Learning Graph ARMA Processes from Time-Vertex Spectra
This work addresses signal interpolation for time-varying graph data, which is incremental as it builds on existing graph ARMA process modeling.
The authors tackled the problem of inferring missing values in time-varying graph signals by modeling them as stationary time-vertex stochastic processes, proposing an algorithm that learns graph ARMA processes from incomplete realizations and achieves high accuracy in signal interpolation.
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.