8.4.3. 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.input_data.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.

8.4.3.1. 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

Out:

/home/emdupre/miniconda3/envs/nilearn/lib/python3.7/site-packages/numpy/lib/npyio.py:2372: 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 images (4D) are at: /home/emdupre/nilearn_data/development_fmri/development_fmri/sub-pixar123_task-pixar_space-MNI152NLin2009cAsym_desc-preproc_bold.nii.gz

8.4.3.2. Extract time series

from nilearn.input_data import NiftiMapsMasker
masker = NiftiMapsMasker(maps_img=atlas_filename, standardize=True,
                         memory='nilearn_cache', verbose=5)

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

Out:

[NiftiMapsMasker.fit_transform] loading regions from /home/emdupre/nilearn_data/msdl_atlas/MSDL_rois/msdl_rois.nii
Resampling maps
/home/emdupre/Desktop/open_source/nilearn/nilearn/_utils/cache_mixin.py:296: UserWarning: memory_level is currently set to 0 but a Memory object has been provided. Setting memory_level to 1.
  warnings.warn("memory_level is currently set to 0 but "
[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

8.4.3.3. Compute the sparse inverse covariance

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

estimator = GraphicalLassoCV()
estimator.fit(time_series)

Out:

GraphicalLassoCV(alphas=4, assume_centered=False, cv=None, enet_tol=0.0001,
                 max_iter=100, mode='cd', n_jobs=None, n_refinements=4,
                 tol=0.0001, verbose=False)

8.4.3.4. 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,
                     title='Covariance')
../../_images/sphx_glr_plot_inverse_covariance_connectome_001.png

Out:

<matplotlib.image.AxesImage object at 0x7f87599d5a10>

8.4.3.5. And now display the corresponding graph

coords = atlas.region_coords

plotting.plot_connectome(estimator.covariance_, coords,
                         title='Covariance')
../../_images/sphx_glr_plot_inverse_covariance_connectome_002.png

Out:

<nilearn.plotting.displays.OrthoProjector object at 0x7f87545eec10>

8.4.3.6. 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')
../../_images/sphx_glr_plot_inverse_covariance_connectome_003.png

Out:

<matplotlib.image.AxesImage object at 0x7f87334e5690>

8.4.3.7. And now display the corresponding graph

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

plotting.show()
../../_images/sphx_glr_plot_inverse_covariance_connectome_004.png

8.4.3.8. 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
view