Signal and graph perturbations via total least-squares

Graphs are pervasive in various applications capturing the complex behavior observed in biological, financial, and social networks, to name a few. Two major learning tasks over graphs are topology identification and inference of signals evolving over graphs. Existing approaches typically aim at identifying the topology when signals on all nodes are observed, or, recovering graph signals over networks with known topologies. In practice however, signal or graph perturbations can be present in both tasks, due to model mismatch, outliers, outages or adversaries. To cope with these perturbations, this work introduces regularized total least-squares (TLS) based approaches and corresponding alternating minimization algorithms with convergence guarantees. Tests on simulated data corroborate the effectiveness of the novel TLS-based approaches.