Note

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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
# Copyright the MNE-Python contributors.
```

Define parameters

```
fname = data_path() / "SubjectCMC.ds"
# Prepare data
raw = mne.io.read_raw_ctf(fname)
raw.crop(50.0, 110.0).load_data() # crop for memory purposes
raw.resample(sfreq=250)
raw.pick_types(meg=True, 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 on stim channel STIM
Event IDs: [ 196608 262144 327680 393216 458752 67108864 67174400
134742016 136314880 268435456]
29 events found on stim channel STIM
Event IDs: [ 196608 262144 327680 393216 458752 67108864 67174400
134742016 136314880 268435456]
NOTE: pick_types() is a legacy function. New code should use inst.pick(...).
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 s)
[Parallel(n_jobs=1)]: Done 17 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 71 tasks | elapsed: 0.1s
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 s)
[Parallel(n_jobs=1)]: Done 17 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 71 tasks | elapsed: 0.1s
Computing rank from data with rank='full'
MAG: rank 151 from info
Reducing data rank from 151 -> 151
Estimating covariance using OAS
Done.
Computing rank from data with rank='full'
MAG: rank 151 from info
Reducing data rank from 151 -> 151
Estimating covariance using OAS
Done.
Computing rank from covariance with rank=None
Using tolerance 1.2e-14 (2.2e-16 eps * 151 dim * 0.37 max singular value)
Estimated rank (mag): 151
MAG: rank 151 computed from 151 data channels with 0 projectors
Computing rank from covariance with rank=None
Using tolerance 2.9e-15 (2.2e-16 eps * 151 dim * 0.086 max singular value)
Estimated rank (mag): 151
MAG: rank 151 computed from 151 data channels with 0 projectors
Preserving covariance rank (151)
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)
Effective window size : 1.000 (s)
```

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=0.0, 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(copy=False))
# 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 s)
[Parallel(n_jobs=1)]: Done 17 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 71 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 161 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 287 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 449 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 647 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 881 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 1151 tasks | elapsed: 0.3s
[Parallel(n_jobs=1)]: Done 1457 tasks | elapsed: 0.3s
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 s)
[Parallel(n_jobs=1)]: Done 17 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 71 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 161 tasks | elapsed: 0.0s
[Parallel(n_jobs=1)]: Done 287 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 449 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 647 tasks | elapsed: 0.1s
[Parallel(n_jobs=1)]: Done 881 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 1151 tasks | elapsed: 0.2s
[Parallel(n_jobs=1)]: Done 1457 tasks | elapsed: 0.3s
Computing rank from data with rank='full'
MAG: rank 151 from info
Reducing data rank from 151 -> 151
Estimating covariance using OAS
Done.
Computing rank from data with rank='full'
MAG: rank 151 from info
Reducing data rank from 151 -> 151
Estimating covariance using OAS
Done.
Computing rank from covariance with rank=None
Using tolerance 1.3e-14 (2.2e-16 eps * 151 dim * 0.38 max singular value)
Estimated rank (mag): 151
MAG: rank 151 computed from 151 data channels with 0 projectors
Computing rank from covariance with rank=None
Using tolerance 3e-15 (2.2e-16 eps * 151 dim * 0.09 max singular value)
Estimated rank (mag): 151
MAG: rank 151 computed from 151 data channels with 0 projectors
Preserving covariance rank (151)
Effective window size : 1.000 (s)
Done.
```

## References#

**Total running time of the script:** (0 minutes 10.509 seconds)

**Estimated memory usage:** 178 MB