Fig. 1. A typical gradient identification workflow.

Starting from an input matrix (here, functional connectivity), we use a kernel function to build the affinity matrix (here capturing the connectivity of each seed region). This matrix is decomposed, often via linear rotations or non-linear manifold learning techniques into a set of principal eigenvectors describing axes of largest variance. The scores of each seed onto the first two axes are shown in the scatter plot, with colors denoting position in this 2D space. These colors may be projected back to the cortical surface and the scores can be used to sort the input connectome.