Note

Click here to download the full example code

Plotting whitened data

This tutorial demonstrates how to plot whitened evoked data.

Data are whitened for many processes, including dipole fitting, source localization and some decoding algorithms. Viewing whitened data thus gives a different perspective on the data that these algorithms operate on.

Let’s start by loading some data and computing a signal (spatial) covariance that we’ll consider to be noise.

import mne
from mne.datasets import sample

Raw data with whitening

Note

In the mne.io.Raw.plot() with noise_cov supplied, you can press they “w” key to turn whitening on and off.

data_path = sample.data_path()
raw_fname = data_path + '/MEG/sample/sample_audvis_filt-0-40_raw.fif'
raw = mne.io.read_raw_fif(raw_fname, preload=True)

events = mne.find_events(raw, stim_channel='STI 014')
event_id = {'auditory/left': 1, 'auditory/right': 2, 'visual/left': 3,
            'visual/right': 4, 'smiley': 5, 'button': 32}
reject = dict(grad=4000e-13, mag=4e-12, eog=150e-6)
epochs = mne.Epochs(raw, events, event_id=event_id, reject=reject)

# baseline noise cov, not a lot of samples
noise_cov = mne.compute_covariance(epochs, tmax=0., method='shrunk', rank=None,
                                   verbose='error')

# butterfly mode shows the differences most clearly
raw.plot(events=events, butterfly=True)
raw.plot(noise_cov=noise_cov, events=events, butterfly=True)
  • plot whitened
  • plot whitened

Out:

Opening raw data file /home/circleci/mne_data/MNE-sample-data/MEG/sample/sample_audvis_filt-0-40_raw.fif...
    Read a total of 4 projection items:
        PCA-v1 (1 x 102)  idle
        PCA-v2 (1 x 102)  idle
        PCA-v3 (1 x 102)  idle
        Average EEG reference (1 x 60)  idle
    Range : 6450 ... 48149 =     42.956 ...   320.665 secs
Ready.
Reading 0 ... 41699  =      0.000 ...   277.709 secs...
319 events found
Event IDs: [ 1  2  3  4  5 32]
Not setting metadata
Not setting metadata
319 matching events found
Applying baseline correction (mode: mean)
Created an SSP operator (subspace dimension = 4)
4 projection items activated
Computing rank from covariance with rank=None
    Using tolerance 8.3e-14 (2.2e-16 eps * 59 dim * 6.3  max singular value)
    Estimated rank (eeg): 58
    EEG: rank 58 computed from 59 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 1.9e-13 (2.2e-16 eps * 203 dim * 4.3  max singular value)
    Estimated rank (grad): 203
    GRAD: rank 203 computed from 203 data channels with 0 projectors
Computing rank from covariance with rank=None
    Using tolerance 2.7e-14 (2.2e-16 eps * 102 dim * 1.2  max singular value)
    Estimated rank (mag): 99
    MAG: rank 99 computed from 102 data channels with 3 projectors

Epochs with whitening

epochs.plot()
epochs.plot(noise_cov=noise_cov)
  • Ch.
  • Ch.

Out:

Loading data for 319 events and 106 original time points ...
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on MAG : ['MEG 1711']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on MAG : ['MEG 1711']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
    Rejecting  epoch based on EOG : ['EOG 061']
51 bad epochs dropped
Loading data for 268 events and 106 original time points ...
Loading data for 20 events and 106 original time points ...
Loading data for 268 events and 106 original time points ...
Computing rank from covariance with rank=None
    Using tolerance 8.3e-14 (2.2e-16 eps * 59 dim * 6.3  max singular value)
    Estimated rank (eeg): 58
    EEG: rank 58 computed from 59 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 1.9e-13 (2.2e-16 eps * 203 dim * 4.3  max singular value)
    Estimated rank (grad): 203
    GRAD: rank 203 computed from 203 data channels with 0 projectors
Computing rank from covariance with rank=None
    Using tolerance 2.7e-14 (2.2e-16 eps * 102 dim * 1.2  max singular value)
    Estimated rank (mag): 99
    MAG: rank 99 computed from 102 data channels with 3 projectors
Loading data for 20 events and 106 original time points ...

