Computing a connectome with sparse inverse covariance

This example constructs a functional connectome using the sparse inverse covariance.

We use the MSDL atlas of functional regions in movie watching, and the NiftiMapsMasker to extract time series.

Note that the inverse covariance (or precision) contains values that can be linked to negated partial correlations, so we negated it for display.

As the MSDL atlas comes with (x, y, z) MNI coordinates for the different regions, we can visualize the matrix as a graph of interaction in a brain. To avoid having too dense a graph, we represent only the edges above 80% of the values.

Retrieve the atlas and the data

from nilearn.datasets import fetch_atlas_msdl, fetch_development_fmri

atlas = fetch_atlas_msdl()

# Loading atlas image stored in 'maps'
atlas_filename = atlas["maps"]

# Loading atlas data stored in 'labels'
labels = atlas["labels"]

# Loading the functional datasets
data = fetch_development_fmri(n_subjects=1)

# print basic information on the dataset
print(f"First subject functional nifti images (4D) are at: {data.func[0]}")

[fetch_atlas_msdl] Dataset directory found: /home/runner/work/nilearn/nilearn/nilearn_data/msdl_atlas
[fetch_development_fmri] Dataset directory found: /home/runner/work/nilearn/nilearn/nilearn_data/development_fmri
First subject functional nifti images (4D) are at: /home/runner/work/nilearn/nilearn/nilearn_data/development_fmri/sub-pixar123_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz

Extract time series

from nilearn.maskers import NiftiMapsMasker

masker = NiftiMapsMasker(
    maps_img=atlas_filename,
    standardize_confounds=True,
    standardize="zscore_sample",
    memory="nilearn_cache",
    memory_level=1,
    verbose=1,
)

time_series = masker.fit_transform(data.func[0], confounds=data.confounds)

[NiftiMapsMasker.wrapped] Loading data from sub-pixar123_task-...
[NiftiMapsMasker.wrapped] Loading regions from .../msdl_rois.nii
[NiftiMapsMasker.wrapped] Resampling regions
[NiftiMapsMasker.wrapped] Finished fit
________________________________________________________________________________
[Memory] Calling nilearn.maskers.base_masker.filter_and_extract...
filter_and_extract('/home/runner/work/nilearn/nilearn/nilearn_data/development_fmri/sub-pixar123_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz',
<nilearn.maskers.nifti_maps_masker._ExtractionFunctor object at 0x7ff8aa045e90>, { 'allow_overlap': True,
  'clean_args': None,
  'clean_kwargs': {},
  'cmap': 'CMRmap_r',
  'detrend': False,
  'dtype': None,
  'high_pass': None,
  'high_variance_confounds': False,
  'low_pass': None,
  'maps_img': '/home/runner/work/nilearn/nilearn/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii',
  'mask_img': None,
  'reports': True,
  'smoothing_fwhm': None,
  'standardize': 'zscore_sample',
  'standardize_confounds': True,
  't_r': None,
  'target_affine': None,
  'target_shape': None}, confounds=[ '/home/runner/work/nilearn/nilearn/nilearn_data/development_fmri/sub-pixar123_task-pixar_desc-reducedConfounds_regressors.tsv'], sample_mask=None, memory=Memory(location=nilearn_cache/joblib), memory_level=1, verbose=1, sklearn_output_config=None)
[NiftiMapsMasker.wrapped] Loading data from sub-pixar123_task-...
[NiftiMapsMasker.wrapped] Extracting region signals
[NiftiMapsMasker.wrapped] Cleaning extracted signals
_______________________________________________filter_and_extract - 0.8s, 0.0min

Compute the sparse inverse covariance

from sklearn.covariance import GraphicalLassoCV

estimator = GraphicalLassoCV(verbose=True)
estimator.fit(time_series)

[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    0.4s finished
[GraphicalLassoCV] Done refinement  1 out of 4:   0s
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    0.5s finished
[GraphicalLassoCV] Done refinement  2 out of 4:   0s
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    0.5s finished
[GraphicalLassoCV] Done refinement  3 out of 4:   1s
[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:    0.5s finished
[GraphicalLassoCV] Done refinement  4 out of 4:   1s

GraphicalLassoCV(verbose=True)

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.

Visualization: covariance

The covariance can be found at estimator.covariance_. We plot it along with its connectome graph.

from nilearn.plotting import (
    plot_connectome,
    plot_matrix,
    show,
    view_connectome,
)

plot_matrix(
    estimator.covariance_,
    labels=labels,
    figure=(9, 7),
    vmax=1,
    vmin=-1,
    title="Covariance",
)

coords = atlas.region_coords

plot_connectome(
    estimator.covariance_, coords, title="Covariance", edge_threshold="80%"
)

show()

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• 

Visualization: sparse inverse covariance

We negate the precision to get partial correlations.

plot_matrix(
    -estimator.precision_,
    labels=labels,
    figure=(9, 7),
    vmax=1,
    vmin=-1,
    title="Sparse inverse covariance",
)

plot_connectome(
    -estimator.precision_,
    coords,
    title="Sparse inverse covariance",
    edge_threshold="80%",
)

show()

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• 

3D visualization in a web browser

An alternative to plot_connectome is to use view_connectome that gives more interactive visualizations in a web browser. See 3D Plots of connectomes for more details.

view = view_connectome(-estimator.precision_, coords, edge_threshold="80%")

# In a notebook, if ``view`` is the output of a cell, it will
# be displayed below the cell
view

# uncomment this to open the plot in a web browser:
# view.open_in_browser()

Estimated memory usage: 988 MB