# GRAND: Unbiased Connectome Atlas of Brain Network by Groupwise Graph Shrinkage and Network Diffusion

## Abstract

Network science is enhancing our understanding of how the human brain works at a systems level. A complete population-wise mapping of region-to-region connections, called *connectome atlas*, is the key to gaining a more full understanding for network-related brain disorders and for discovering biomarkers for early diagnosis. Since a brain network is commonly encoded in an adjacency matrix, it is difficult to apply the state-of-the-art atlas construction approaches by normalizing and averaging the individual adjacency matrices into a common space. In this paper, we propose a novel data-driven approach to construct an unbiased *connectome atlas* to capture both shared and complementary network topologies across individual brain networks, offering insight into the full spectrum of brain connectivity. Specifically, we employ a hypergraph to model the manifold of a population of brain networks. In this hypergraph, each node represents the individual participant’s brain network, and the edge weight captures the distance between two participants’ brain networks. The construction of a *connectome atlas* can be achieved using a hierarchical process of graph shrinkage toward the latent common space where the network topologies of all individual brain networks gradually become similar to each other. During the graph shrinkage, the adjacency matrix of each brain network is transformed to the common space by a series of diffusion matrices which exchange the connectome information with respect to the adjacency matrices on the neighboring hypergraph nodes such that the most representative characteristics of network topology are eventually propagated to the final *connectome atlas*. We have validated our *connectome atlas* construction method on the simulated brain network data and DTI data of 111 twin pairs in determining the genetic contribution of the structural connectivity.

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