Information Storage as a Proxy for Persistent Homology of Human Connectome

Persistent homology allows one to measure the structural complexity of a network, which has been interpreted as a proxy for the amount of active memory, yet it is rarely used because of high computational demands. This paper shows that active information storage (AIS) is strongly associated with persistence diagram-based topological complexity while being far cheaper to compute. We evaluate both quantities on the human connectome of 137 subjects across five cognitive tasks and two resting-state conditions from the WU-Minn HCP dataset. Averaged over subjects, the association between the mean AIS and the persistence diagram distance to the resting-state anchor is high for all four persistence diagram distances considered, with Pearson coefficients between 0.74 and 0.80 and Spearman coefficients between 0.85 and 0.90; all four rank associations are significant at the group level and remain so after Holm–Bonferroni correction across the four distances. On a single consumer-grade workstation, persistence diagrams become intractable beyond a few hundred nodes, whereas AIS is evaluated for n = 15,000 in approximately one minute. We also state explicitly the conditions under which the two quantities are expected to agree and the caveats—anchor choice, hemodynamic autocorrelation and the limited number of experimental conditions—that qualify the interpretation of AIS as a measure of active memory.