Forecasting Models for Graph Processes

Abstract

In the current Big Data era, large amounts of data are collected from complex systems, such as sensor networks and social networks. The emerging field of graph signal processing (GSP) leverages a network structure (graph) to process signals on an irregular domain. This thesis studies the forecasting of multi-dimensional graph processes, i.e., where each entity in the network carries a multivariate time series. Recent research has proposed to use product graphs to model the dependencies between different variables in multi-dimensional graph processes and employ them in graph-based vector autoregressive models to predict future values. A problem with these product graph-based models is that they can be too restrictive. In this work, it is proposed to combine product graph-based models with multiple one-dimensional models to implement more estimation flexibility. To further increase the degrees of freedom, the use of multiple-input-multiple-output graph filters is also proposed. The proposed models are implemented and tested on synthetic and real-world data sets, which shows an improved forecasting performance compared to state-of-the-art alternatives.