Graphs are pervasive in different fields unveiling complex relationships between data. Two major graph-based learning tasks are topology identification and inference of signals over graphs. Among the possible models to explain data interdependencies, structural equation models (SEMs) accommodate a gamut of applications involving topology identification. Obtaining conventional SEMs though requires measurements across nodes. On the other hand, typical signal inference approaches 'blindly trust' a given nominal topology. In practice however, signal or topology perturbations may be present in both tasks, due to model mismatch, outliers, outages or adversarial behavior. To cope with such perturbations, this work introduces a regularized total least-squares (TLS) approach and iterative algorithms with convergence guarantees to solve both tasks. Further generalizations are also considered relying on structured and/or weighted TLS when extra prior information on the perturbation is available. Analyses with simulated and real data corroborate the effectiveness of the novel TLS-based approaches.
Bibliographical noteFunding Information:
Manuscript received June 28, 2019; revised January 31, 2020 and March 13, 2020; accepted March 13, 2020. Date of publication March 23, 2020; date of current version May 22, 2020. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Pierre Borgnat. This work was supported in part by the NSF under Grants 1711471 and 1500713, in part by the NIH under Grant 1R01GM104975-01, and in part by the H2020 EUJ Project 5G-MiEdge under Grant 723171. This article was presented in part at the . (Corresponding author: Elena Ceci.) Elena Ceci and Sergio Barbarossa are with the Department of Information Engineering, Electronics and Telecommunications, Sapienza University of Rome, Rome 00184, Italy (e-mail: email@example.com; sergio.barbarossa@ uniroma1.it).
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- Graph and signal perturbations
- graph signal reconstruction
- structural equation models
- topology identification
- total least-squares