9.4.7. Group Sparse inverse covariance for multi-subject connectome¶

This example shows how to estimate a connectome on a group of subjects using the group sparse inverse covariance estimate.

```import numpy as np

from nilearn import plotting

n_subjects = 4  # subjects to consider for group-sparse covariance (max: 40)

def plot_matrices(cov, prec, title, labels):
"""Plot covariance and precision matrices, for a given processing. """

prec = prec.copy()  # avoid side effects

# Put zeros on the diagonal, for graph clarity.
size = prec.shape[0]
prec[list(range(size)), list(range(size))] = 0
span = max(abs(prec.min()), abs(prec.max()))

# Display covariance matrix
plotting.plot_matrix(cov, cmap=plotting.cm.bwr,
vmin=-1, vmax=1, title="%s / covariance" % title,
labels=labels)
# Display precision matrix
plotting.plot_matrix(prec, cmap=plotting.cm.bwr,
vmin=-span, vmax=span, title="%s / precision" % title,
labels=labels)
```

9.4.7.1. Fetching datasets¶

```from nilearn import datasets
msdl_atlas_dataset = datasets.fetch_atlas_msdl()
rest_dataset = datasets.fetch_development_fmri(n_subjects=n_subjects)

# print basic information on the dataset
print('First subject functional nifti image (4D) is at: %s' %
rest_dataset.func[0])  # 4D data
```

Out:

```/home/nicolas/anaconda3/envs/nilearn/lib/python3.8/site-packages/numpy/lib/npyio.py:2405: VisibleDeprecationWarning: Reading unicode strings without specifying the encoding argument is deprecated. Set the encoding, use None for the system default.
output = genfromtxt(fname, **kwargs)
First subject functional nifti image (4D) is at: /home/nicolas/nilearn_data/development_fmri/development_fmri/sub-pixar123_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz
```

9.4.7.2. Extracting region signals¶

```from nilearn import input_data

# A "memory" to avoid recomputation
from joblib import Memory
mem = Memory('nilearn_cache')

msdl_atlas_dataset.maps, resampling_target="maps", detrend=True,
high_variance_confounds=True, low_pass=None, high_pass=0.01,
t_r=2, standardize=True, memory='nilearn_cache', memory_level=1,
verbose=2)

subject_time_series = []
func_filenames = rest_dataset.func
confound_filenames = rest_dataset.confounds
for func_filename, confound_filename in zip(func_filenames,
confound_filenames):
print("Processing file %s" % func_filename)

confounds=confound_filename)
subject_time_series.append(region_ts)
```

Out:

```[NiftiMapsMasker.fit] loading regions from /home/nicolas/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii
/home/nicolas/GitRepos/nilearn-fork/nilearn/image/image.py:1106: FutureWarning: The parameter "sessions" will be removed in 0.9.0 release of Nilearn. Please use the parameter "runs" instead.
data = signal.clean(
________________________________________________________________________________
[Memory] Calling nilearn.image.image.high_variance_confounds...
__________________________________________high_variance_confounds - 0.8s, 0.0min
________________________________________________________________________________
{ 'allow_overlap': True,
'detrend': True,
'dtype': None,
'high_pass': 0.01,
'high_variance_confounds': True,
'low_pass': None,
'maps_img': '/home/nicolas/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii',
'smoothing_fwhm': None,
'standardize': True,
'standardize_confounds': True,
't_r': 2,
'target_affine': array([[   4.,    0.,    0.,  -78.],
[   0.,    4.,    0., -111.],
[   0.,    0.,    4.,  -51.],
[   0.,    0.,    0.,    1.]]),
'target_shape': (40, 48, 35)}, confounds=[ array([[-0.174325, ..., -0.048779],
...,
[-0.044073, ...,  0.155444]]),
_______________________________________________filter_and_extract - 5.4s, 0.1min
________________________________________________________________________________
[Memory] Calling nilearn.image.image.high_variance_confounds...
__________________________________________high_variance_confounds - 0.8s, 0.0min
________________________________________________________________________________
{ 'allow_overlap': True,
'detrend': True,
'dtype': None,
'high_pass': 0.01,
'high_variance_confounds': True,
'low_pass': None,
'maps_img': '/home/nicolas/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii',
'smoothing_fwhm': None,
'standardize': True,
'standardize_confounds': True,
't_r': 2,
'target_affine': array([[   4.,    0.,    0.,  -78.],
[   0.,    4.,    0., -111.],
[   0.,    0.,    4.,  -51.],
[   0.,    0.,    0.,    1.]]),
'target_shape': (40, 48, 35)}, confounds=[ array([[-0.151677, ..., -0.057023],
...,
[-0.206928, ...,  0.102714]]),
_______________________________________________filter_and_extract - 5.4s, 0.1min
________________________________________________________________________________
[Memory] Calling nilearn.image.image.high_variance_confounds...
__________________________________________high_variance_confounds - 0.8s, 0.0min
________________________________________________________________________________
{ 'allow_overlap': True,
'detrend': True,
'dtype': None,
'high_pass': 0.01,
'high_variance_confounds': True,
'low_pass': None,
'maps_img': '/home/nicolas/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii',
'smoothing_fwhm': None,
'standardize': True,
'standardize_confounds': True,
't_r': 2,
'target_affine': array([[   4.,    0.,    0.,  -78.],
[   0.,    4.,    0., -111.],
[   0.,    0.,    4.,  -51.],
[   0.,    0.,    0.,    1.]]),
'target_shape': (40, 48, 35)}, confounds=[ array([[ 0.127944, ..., -0.087084],
...,
[-0.015679, ..., -0.02587 ]]),
_______________________________________________filter_and_extract - 5.5s, 0.1min
________________________________________________________________________________
[Memory] Calling nilearn.image.image.high_variance_confounds...
__________________________________________high_variance_confounds - 0.8s, 0.0min
________________________________________________________________________________
{ 'allow_overlap': True,
'detrend': True,
'dtype': None,
'high_pass': 0.01,
'high_variance_confounds': True,
'low_pass': None,
'maps_img': '/home/nicolas/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii',
'smoothing_fwhm': None,
'standardize': True,
'standardize_confounds': True,
't_r': 2,
'target_affine': array([[   4.,    0.,    0.,  -78.],
[   0.,    4.,    0., -111.],
[   0.,    0.,    4.,  -51.],
[   0.,    0.,    0.,    1.]]),
'target_shape': (40, 48, 35)}, confounds=[ array([[-0.089762, ..., -0.062316],
...,
[-0.065223, ..., -0.022868]]),
_______________________________________________filter_and_extract - 5.1s, 0.1min
```

