbose() for more info). If used, it should be passed as a keyword-argument only.

Returns:

conarray | list of array

Computed connectivity measure(s). Either an instance of SpectralConnectivity or SpectroTemporalConnectivity. The shape of the connectivity result will be:

(n_cons, n_freqs) for multitaper or fourier modes
(n_cons, n_freqs, n_times) for cwt_morlet mode
n_cons = n_signals ** 2 for bivariate methods with indices=None
n_cons = 1 for multivariate methods with indices=None
n_cons = len(indices[0]) for bivariate and multivariate methods when indices is supplied.

See also

mne_connectivity.spectral_connectivity_time
mne_connectivity.SpectralConnectivity
mne_connectivity.SpectroTemporalConnectivity

Notes

Please note that the interpretation of the measures in this function depends on the data and underlying assumptions and does not necessarily reflect a causal relationship between brain regions.

These measures are not to be interpreted over time. Each Epoch passed into the dataset is interpreted as an independent sample of the same connectivity structure. Within each Epoch, it is assumed that the spectral measure is stationary. The spectral measures implemented in this function are computed across Epochs. Thus, spectral measures computed with only one Epoch will result in errorful values and spectral measures computed with few Epochs will be unreliable. Please see spectral_connectivity_time for time-resolved connectivity estimation.

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 = spectral_connectivity_epochs(data, method='coh',
                                   indices=indices, ...)

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

For multivariate methods, this is handled differently. If “indices” is None, connectivity between all signals will be computed and a single connectivity spectrum will be returned (this is not possible if a Granger causality method is called). If “indices” is specified, seed and target indices for each connection should be specified as nested array-likes. For example, to compute the connectivity between signals (0, 1) -> (2, 3) and (0, 1) -> (4, 5), indices should be specified as:

indices = (np.array([[0, 1], [0, 1]]),  # seeds
           np.array([[2, 3], [4, 5]]))  # targets

More information on working with multivariate indices and handling connections where the number of seeds and targets are not equal can be found in the Working with ragged indices for multivariate connectivity example.

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 [1] given by:
          Im(E[Sxy])
C = ----------------------
    sqrt(E[Sxx] * E[Syy])
‘mic’ : Maximised Imaginary part of Coherency (MIC) [2] given by:

\(MIC=\Large{\frac{\boldsymbol{\alpha}^T \boldsymbol{E \beta}} {\parallel\boldsymbol{\alpha}\parallel \parallel\boldsymbol{\beta} \parallel}}\)

where: \(\boldsymbol{E}\) is the imaginary part of the transformed cross-spectral density between seeds and targets; and \(\boldsymbol{\alpha}\) and \(\boldsymbol{\beta}\) are eigenvectors for the seeds and targets, such that \(\boldsymbol{\alpha}^T \boldsymbol{E \beta}\) maximises connectivity between the seeds and targets.

‘mim’ : Multivariate Interaction Measure (MIM) [2] given by:

\(MIM=tr(\boldsymbol{EE}^T)\)

‘plv’ : Phase-Locking Value (PLV) [3] given by:
PLV = |E[Sxy/|Sxy|]|
‘ciplv’ : corrected imaginary PLV (ciPLV) [4] given by:
                 |E[Im(Sxy/|Sxy|)]|
ciPLV = ------------------------------------
         sqrt(1 - |E[real(Sxy/|Sxy|)]| ** 2)
‘ppc’ : Pairwise Phase Consistency (PPC), an unbiased estimator of squared PLV [5].

‘pli’ : Phase Lag Index (PLI) [6] given by:
PLI = |E[sign(Im(Sxy))]|
‘pli2_unbiased’ : Unbiased estimator of squared PLI [7].

‘dpli’ : Directed Phase Lag Index (DPLI) [8] given by (where H is the Heaviside function):
DPLI = E[H(Im(Sxy))]
‘wpli’ : Weighted Phase Lag Index (WPLI) [7] given by:
          |E[Im(Sxy)]|
WPLI = ------------------
          E[|Im(Sxy)|]
‘wpli2_debiased’ : Debiased estimator of squared WPLI [7].

‘gc’ : State-space Granger Causality (GC) [9] given by:

\(GC = ln\Large{(\frac{\lvert\boldsymbol{S}_{tt}\rvert}{\lvert \boldsymbol{S}_{tt}-\boldsymbol{H}_{ts}\boldsymbol{\Sigma}_{ss \lvert t}\boldsymbol{H}_{ts}^*\rvert}})\),

where: \(s\) and \(t\) represent the seeds and targets, respectively; \(\boldsymbol{H}\) is the spectral transfer function; \(\boldsymbol{\Sigma}\) is the residuals matrix of the autoregressive model; and \(\boldsymbol{S}\) is \(\boldsymbol{\Sigma}\) transformed by \(\boldsymbol{H}\).

‘gc_tr’ : State-space GC on time-reversed signals [9][10] given by the same equation as for ‘gc’, but where the autocovariance sequence from which the autoregressive model is produced is transposed to mimic the reversal of the original signal in time.

References

Examples using `mne_connectivity.spectral_connectivity_epochs`#

Comparing PLI, wPLI, and dPLI

Comparing spectral connectivity computed over time or over trials

Compute all-to-all connectivity in sensor space

Compute coherence in source space using a MNE inverse solution

Compute directionality of connectivity with multivariate Granger causality

Compute full spectrum source space connectivity between labels

Compute mixed source space connectivity and visualize it using a circular graph

Compute multivariate measures of the imaginary part of coherency

Compute seed-based time-frequency connectivity in sensor space

Compute source space connectivity and visualize it using a circular graph

Using the connectivity classes

Working with ragged indices for multivariate connectivity

mne_connectivity.spectral_connectivity_epochs#

Examples using mne_connectivity.spectral_connectivity_epochs#

Examples using `mne_connectivity.spectral_connectivity_epochs`#