Predicting the evolution of stationary graph signals
This work addresses the challenge of dimensionality in modeling multivariate processes for applications like sensor networks or social media analysis, though it is incremental as it builds on existing joint stationarity frameworks.
The paper tackles the problem of predicting time-evolving multivariate processes on graphs by introducing a method based on joint stationarity, achieving similar accuracy to the joint mean-squared error estimator with lower complexity and outperforming purely time-based methods.
An emerging way of tackling the dimensionality issues arising in the modeling of a multivariate process is to assume that the inherent data structure can be captured by a graph. Nevertheless, though state-of-the-art graph-based methods have been successful for many learning tasks, they do not consider time-evolving signals and thus are not suitable for prediction. Based on the recently introduced joint stationarity framework for time-vertex processes, this letter considers multivariate models that exploit the graph topology so as to facilitate the prediction. The resulting method yields similar accuracy to the joint (time-graph) mean-squared error estimator but at lower complexity, and outperforms purely time-based methods.