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March 2019 Common and individual structure of brain networks
Lu Wang, Zhengwu Zhang, David Dunson
Ann. Appl. Stat. 13(1): 85-112 (March 2019). DOI: 10.1214/18-AOAS1193


This article focuses on the problem of studying shared- and individual-specific structure in replicated networks or graph-valued data. In particular, the observed data consist of $n$ graphs, $G_{i},i=1,\ldots,n$, with each graph consisting of a collection of edges between $V$ nodes. In brain connectomics, the graph for an individual corresponds to a set of interconnections among brain regions. Such data can be organized as a $V\times V$ binary adjacency matrix $A_{i}$ for each $i$, with ones indicating an edge between a pair of nodes and zeros indicating no edge. When nodes have a shared meaning across replicates $i=1,\ldots,n$, it becomes of substantial interest to study similarities and differences in the adjacency matrices. To address this problem, we propose a method to estimate a common structure and low-dimensional individual-specific deviations from replicated networks. The proposed Multiple GRAph Factorization (M-GRAF) model relies on a logistic regression mapping combined with a hierarchical eigenvalue decomposition. We develop an efficient algorithm for estimation and study basic properties of our approach. Simulation studies show excellent operating characteristics and we apply the method to human brain connectomics data.


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Lu Wang. Zhengwu Zhang. David Dunson. "Common and individual structure of brain networks." Ann. Appl. Stat. 13 (1) 85 - 112, March 2019.


Received: 1 July 2017; Revised: 1 April 2018; Published: March 2019
First available in Project Euclid: 10 April 2019

zbMATH: 07057421
MathSciNet: MR3937422
Digital Object Identifier: 10.1214/18-AOAS1193

Keywords: Binary networks , multiple graphs , penalized logistic regression , random effects , spectral embedding

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.13 • No. 1 • March 2019
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