Learning Graph ARMA Processes from Time-Vertex Spectra

TL;DR

This paper introduces a novel algorithm for learning graph ARMA processes from incomplete data by estimating and refining the joint time-vertex spectrum, enabling accurate signal interpolation on dynamic graph signals.

Contribution

It presents a new method to learn graph ARMA models from partial observations by spectral estimation and convex relaxation, improving time-vertex signal interpolation.

Findings

High accuracy in signal estimation demonstrated

Effective handling of incomplete data in dynamic graphs

Spectral-based approach outperforms existing methods

Abstract

The modeling of time-varying graph signals as stationary time-vertex stochastic processes permits the inference of missing signal values by efficiently employing the correlation patterns of the process across different graph nodes and time instants. In this study, we propose an algorithm for computing graph autoregressive moving average (graph ARMA) processes based on learning the joint time-vertex power spectral density of the process from its incomplete realizations for the task of signal interpolation. Our solution relies on first roughly estimating the joint spectrum of the process from partially observed realizations and then refining this estimate by projecting it onto the spectrum manifold of the graph ARMA process through convex relaxations. The initially missing signal values are then estimated based on the learnt model. Experimental results show that the proposed approach achieves high accuracy in time-vertex signal estimation problems.