Forecasting Multi-Dimensional Processes over Graphs
This addresses a representation and processing bottleneck in graph-based forecasting for multi-variate time series with vector data, which is incremental as it builds on existing graph signal processing methods.
The paper tackled the problem of forecasting multi-dimensional processes over graphs, where each node has a vector of quantities, by proposing a new framework based on graph vector autoregressive models with product graphs, achieving a linear computational complexity and parameter count independent of the number of time series.
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 multi-dimensional 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.