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# Compute Spectro-Spatial Decomposition (SSD) spatial filters#

In this example, we will compute spatial filters for retaining oscillatory brain activity and down-weighting 1/f background signals as proposed by [1]. The idea is to learn spatial filters that separate oscillatory dynamics from surrounding non-oscillatory noise based on the covariance in the frequency band of interest and the noise covariance based on surrounding frequencies.

```
# Author: Denis A. Engemann <denis.engemann@gmail.com>
# Victoria Peterson <victoriapeterson09@gmail.com>
# License: BSD-3-Clause
```

Define parameters

```
fname = data_path() / 'SubjectCMC.ds'
# Prepare data
raw = mne.io.read_raw_ctf(fname)
raw.crop(50., 110.).load_data() # crop for memory purposes
raw.resample(sfreq=250)
raw.pick_types(meg=True, eeg=False, ref_meg=False)
freqs_sig = 9, 12
freqs_noise = 8, 13
ssd = SSD(info=raw.info,
reg='oas',
sort_by_spectral_ratio=False, # False for purpose of example.
filt_params_signal=dict(l_freq=freqs_sig[0], h_freq=freqs_sig[1],
l_trans_bandwidth=1, h_trans_bandwidth=1),
filt_params_noise=dict(l_freq=freqs_noise[0], h_freq=freqs_noise[1],
l_trans_bandwidth=1, h_trans_bandwidth=1))
ssd.fit(X=raw.get_data())
```

```
ds directory : /home/circleci/mne_data/MNE-fieldtrip_cmc-data/SubjectCMC.ds
res4 data read.
hc data read.
Separate EEG position data file not present.
Quaternion matching (desired vs. transformed):
0.33 78.32 0.00 mm <-> 0.33 78.32 0.00 mm (orig : -71.62 40.46 -256.48 mm) diff = 0.000 mm
-0.33 -78.32 -0.00 mm <-> -0.33 -78.32 -0.00 mm (orig : 39.27 -70.16 -258.60 mm) diff = 0.000 mm
114.65 0.00 -0.00 mm <-> 114.65 0.00 -0.00 mm (orig : 64.35 66.64 -262.01 mm) diff = 0.000 mm
Coordinate transformations established.
Polhemus data for 3 HPI coils added
Device coordinate locations for 3 HPI coils added
Picked positions of 4 EEG channels from channel info
4 EEG locations added to Polhemus data.
Measurement info composed.
Finding samples for /home/circleci/mne_data/MNE-fieldtrip_cmc-data/SubjectCMC.ds/SubjectCMC.meg4:
System clock channel is available, checking which samples are valid.
75 x 12000 = 911610 samples from 191 chs
390 samples omitted at the end
Current compensation grade : 0
Reading 0 ... 72000 = 0.000 ... 60.000 secs...
29 events found
Event IDs: [ 196608 262144 327680 393216 458752 67108864 67174400
134742016 136314880 268435456]
29 events found
Event IDs: [ 196608 262144 327680 393216 458752 67108864 67174400
134742016 136314880 268435456]
Removing 5 compensators from info because not all compensation channels were picked.
Setting up band-pass filter from 9 - 12 Hz
FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal bandpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower passband edge: 9.00
- Lower transition bandwidth: 1.00 Hz (-6 dB cutoff frequency: 8.50 Hz)
- Upper passband edge: 12.00 Hz
- Upper transition bandwidth: 1.00 Hz (-6 dB cutoff frequency: 12.50 Hz)
- Filter length: 825 samples (3.300 sec)
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 2 out of 2 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 3 out of 3 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 4 out of 4 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 151 out of 151 | elapsed: 0.1s finished
Setting up band-pass filter from 8 - 13 Hz
FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal bandpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower passband edge: 8.00
- Lower transition bandwidth: 1.00 Hz (-6 dB cutoff frequency: 7.50 Hz)
- Upper passband edge: 13.00 Hz
- Upper transition bandwidth: 1.00 Hz (-6 dB cutoff frequency: 13.50 Hz)
- Filter length: 825 samples (3.300 sec)
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 2 out of 2 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 3 out of 3 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 4 out of 4 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 151 out of 151 | elapsed: 0.1s finished
Computing rank from data with rank=None
Using tolerance 2.5e-12 (2.2e-16 eps * 151 dim * 75 max singular value)
Estimated rank (mag): 151
MAG: rank 151 computed from 151 data channels with 0 projectors
Reducing data rank from 151 -> 151
Estimating covariance using OAS
Done.
Computing rank from data with rank=None
Using tolerance 1.2e-12 (2.2e-16 eps * 151 dim * 36 max singular value)
Estimated rank (mag): 151
MAG: rank 151 computed from 151 data channels with 0 projectors
Reducing data rank from 151 -> 151
Estimating covariance using OAS
Done.
```

