Graph-based Learning under Perturbations via Total Least-Squares release_6tda27vy5ra5fa6xxmni2goi5m

by Elena Ceci, Yanning Shen, Georgios B. Giannakis, Sergio Barbarossa

Published in IEEE Transactions on Signal Processing by Institute of Electrical and Electronics Engineers (IEEE).

2020   Volume 68, p1-1

Abstract

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.
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Date   2020-03-23
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