Forecasting Multi-Dimensional Processes Over Graphs
Alberto Natali (TU Delft - Signal Processing Systems)
Elvin Isufi (TU Delft - Multimedia Computing)
Geert Leus (TU Delft - Signal Processing Systems)
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Abstract
The forecasting of multi-variate time processes through graph-based techniques has recently been addressed under the graph signal processing framework. However, problems in the representation and the processing arise when each time series carries a vector of quantities rather than a scalar one. To tackle this issue, we devise a new framework and propose new methodologies based on the graph vector autoregressive model. More explicitly, we leverage product graphs to model the high-dimensional graph data and develop multidimensional graph-based vector autoregressive models to forecast future trends with a number of parameters that is independent of the number of time series and a linear computational complexity. Numerical results demonstrating the prediction of moving point clouds corroborate our findings.