Note

Go to the end to download the full example code. or to run this example in your browser via Binder

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.

Note

If you are using Nilearn with a version older than 0.9.0, then you should either upgrade your version or import maskers from the input_data module instead of the maskers module.

That is, you should manually replace in the following example all occurrences of:

from nilearn.maskers import NiftiMasker

with:

from nilearn.input_data import NiftiMasker

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=f"{title} / covariance",
        labels=labels,
    )
    # Display precision matrix
    plotting.plot_matrix(
        prec,
        cmap=plotting.cm.bwr,
        vmin=-span,
        vmax=span,
        title=f"{title} / precision",
        labels=labels,
    )

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(
    f"First subject functional nifti image (4D) is at: {rest_dataset.func[0]}"
)

[get_dataset_dir] Dataset found in /home/runner/nilearn_data/msdl_atlas
[get_dataset_dir] Dataset found in /home/runner/nilearn_data/development_fmri
[get_dataset_dir] Dataset found in
/home/runner/nilearn_data/development_fmri/development_fmri
[get_dataset_dir] Dataset found in
/home/runner/nilearn_data/development_fmri/development_fmri
[fetch_single_file] Downloading data from
https://osf.io/download/5cb4701e3992690018133d4f/ ...
[fetch_single_file]  ...done. (1 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5cb46e6b353c58001b9cb34f/ ...
[fetch_single_file]  ...done. (2 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5c8ff37d4712b400193b5b54/ ...
[fetch_single_file]  ...done. (1 seconds, 0 min)

[fetch_single_file] Downloading data from
https://osf.io/download/5c8ff37d4712b400183b7011/ ...
[fetch_single_file]  ...done. (1 seconds, 0 min)

First subject functional nifti image (4D) is at: /home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar123_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz

Extracting region signals¶

from nilearn.maskers import NiftiMapsMasker

masker = NiftiMapsMasker(
    msdl_atlas_dataset.maps,
    resampling_target="maps",
    detrend=True,
    high_variance_confounds=True,
    low_pass=None,
    high_pass=0.01,
    t_r=2,
    standardize="zscore_sample",
    standardize_confounds="zscore_sample",
    memory="nilearn_cache",
    memory_level=1,
    verbose=2,
)
masker.fit()

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(f"Processing file {func_filename}")

    region_ts = masker.transform(func_filename, confounds=confound_filename)
    subject_time_series.append(region_ts)

