Computational Fingerprints: Modeling Interactions Between Brain Regions as Points in a Function Space

Abstract

In this paper we propose a novel technique to investigate the nonlinear interactions between brain regions that captures both the strength and the type of the functional relationship. Inspired by the field of functional analysis, we propose that the relationship between activity in two different brain areas can be viewed as a point in function space, identified by coordinates along an infinite set of basis functions. Using Hermite Polynomials as basis functions, we estimate from fMRI data a truncated set of coordinates that serve as a "computational fingerprint," characterizing the interaction between two brain areas. We provide a proof of the convergence of the estimates in the limit, and we validate the method with simulations in which the ground truth is known, additionally showing that computational fingerprints detect statistical dependence also when correlations ("functional connectivity") is near zero. We then use computational fingerprints to examine the neural interactions with a seed region of choice: the Fusiform Face Area (FFA). Using k-means clustering across each voxel's computational fingerprint, we illustrate that the addition of the nonlinear basis functions allows for the discrimination of inter-regional interactions that are otherwise grouped together when only linear dependence is used. Finally, we show that regions in V5 and medial occipital and temporal lobes exhibit significant nonlinear interactions with the FFA.