Topology-Aware Joint Graph Filter and Edge Weight Identification for Network Processes

TL;DR

This paper introduces an iterative method for jointly identifying graph filter coefficients and edge weights in network data, ensuring convergence and improving modeling accuracy in scenarios with known network support.

Contribution

It proposes a novel iterative approach for simultaneous graph filter and edge weight identification, guaranteeing convergence and leveraging known network support.

Findings

Method guarantees non-increasing cost at each iteration

Numerical experiments validate the approach's effectiveness

Applicable to networks with known connectivity but unknown weights

Abstract

Data defined over a network have been successfully modelled by means of graph filters. However, although in many scenarios the connectivity of the network is known, e.g., smart grids, social networks, etc., the lack of well-defined interaction weights hinders the ability to model the observed networked data using graph filters. Therefore, in this paper, we focus on the joint identification of coefficients and graph weights defining the graph filter that best models the observed input/output network data. While these two problems have been mostly addressed separately, we here propose an iterative method that exploits the knowledge of the support of the graph for the joint identification of graph filter coefficients and edge weights. We further show that our iterative scheme guarantees a non-increasing cost at every iteration, ensuring a globally-convergent behavior. Numerical experiments confirm the applicability of our proposed approach.