Forecasting Graph Signals with Recursive MIMO Graph Filters
This work addresses forecasting of vector-valued time series on graphs, which is important for applications like sensor networks or social media analysis, but it appears incremental as it extends existing models.
The paper tackles the problem of forecasting multidimensional time series on graphs by proposing a recursive multiple-input multiple-output graph filter, which addresses limitations of existing product graph approaches and offers greater flexibility. Numerical simulations on real-world data demonstrate the effectiveness of the proposed models.
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.