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 nilearn.maskers.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 20% edges with the highest values.


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


from nilearn.input_data import NiftiMasker

Retrieve the atlas and the data#

from nilearn import datasets
atlas = datasets.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 = datasets.fetch_development_fmri(n_subjects=1)

# print basic information on the dataset
print('First subject functional nifti images (4D) are at: %s' %
      data.func[0])  # 4D data
First subject functional nifti images (4D) are at: /home/runner/work/nilearn/nilearn/nilearn_data/development_fmri/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=True,
                         memory='nilearn_cache', verbose=5)

time_series = masker.fit_transform(data.func[0],
[NiftiMapsMasker.fit_transform] loading regions from /home/runner/work/nilearn/nilearn/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii
Resampling maps
/usr/share/miniconda3/envs/testenv/lib/python3.9/site-packages/nilearn/_utils/ UserWarning:

memory_level is currently set to 0 but a Memory object has been provided. Setting memory_level to 1.

[Memory]0.0s, 0.0min    : Loading resample_img...
________________________________________resample_img cache loaded - 0.0s, 0.0min
[Memory]0.1s, 0.0min    : Loading _filter_and_extract...
__________________________________filter_and_extract cache loaded - 0.0s, 0.0min

Compute the sparse inverse covariance#

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

estimator = GraphicalLassoCV()
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

Display the connectome matrix#

from nilearn import plotting
# Display the covariance

# The covariance can be found at estimator.covariance_
plotting.plot_matrix(estimator.covariance_, labels=labels,
                     figure=(9, 7), vmax=1, vmin=-1,
plot inverse covariance connectome
<matplotlib.image.AxesImage object at 0x7f6b2b4e8d00>

And now display the corresponding graph#

plot inverse covariance connectome
<nilearn.plotting.displays._projectors.OrthoProjector object at 0x7f6b22e55fa0>

Display the sparse inverse covariance#

we negate it to get partial correlations

plotting.plot_matrix(-estimator.precision_, labels=labels,
                     figure=(9, 7), vmax=1, vmin=-1,
                     title='Sparse inverse covariance')
plot inverse covariance connectome
<matplotlib.image.AxesImage object at 0x7f6b11dc2490>

And now display the corresponding graph#

plotting.plot_connectome(-estimator.precision_, coords,
                         title='Sparse inverse covariance')
plot inverse covariance connectome

3D visualization in a web browser#

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

view = plotting.view_connectome(-estimator.precision_, coords)

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