Online Time-Varying Topology Identification via Prediction-Correction Algorithms
This addresses the problem of dynamic graph learning for signal processing and machine learning applications where topology is unknown and time-varying, but it appears incremental as it builds on existing time-varying optimization results.
The paper tackles the problem of identifying time-varying graph topologies from data, which is challenging due to ill-posedness and non-stationarity, by developing an online algorithm based on time-varying optimization that intrinsically regularizes the topology without explicit enforcement. As a case-study applied to Gaussian graphical models, the method's performance is corroborated, though no concrete numbers are provided in the abstract.
Signal processing and machine learning algorithms for data supported over graphs, require the knowledge of the graph topology. Unless this information is given by the physics of the problem (e.g., water supply networks, power grids), the topology has to be learned from data. Topology identification is a challenging task, as the problem is often ill-posed, and becomes even harder when the graph structure is time-varying. In this paper, we address the problem of dynamic topology identification by building on recent results from time-varying optimization, devising a general-purpose online algorithm operating in non-stationary environments. Because of its iteration-constrained nature, the proposed approach exhibits an intrinsic temporal-regularization of the graph topology without explicitly enforcing it. As a case-study, we specialize our method to the Gaussian graphical model (GGM) problem and corroborate its performance.