Low Dimensional Embedding of fMRI datasets

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 network of functionally connected voxels and represent it with a graph. A spectral decomposition of the graph probability transition matrix produces a set of eigenvectors that are used to define the embedding. After embedding the dataset in low dimensions, coherent structures emerge that can be interpreted as task-related hemodynamic responses, and non-task-related physiological artifacts. We performed an extensive evaluation of our method comparing it to linear and nonlinear techniques using synthetic datasets and {\em in vivo} datasets.