.. only:: html
.. note::
:class: sphx-glr-download-link-note
Click :ref:`here <sphx_glr_download_auto_examples_03_connectivity_plot_simulated_connectome.py>` to download the full example code or to run this example in your browser via Binder
.. rst-class:: sphx-glr-example-title
.. _sphx_glr_auto_examples_03_connectivity_plot_simulated_connectome.py:
Connectivity structure estimation on simulated data
===================================================
This example shows a comparison of graph lasso and group-sparse covariance
estimation of connectivity structre for a synthetic dataset.
.. image:: /auto_examples/03_connectivity/images/sphx_glr_plot_simulated_connectome_001.png
:alt: ground truth, group-sparse $\alpha=0.04$, graph lasso, graph lasso, all subjects $\alpha=0.03$
:class: sphx-glr-single-img
.. rst-class:: sphx-glr-script-out
Out:
.. code-block:: none
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.7s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement 1 out of 4
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.6s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement 2 out of 4
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.7s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement 3 out of 4
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.6s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement 4 out of 4
[GroupSparseCovarianceCV.fit] Final optimization
/home/nicolas/GitRepos/nilearn-fork/nilearn/connectome/group_sparse_cov.py:245: UserWarning: input signals do not all have unit variance. This can lead to numerical instability.
warnings.warn("input signals do not all have unit variance. This "
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s 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 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 2 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 3 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 4 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s 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 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 2 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 3 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 4 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s 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 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 2 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 3 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 4 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s 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 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 2 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 3 out of 4: 0s
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.1s finished
[GraphicalLassoCV] Done refinement 4 out of 4: 0s
|
.. code-block:: default
import matplotlib.pyplot as plt
# Generate synthetic data
from nilearn._utils.data_gen import generate_group_sparse_gaussian_graphs
from nilearn.plotting import show
n_subjects = 20 # number of subjects
n_displayed = 3 # number of subjects displayed
subjects, precisions, topology = generate_group_sparse_gaussian_graphs(
n_subjects=n_subjects, n_features=10, min_n_samples=30, max_n_samples=50,
density=0.1)
from nilearn import plotting
fig = plt.figure(figsize=(10, 7))
plt.subplots_adjust(hspace=0.4)
for n in range(n_displayed):
ax = plt.subplot(n_displayed, 4, 4 * n + 1)
max_precision = precisions[n].max()
plotting.plot_matrix(precisions[n], vmin=-max_precision,
vmax=max_precision, axes=ax, colorbar=False)
if n == 0:
plt.title("ground truth")
plt.ylabel("subject %d" % n)
# Run group-sparse covariance on all subjects
from nilearn.connectome import GroupSparseCovarianceCV
gsc = GroupSparseCovarianceCV(max_iter=50, verbose=1)
gsc.fit(subjects)
for n in range(n_displayed):
ax = plt.subplot(n_displayed, 4, 4 * n + 2)
max_precision = gsc.precisions_[..., n].max()
plotting.plot_matrix(gsc.precisions_[..., n], axes=ax, vmin=-max_precision,
vmax=max_precision, colorbar=False)
if n == 0:
plt.title("group-sparse\n$\\alpha=%.2f$" % gsc.alpha_)
# Fit one graph lasso per subject
try:
from sklearn.covariance import GraphicalLassoCV
except ImportError:
# for Scitkit-Learn < v0.20.0
from sklearn.covariance import GraphLassoCV as GraphicalLassoCV
gl = GraphicalLassoCV(verbose=1)
for n, subject in enumerate(subjects[:n_displayed]):
gl.fit(subject)
ax = plt.subplot(n_displayed, 4, 4 * n + 3)
max_precision = gl.precision_.max()
plotting.plot_matrix(gl.precision_, axes=ax, vmin=-max_precision,
vmax=max_precision, colorbar=False)
if n == 0:
plt.title("graph lasso")
plt.ylabel("$\\alpha=%.2f$" % gl.alpha_)
# Fit one graph lasso for all subjects at once
import numpy as np
gl.fit(np.concatenate(subjects))
ax = plt.subplot(n_displayed, 4, 4)
max_precision = gl.precision_.max()
plotting.plot_matrix(gl.precision_, axes=ax, vmin=-max_precision,
vmax=max_precision, colorbar=False)
plt.title("graph lasso, all subjects\n$\\alpha=%.2f$" % gl.alpha_)
show()
.. rst-class:: sphx-glr-timing
**Total running time of the script:** ( 0 minutes 4.458 seconds)
.. _sphx_glr_download_auto_examples_03_connectivity_plot_simulated_connectome.py:
.. only :: html
.. container:: sphx-glr-footer
:class: sphx-glr-footer-example
.. container:: binder-badge
.. image:: images/binder_badge_logo.svg
:target: https://mybinder.org/v2/gh/nilearn/nilearn.github.io/main?filepath=examples/auto_examples/03_connectivity/plot_simulated_connectome.ipynb
:alt: Launch binder
:width: 150 px
.. container:: sphx-glr-download sphx-glr-download-python
:download:`Download Python source code: plot_simulated_connectome.py <plot_simulated_connectome.py>`
.. container:: sphx-glr-download sphx-glr-download-jupyter
:download:`Download Jupyter notebook: plot_simulated_connectome.ipynb <plot_simulated_connectome.ipynb>`
.. only:: html
.. rst-class:: sphx-glr-signature
`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_