Dynamic Graph Learning: A Structure-Driven Approach

Bo Jiang, Yuming Huang, Ashkan Panahi, Yiyi Yu, Hamid Krim and Spencer L. Smith
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Bo Jiang: Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695, USA
Yuming Huang: Department of Physics, North Carolina State University, Raleigh, NC 27695, USA
Ashkan Panahi: Department of Computer Science and Engineering, Chalmers University of Technology, SE-412 96 Göteborg, Sweden
Yiyi Yu: Department of Electrical and Computer Engineering, University of California Santa Barbara, Santa Barbara, CA 93106, USA
Hamid Krim: Department of Electrical and Computer Engineering, North Carolina State University, Raleigh, NC 27695, USA
Spencer L. Smith: Department of Electrical and Computer Engineering, University of California Santa Barbara, Santa Barbara, CA 93106, USA

Mathematics, 2021, vol. 9, issue 2, 1-20

Abstract: The purpose of this paper is to infer a dynamic graph as a global (collective) model of time-varying measurements at a set of network nodes. This model captures both pairwise as well as higher order interactions (i.e., more than two nodes) among the nodes. The motivation of this work lies in the search for a connectome model which properly captures brain functionality across all regions of the brain, and possibly at individual neurons. We formulate it as an optimization problem, a quadratic objective functional and tensor information of observed node signals over short time intervals. The proper regularization constraints reflect the graph smoothness and other dynamics involving the underlying graph’s Laplacian, as well as the time evolution smoothness of the underlying graph. The resulting joint optimization is solved by a continuous relaxation of the weight parameters and an introduced novel gradient-projection scheme. While the work may be applicable to any time-evolving data set (e.g., fMRI), we apply our algorithm to a real-world dataset comprising recorded activities of individual brain cells. The resulting model is shown to be not only viable but also efficiently computable.

Keywords: dynamic graph learning; graph signal processing; sparse signal; convex optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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