[NiftiMapsMasker.fit] loading regions from None
Processing file /home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar123_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz
________________________________________________________________________________
[Memory] Calling nilearn.image.image.high_variance_confounds...
high_variance_confounds('/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar123_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz')
__________________________________________high_variance_confounds - 0.5s, 0.0min
________________________________________________________________________________
[Memory] Calling nilearn.maskers.base_masker._filter_and_extract...
_filter_and_extract('/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar123_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz',
<nilearn.maskers.nifti_maps_masker._ExtractionFunctor object at 0x7f5827f40b50>, { 'allow_overlap': True,
  'clean_kwargs': {},
  'detrend': True,
  'dtype': None,
  'high_pass': 0.01,
  'high_variance_confounds': True,
  'keep_masked_maps': True,
  'low_pass': None,
  'maps_img': '/home/runner/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii',
  'mask_img': None,
  'reports': True,
  'smoothing_fwhm': None,
  'standardize': 'zscore_sample',
  'standardize_confounds': 'zscore_sample',
  '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]]),
  '/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar123_task-pixar_desc-reducedConfounds_regressors.tsv'], sample_mask=None, dtype=None, memory=Memory(location=nilearn_cache/joblib), memory_level=1, verbose=2)
[NiftiMapsMasker.wrapped] Loading data from
/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar123_task-pi
xar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz
[NiftiMapsMasker.wrapped] Resampling images
[NiftiMapsMasker.wrapped] Extracting region signals
[NiftiMapsMasker.wrapped] Cleaning extracted signals
_______________________________________________filter_and_extract - 5.0s, 0.1min
Processing file /home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar001_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz
________________________________________________________________________________
[Memory] Calling nilearn.image.image.high_variance_confounds...
high_variance_confounds('/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar001_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz')
__________________________________________high_variance_confounds - 0.4s, 0.0min
________________________________________________________________________________
[Memory] Calling nilearn.maskers.base_masker._filter_and_extract...
_filter_and_extract('/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar001_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz',
<nilearn.maskers.nifti_maps_masker._ExtractionFunctor object at 0x7f582840d4c0>, { 'allow_overlap': True,
  'clean_kwargs': {},
  'detrend': True,
  'dtype': None,
  'high_pass': 0.01,
  'high_variance_confounds': True,
  'keep_masked_maps': True,
  'low_pass': None,
  'maps_img': '/home/runner/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii',
  'mask_img': None,
  'reports': True,
  'smoothing_fwhm': None,
  'standardize': 'zscore_sample',
  'standardize_confounds': 'zscore_sample',
  '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]]),
  '/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar001_task-pixar_desc-reducedConfounds_regressors.tsv'], sample_mask=None, dtype=None, memory=Memory(location=nilearn_cache/joblib), memory_level=1, verbose=2)
[NiftiMapsMasker.wrapped] Loading data from
/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar001_task-pi
xar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz
[NiftiMapsMasker.wrapped] Resampling images
[NiftiMapsMasker.wrapped] Extracting region signals
[NiftiMapsMasker.wrapped] Cleaning extracted signals
_______________________________________________filter_and_extract - 5.0s, 0.1min
Processing file /home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar002_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz
________________________________________________________________________________
[Memory] Calling nilearn.image.image.high_variance_confounds...
high_variance_confounds('/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar002_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz')
__________________________________________high_variance_confounds - 0.4s, 0.0min
________________________________________________________________________________
[Memory] Calling nilearn.maskers.base_masker._filter_and_extract...
_filter_and_extract('/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar002_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz',
<nilearn.maskers.nifti_maps_masker._ExtractionFunctor object at 0x7f5827f40eb0>, { 'allow_overlap': True,
  'clean_kwargs': {},
  'detrend': True,
  'dtype': None,
  'high_pass': 0.01,
  'high_variance_confounds': True,
  'keep_masked_maps': True,
  'low_pass': None,
  'maps_img': '/home/runner/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii',
  'mask_img': None,
  'reports': True,
  'smoothing_fwhm': None,
  'standardize': 'zscore_sample',
  'standardize_confounds': 'zscore_sample',
  '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 ]]),
  '/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar002_task-pixar_desc-reducedConfounds_regressors.tsv'], sample_mask=None, dtype=None, memory=Memory(location=nilearn_cache/joblib), memory_level=1, verbose=2)
[NiftiMapsMasker.wrapped] Loading data from
/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar002_task-pi
xar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz
[NiftiMapsMasker.wrapped] Resampling images
[NiftiMapsMasker.wrapped] Extracting region signals
[NiftiMapsMasker.wrapped] Cleaning extracted signals
_______________________________________________filter_and_extract - 5.1s, 0.1min
Processing file /home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar003_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz
________________________________________________________________________________
[Memory] Calling nilearn.image.image.high_variance_confounds...
high_variance_confounds('/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar003_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz')
__________________________________________high_variance_confounds - 0.4s, 0.0min
________________________________________________________________________________
[Memory] Calling nilearn.maskers.base_masker._filter_and_extract...
_filter_and_extract('/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar003_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz',
<nilearn.maskers.nifti_maps_masker._ExtractionFunctor object at 0x7f582840d4c0>, { 'allow_overlap': True,
  'clean_kwargs': {},
  'detrend': True,
  'dtype': None,
  'high_pass': 0.01,
  'high_variance_confounds': True,
  'keep_masked_maps': True,
  'low_pass': None,
  'maps_img': '/home/runner/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii',
  'mask_img': None,
  'reports': True,
  'smoothing_fwhm': None,
  'standardize': 'zscore_sample',
  'standardize_confounds': 'zscore_sample',
  '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]]),
  '/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar003_task-pixar_desc-reducedConfounds_regressors.tsv'], sample_mask=None, dtype=None, memory=Memory(location=nilearn_cache/joblib), memory_level=1, verbose=2)
[NiftiMapsMasker.wrapped] Loading data from
/home/runner/nilearn_data/development_fmri/development_fmri/sub-pixar003_task-pi
xar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz
[NiftiMapsMasker.wrapped] Resampling images
[NiftiMapsMasker.wrapped] Extracting region signals
[NiftiMapsMasker.wrapped] Cleaning extracted signals
_______________________________________________filter_and_extract - 5.1s, 0.1min

Computing group-sparse precision matrices¶

from nilearn.connectome import GroupSparseCovarianceCV

gsc = GroupSparseCovarianceCV(verbose=2)
gsc.fit(subject_time_series)


from sklearn.covariance import GraphicalLassoCV

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

[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:    1.6s 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 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:    8.5s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement  0 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:    1.7s 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:   14.4s 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 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
[Parallel(n_jobs=1)]: Done   1 out of   1 | elapsed:    2.3s 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:   16.8s 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 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:    2.1s remaining:    0.0s
[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 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:   13.4s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement  3 out
of 4
[GroupSparseCovarianceCV.fit] Final optimization
[GroupSparseCovarianceCV.fit] tolerance reached at iteration number 19:
8.841e-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:    0.5s finished
[GraphicalLassoCV] Done refinement  1 out of 4:   0s
[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:    0.5s finished
[GraphicalLassoCV] Done refinement  2 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:    0.6s finished
[GraphicalLassoCV] Done refinement  3 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:    0.1s remaining:    0.0s
................[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    0.6s finished
[GraphicalLassoCV] Done refinement  4 out of 4:   2s
[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)

In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook.
On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.

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=0.5,
    edge_vmin=-0.5,
)
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=0.5,
    edge_vmin=-0.5,
)
plot_matrices(gsc.covariances_[..., 0], gsc.precisions_[..., 0], title, labels)

plotting.show()