Note

Go to the end 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)
```

```
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
319 matching events found
Setting baseline interval to [-0.19979521315838786, 0.0] sec
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#

```
Using data from preloaded Raw 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
Using data from preloaded Raw for 20 events and 106 original time points ...
Using data from preloaded Raw for 20 events and 106 original time points ...
Using data from preloaded Raw for 20 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
Using data from preloaded Raw for 20 events and 106 original time points ...
Using data from preloaded Raw for 20 events and 106 original time points ...
Using data from preloaded Raw 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')
```

```
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')
```

```
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')
```

```
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 23.799 seconds)

**Estimated memory usage:** 12 MB