17 research outputs found
Bayesian topology learning and noise removal from network data
Learning the topology of a graph from available data is of great interest in many emerging applications. Some examples are social networks, internet of things networks (intelligent IoT and industrial IoT), biological connection networks, sensor networks and traffic network patterns. In this paper, a graph topology inference approach is proposed to learn the underlying graph structure from a given set of noisy multi-variate observations, which are modeled as graph signals generated from a Gaussian Markov Random Field (GMRF) process. A factor analysis model is applied to represent the graph signals in a latent space where the basis is related to the underlying graph structure. An optimal graph filter is also developed to recover the graph signals from noisy observations. In the final step, an optimization problem is proposed to learn the underlying graph topology from the recovered signals. Moreover, a fast algorithm employing the proximal point method has been proposed to solve the problem efficiently. Experimental results employing both synthetic and real data show the effectiveness of the proposed method in recovering the signals and inferring the underlying graph
State-Space Network Topology Identification from Partial Observations
In this work, we explore the state-space formulation of a network process to
recover, from partial observations, the underlying network topology that drives
its dynamics. To do so, we employ subspace techniques borrowed from system
identification literature and extend them to the network topology
identification problem. This approach provides a unified view of the
traditional network control theory and signal processing on graphs. In
addition, it provides theoretical guarantees for the recovery of the
topological structure of a deterministic continuous-time linear dynamical
system from input-output observations even though the input and state
interaction networks might be different. The derived mathematical analysis is
accompanied by an algorithm for identifying, from data, a network topology
consistent with the dynamics of the system and conforms to the prior
information about the underlying structure. The proposed algorithm relies on
alternating projections and is provably convergent. Numerical results
corroborate the theoretical findings and the applicability of the proposed
algorithm.Comment: 13 pages, 3 appendix page