9.4.7.3. Computing group-sparse precision matrices¶

```from nilearn.connectome import GroupSparseCovarianceCV
gsc = GroupSparseCovarianceCV(verbose=2)
gsc.fit(subject_time_series)

try:
from sklearn.covariance import GraphicalLassoCV
except ImportError:
# for Scitkit-Learn < v0.20.0
from sklearn.covariance import GraphLassoCV as GraphicalLassoCV

gl = GraphicalLassoCV(verbose=2)
gl.fit(np.concatenate(subject_time_series))
```

Out:

```[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 2
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 7
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    3.0s remaining:    0.0s
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 2
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 2
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 1
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 2
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 6
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:   13.4s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement  1 out of 4
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 3
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 6
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 1
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    2.8s remaining:    0.0s
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 4
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 3
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 3
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 6
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:   22.8s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement  2 out of 4
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 5
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 1
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 1
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 1
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    2.8s remaining:    0.0s
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 9
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 10
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 5
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:   25.1s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement  3 out of 4
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 6
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 1
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 1
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    3.3s remaining:    0.0s
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 10
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 11
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 5
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[GroupSparseCovarianceCV.fit] Log-likelihood on test set is decreasing. Stopping at iteration 0
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:   20.8s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement  4 out of 4
[GroupSparseCovarianceCV.fit] Final optimization
[GroupSparseCovarianceCV.fit] tolerance reached at iteration number 19: 8.789e-04
[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   5 out of   5 | elapsed:    1.0s finished
[GraphicalLassoCV] Done refinement  1 out of 4:   1s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
....[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.2s remaining:    0.0s
................[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    1.1s finished
[GraphicalLassoCV] Done refinement  2 out of 4:   2s
[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   5 out of   5 | elapsed:    1.4s finished
[GraphicalLassoCV] Done refinement  3 out of 4:   3s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
....[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    0.4s remaining:    0.0s
................[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    1.4s finished
[GraphicalLassoCV] Done refinement  4 out of 4:   5s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    0.0s finished
[graphical_lasso] Iteration   0, cost  1.68e+02, dual gap 1.123e+00
[graphical_lasso] Iteration   1, cost  1.68e+02, dual gap -1.664e-03
[graphical_lasso] Iteration   2, cost  1.68e+02, dual gap 1.158e-04
[graphical_lasso] Iteration   3, cost  1.68e+02, dual gap 1.389e-04
[graphical_lasso] Iteration   4, cost  1.68e+02, dual gap 1.530e-04
[graphical_lasso] Iteration   5, cost  1.68e+02, dual gap 1.318e-04
[graphical_lasso] Iteration   6, cost  1.68e+02, dual gap 6.844e-05

GraphicalLassoCV(verbose=2)
```

9.4.7.4. Displaying results¶

```atlas_img = msdl_atlas_dataset.maps
atlas_region_coords = plotting.find_probabilistic_atlas_cut_coords(atlas_img)
labels = msdl_atlas_dataset.labels

plotting.plot_connectome(gl.covariance_,
atlas_region_coords, edge_threshold='90%',
title="Covariance",
display_mode="lzr")
plotting.plot_connectome(-gl.precision_, atlas_region_coords,
edge_threshold='90%',
title="Sparse inverse covariance (GraphicalLasso)",
display_mode="lzr",
edge_vmax=.5, edge_vmin=-.5)
plot_matrices(gl.covariance_, gl.precision_, "GraphicalLasso", labels)

title = "GroupSparseCovariance"
plotting.plot_connectome(-gsc.precisions_[..., 0],
atlas_region_coords, edge_threshold='90%',
title=title,
display_mode="lzr",
edge_vmax=.5, edge_vmin=-.5)
plot_matrices(gsc.covariances_[..., 0],
gsc.precisions_[..., 0], title, labels)

plotting.show()
```

Total running time of the script: ( 2 minutes 5.127 seconds)

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