Let’s investigate spatial filter with max power ratio. We will first inspect the topographies. According to Nikulin et al. 2011 this is done by either inverting the filters (W^{-1}) or by multiplying the noise cov with the filters Eq. (22) (C_n W)^t. We rely on the inversion approach here.

```
pattern = mne.EvokedArray(data=ssd.patterns_[:4].T,
info=ssd.info)
pattern.plot_topomap(units=dict(mag='A.U.'), time_format='')
# The topographies suggest that we picked up a parietal alpha generator.
# Transform
ssd_sources = ssd.transform(X=raw.get_data())
# Get psd of SSD-filtered signals.
psd, freqs = mne.time_frequency.psd_array_welch(
ssd_sources, sfreq=raw.info['sfreq'], n_fft=4096)
# Get spec_ratio information (already sorted).
# Note that this is not necessary if sort_by_spectral_ratio=True (default).
spec_ratio, sorter = ssd.get_spectral_ratio(ssd_sources)
# Plot spectral ratio (see Eq. 24 in Nikulin 2011).
fig, ax = plt.subplots(1)
ax.plot(spec_ratio, color='black')
ax.plot(spec_ratio[sorter], color='orange', label='sorted eigenvalues')
ax.set_xlabel("Eigenvalue Index")
ax.set_ylabel(r"Spectral Ratio $\frac{P_f}{P_{sf}}$")
ax.legend()
ax.axhline(1, linestyle='--')
# We can see that the initial sorting based on the eigenvalues
# was already quite good. However, when using few components only
# the sorting might make a difference.
```

```
Effective window size : 16.384 (s)
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s finished
Effective window size : 1.000 (s)
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.1s finished
```

Let’s also look at the power spectrum of that source and compare it to to the power spectrum of the source with lowest SNR.

```
below50 = freqs < 50
# for highlighting the freq. band of interest
bandfilt = (freqs_sig[0] <= freqs) & (freqs <= freqs_sig[1])
fig, ax = plt.subplots(1)
ax.loglog(freqs[below50], psd[0, below50], label='max SNR')
ax.loglog(freqs[below50], psd[-1, below50], label='min SNR')
ax.loglog(freqs[below50], psd[:, below50].mean(axis=0), label='mean')
ax.fill_between(freqs[bandfilt], 0, 10000, color='green', alpha=0.15)
ax.set_xlabel('log(frequency)')
ax.set_ylabel('log(power)')
ax.legend()
# We can clearly see that the selected component enjoys an SNR that is
# way above the average power spectrum.
```

## Epoched data#

Although we suggest to use this method before epoching, there might be some situations in which data can only be treated by chunks.

```
# Build epochs as sliding windows over the continuous raw file.
events = mne.make_fixed_length_events(raw, id=1, duration=5.0, overlap=0.0)
# Epoch length is 5 seconds.
epochs = Epochs(raw, events, tmin=0., tmax=5,
baseline=None, preload=True)
ssd_epochs = SSD(info=epochs.info,
reg='oas',
filt_params_signal=dict(l_freq=freqs_sig[0],
h_freq=freqs_sig[1],
l_trans_bandwidth=1,
h_trans_bandwidth=1),
filt_params_noise=dict(l_freq=freqs_noise[0],
h_freq=freqs_noise[1],
l_trans_bandwidth=1,
h_trans_bandwidth=1))
ssd_epochs.fit(X=epochs.get_data())
# Plot topographies.
pattern_epochs = mne.EvokedArray(data=ssd_epochs.patterns_[:4].T,
info=ssd_epochs.info)
pattern_epochs.plot_topomap(units=dict(mag='A.U.'), time_format='')
```

```
Not setting metadata
12 matching events found
No baseline correction applied
0 projection items activated
Using data from preloaded Raw for 12 events and 1251 original time points ...
1 bad epochs dropped
Setting up band-pass filter from 9 - 12 Hz
FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal bandpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower passband edge: 9.00
- Lower transition bandwidth: 1.00 Hz (-6 dB cutoff frequency: 8.50 Hz)
- Upper passband edge: 12.00 Hz
- Upper transition bandwidth: 1.00 Hz (-6 dB cutoff frequency: 12.50 Hz)
- Filter length: 825 samples (3.300 sec)
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 2 out of 2 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 3 out of 3 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 4 out of 4 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1661 out of 1661 | elapsed: 0.4s finished
Setting up band-pass filter from 8 - 13 Hz
FIR filter parameters
---------------------
Designing a one-pass, zero-phase, non-causal bandpass filter:
- Windowed time-domain design (firwin) method
- Hamming window with 0.0194 passband ripple and 53 dB stopband attenuation
- Lower passband edge: 8.00
- Lower transition bandwidth: 1.00 Hz (-6 dB cutoff frequency: 7.50 Hz)
- Upper passband edge: 13.00 Hz
- Upper transition bandwidth: 1.00 Hz (-6 dB cutoff frequency: 13.50 Hz)
- Filter length: 825 samples (3.300 sec)
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 2 out of 2 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 3 out of 3 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 4 out of 4 | elapsed: 0.0s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1661 out of 1661 | elapsed: 0.3s finished
Computing rank from data with rank=None
Using tolerance 2.4e-12 (2.2e-16 eps * 151 dim * 73 max singular value)
Estimated rank (mag): 151
MAG: rank 151 computed from 151 data channels with 0 projectors
Reducing data rank from 151 -> 151
Estimating covariance using OAS
Done.
Computing rank from data with rank=None
Using tolerance 1.2e-12 (2.2e-16 eps * 151 dim * 35 max singular value)
Estimated rank (mag): 151
MAG: rank 151 computed from 151 data channels with 0 projectors
Reducing data rank from 151 -> 151
Estimating covariance using OAS
Done.
Effective window size : 1.000 (s)
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.5s remaining: 0.0s
[Parallel(n_jobs=1)]: Done 1 out of 1 | elapsed: 0.5s finished
```

## References#

**Total running time of the script:** ( 0 minutes 9.487 seconds)

**Estimated memory usage:** 114 MB