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June 2023 LOCUS: A regularized blind source separation method with low-rank structure for investigating brain connectivity
Yikai Wang, Ying Guo
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Ann. Appl. Stat. 17(2): 1307-1332 (June 2023). DOI: 10.1214/22-AOAS1670


Network-oriented research has been increasingly popular in many scientific areas. In neuroscience research, imaging-based network connectivity measures have become the key for understanding brain organizations, potentially serving as individual neural fingerprints. There are major challenges in analyzing connectivity matrices, including the high dimensionality of brain networks, unknown latent sources underlying the observed connectivity, and the large number of brain connections leading to spurious findings. In this paper we propose a novel blind source separation method with low-rank structure and uniform sparsity (LOCUS) as a fully data-driven decomposition method for network measures. Compared with the existing method that vectorizes connectivity matrices ignoring brain network topology, LOCUS achieves more efficient and accurate source separation for connectivity matrices using low-rank structure. We propose a novel angle-based uniform sparsity regularization that demonstrates better performance than the existing sparsity controls for low-rank tensor methods. We propose a highly efficient iterative node-rotation algorithm that exploits the block multiconvexity of the objective function to solve the nonconvex optimization problem for learning LOCUS. We illustrate the advantage of LOCUS through extensive simulation studies. Application of LOCUS to Philadelphia Neurodevelopmental Cohort neuroimaging study reveals biologically insightful connectivity traits which are not found using the existing method.

Funding Statement

Research reported in this publication was supported by the National Institute of Mental Health of the National Institutes of Health under Award Number R01MH105561 and R01MH118771. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health or Philadelphia Neurodevelopmental Cohort: Support for the collection of the data sets was provided by grant RC2MH089983 awarded to Raquel Gur and RC2MH089924 awarded to Hakon Hakorson. All subjects were recruited through the Center for Applied Genomics at The Children’s Hospital in Philadelphia.


The authors would like to thank the anonymous referees, an Associate Editor, and the Editor for their constructive comments that improved the quality of this paper.


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Yikai Wang. Ying Guo. "LOCUS: A regularized blind source separation method with low-rank structure for investigating brain connectivity." Ann. Appl. Stat. 17 (2) 1307 - 1332, June 2023.


Received: 1 October 2021; Revised: 1 May 2022; Published: June 2023
First available in Project Euclid: 1 May 2023

MathSciNet: MR4582714
zbMATH: 07692384
Digital Object Identifier: 10.1214/22-AOAS1670

Keywords: blind source separation , low rank , matrix factorization , network connectivity , neuroimaging

Rights: Copyright © 2023 Institute of Mathematical Statistics

Vol.17 • No. 2 • June 2023
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