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Connectivity structure estimation on simulated data¶
This example shows a comparison of graph lasso and group-sparse covariance estimation of connectivity structure for a synthetic dataset.
from nilearn import plotting
Generate synthetic data
from nilearn._utils.data_gen import generate_group_sparse_gaussian_graphs
n_subjects = 20
n_displayed = 3
subjects, precisions, _ = generate_group_sparse_gaussian_graphs(
n_subjects=n_subjects,
n_features=10,
min_n_samples=30,
max_n_samples=50,
density=0.1,
)
Run connectome estimations and plot the results
import matplotlib.pyplot as plt
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(f"subject {int(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(f"group-sparse\n$\\alpha={gsc.alpha_:.2f}$")
# Fit one graph lasso per subject
from sklearn.covariance import 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(f"$\\alpha={gl.alpha_:.2f}$")
# 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(f"graph lasso, all subjects\n$\\alpha={gl.alpha_:.2f}$")
plotting.show()
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.5s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement 0 out
of 4
[Parallel(n_jobs=1)]: Using backend SequentialBackend with 1 concurrent workers.
[Parallel(n_jobs=1)]: Done 5 out of 5 | elapsed: 0.5s 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: 0.5s 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: 0.5s finished
[GroupSparseCovarianceCV.fit] [GroupSparseCovarianceCV] Done refinement 3 out
of 4
[GroupSparseCovarianceCV.fit] Final optimization
/home/runner/work/nilearn/nilearn/.tox/doc/lib/python3.9/site-packages/nilearn/connectome/group_sparse_cov.py:268: UserWarning:
input signals do not all have unit variance. This can lead to numerical instability.
[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: 0.0s 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: 0.0s finished
[GraphicalLassoCV] Done refinement 4 out of 4: 0s
Total running time of the script: (0 minutes 4.113 seconds)
Estimated memory usage: 147 MB