Figure 4.

Neuroimaging data. We consider the BOLD time series of $N\sim 30,000$ voxels in an fMRI experiment with $D=202$ scans. Hidalgo detects a low-dimensional manifold ($d=16.2$) and a high-dimensional one ($d=31.9$). We compute the clustering frequency $\mathrm{\Phi }$, which measures the participation of each voxel to coherent activation patterns and is a proxy for voxel involvement in the task³¹. Panel (a) shows the probability distribution of $\mathrm{\Phi }$ in the two manifolds. Strongly activated voxels ($\mathrm{\Phi }>0.2$) are consistently assigned to the high-dimensional manifold. Panel (b) shows the rendering of the cortical surface (left: left hemisphere; right: right hemisphere). Blue voxels have high clustering frequency ($\mathrm{\Phi }>0.2$), red voxels are those assigned to the high-dimensional manifold, and green voxels satisfying both criteria. Almost all voxels with high clustering frequency are assigned to the high-dimensional manifold, and are concentrated in the occipital, temporal, and parietal cortex. Results are obtained with $q=3$ and $\xi =0.8$. The distance between two time series is computed by a Euclidean metric, after standard pre-processing steps³².