Forecasting Graph Signals with Recursive MIMO Graph Filters

TL;DR

This paper introduces a recursive MIMO graph filter for forecasting graph signals, effectively handling multidimensional data without enlarging the graph, and demonstrates its superior performance through real-world simulations.

Contribution

It proposes a flexible recursive MIMO graph filter that generalizes existing models and overcomes limitations of product graph approaches for multidimensional graph signal forecasting.

Findings

Effective on real-world data set

Outperforms existing models

Flexible and generalizable approach

Abstract

Forecasting time series on graphs is a fundamental problem in graph signal processing. When each entity of the network carries a vector of values for each time stamp instead of a scalar one, existing approaches resort to the use of product graphs to combine this multidimensional information, at the expense of creating a larger graph. In this paper, we show the limitations of such approaches, and propose extensions to tackle them. Then, we propose a recursive multiple-input multiple-output graph filter which encompasses many already existing models in the literature while being more flexible. Numerical simulations on a real world data set show the effectiveness of the proposed models.