Evoked data with whitening

evoked = epochs.average()
evoked.plot(time_unit='s')
evoked.plot(noise_cov=noise_cov, time_unit='s')
  • EEG (59 channels), Gradiometers (203 channels), Magnetometers (102 channels)
  • EEG (59 channels), Gradiometers (203 channels), Magnetometers (102 channels)

Out:

Computing rank from covariance with rank=None
    Using tolerance 8.3e-14 (2.2e-16 eps * 59 dim * 6.3  max singular value)
    Estimated rank (eeg): 58
    EEG: rank 58 computed from 59 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 1.9e-13 (2.2e-16 eps * 203 dim * 4.3  max singular value)
    Estimated rank (grad): 203
    GRAD: rank 203 computed from 203 data channels with 0 projectors
Computing rank from covariance with rank=None
    Using tolerance 2.7e-14 (2.2e-16 eps * 102 dim * 1.2  max singular value)
    Estimated rank (mag): 99
    MAG: rank 99 computed from 102 data channels with 3 projectors

Evoked data with scaled whitening

The mne.Evoked.plot_white() function takes an additional step of scaling the whitened plots to show how well the assumption of Gaussian noise is satisfied by the data:

evoked.plot_white(noise_cov=noise_cov, time_unit='s')
EEG (59 channels), Gradiometers (203 channels), Magnetometers (102 channels), Whitened GFP, method = "shrunk"

Out:

Computing rank from covariance with rank=None
    Using tolerance 8.3e-14 (2.2e-16 eps * 59 dim * 6.3  max singular value)
    Estimated rank (eeg): 58
    EEG: rank 58 computed from 59 data channels with 1 projector
Computing rank from covariance with rank=None
    Using tolerance 1.9e-13 (2.2e-16 eps * 203 dim * 4.3  max singular value)
    Estimated rank (grad): 203
    GRAD: rank 203 computed from 203 data channels with 0 projectors
Computing rank from covariance with rank=None
    Using tolerance 2.7e-14 (2.2e-16 eps * 102 dim * 1.2  max singular value)
    Estimated rank (mag): 99
    MAG: rank 99 computed from 102 data channels with 3 projectors
    Created an SSP operator (subspace dimension = 4)
Computing rank from covariance with rank={'eeg': 58, 'grad': 203, 'mag': 99, 'meg': 302}
    Setting small MEG eigenvalues to zero (without PCA)
    Setting small EEG eigenvalues to zero (without PCA)
    Created the whitener using a noise covariance matrix with rank 360 (4 small eigenvalues omitted)

Topographic plot with whitening

evoked.comment = 'All trials'
evoked.plot_topo(title='Evoked data')
evoked.plot_topo(noise_cov=noise_cov, title='Whitened evoked data')
  • plot whitened
  • plot whitened

Out:

    Created an SSP operator (subspace dimension = 4)
Computing rank from covariance with rank=None
    Using tolerance 3.6e-13 (2.2e-16 eps * 305 dim * 5.3  max singular value)
    Estimated rank (mag + grad): 302
    MEG: rank 302 computed from 305 data channels with 3 projectors
    Using tolerance 8.3e-14 (2.2e-16 eps * 59 dim * 6.3  max singular value)
    Estimated rank (eeg): 58
    EEG: rank 58 computed from 59 data channels with 1 projector
    Setting small MEG eigenvalues to zero (without PCA)
    Setting small EEG eigenvalues to zero (without PCA)
    Created the whitener using a noise covariance matrix with rank 360 (4 small eigenvalues omitted)

Total running time of the script: ( 0 minutes 25.547 seconds)

Estimated memory usage: 266 MB

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