Going beyond linear dependencies to unveil connectivity of meshed grids

Liang Zhang, Gang Wang, Georgios B Giannakis

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

Partial correlations (PCs) are well suited for revealing linearly dependent (un)mediated connections in a graph when measurements (e.g., time courses) are available per node. Unfortunately, PC-based approaches to identifying the topology of a graph are less effective if nonlinear dependencies between given nodal measurements are present. To bypass this hurdle, nonlinear PCs relying on the ℓ2-norm regularized multi-kernel ridge regression (MKRR) have been recently proposed for brain network connectivity analysis. However, ℓ2-norm regularization limits the flexibility in combining kernels, which can compromise performance. For this reason, the present paper broadens the nonlinear PC approach to account for general ℓp-norm regularized MKRR, in which the user-selected parameter p ≥ 1 is attuned to the problem at hand. Aiming at a scalable algorithm, the Frank-Wolfe iterations are invoked to solve the ℓp-norm based MKRR, which not only features simple closed-form updates, but it is also fast convergent. The end result is a novel scheme that leverages nonlinear dependencies captured by the generalized PC model to identify the topology of not only radial but also meshed autonomous energy grids. Improved performance is achieved at affordable computational complexity relative to existing alternatives. Simulated tests showcase the merits of the proposed schemes.

Original languageEnglish (US)
Title of host publication2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1-5
Number of pages5
ISBN (Electronic)9781538612514
DOIs
StatePublished - Mar 9 2018
Event7th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017 - Curacao
Duration: Dec 10 2017Dec 13 2017

Publication series

Name2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017
Volume2017-December

Conference

Conference7th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017
CityCuracao
Period12/10/1712/13/17

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    Zhang, L., Wang, G., & Giannakis, G. B. (2018). Going beyond linear dependencies to unveil connectivity of meshed grids. In 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017 (pp. 1-5). (2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2017; Vol. 2017-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CAMSAP.2017.8313078