Fig. 1:

Functional connectivity matrices and their underlying geometry. (A) Similarity of functional connectivity (FC) matrices. Is the FC matrix X more similar to A or B? This question arises when the goal is to determine the task being being performed, the mental state, or the participant. (B) Illustration of geodesic distance (red) and Euclidean distance (green) on the so-called positive semidefinite cone. The geodesic and Euclidean distances between two points can differ substantially. (C) Is X, Alice or Bob? Equivalently, is the FC X more similar to that of Alice or Bob? Identification involves mapping an unknown participant’s data to one of the participants in the database (only two in this case). In this example, X is correctly labeled as Alice using geodesic distance, but incorrectly labeled as Bob using Pearson dissimilarity.