  We propose a novel method to embed a functional magnetic resonance imaging
(fMRI) dataset in a low-dimensional space. The embedding optimally preserves
the local functional coupling between fMRI time series and provides a
low-dimensional coordinate system for detecting activated voxels. To compute
the embedding, we build a graph of functionally connected voxels. We use the
commute time, instead of the geodesic distance, to measure functional distances
on the graph. Because the commute time can be computed directly from the
eigenvectors of (a symmetric version) the graph probability transition matrix,
we use these eigenvectors to embed the dataset in low dimensions. After
clustering the datasets in low dimensions, coherent structures emerge that can
be easily interpreted. We performed an extensive evaluation of our method
comparing it to linear and nonlinear techniques using synthetic datasets and in
vivo datasets. We analyzed datasets from the EBC competition obtained with
subjects interacting in an urban virtual reality environment. Our exploratory
approach is able to detect independently visual areas (V1/V2, V5/MT), auditory
areas, and language areas. Our method can be used to analyze fMRI collected
during ``natural stimuli''.
