Description

Abstract: Multivariate time series over networks are commonly present in infrastructure (water, power, transport) networks, financial markets, and biological networks. Devising and analyzing learning models for these data is of importance for tasks such as forecasting, anomaly detection as well as classification, and data reconstruction. These models however have to cope with the challenge of extracting patterns in a spatiotemporal manner to capture the intrinsic hidden dependencies in the data. Following advances in graph signal processing and graph machine learning, this talk will provide a principled approach to learning representations from multivariate time series over networks. In particular, it will follow the principle of convolution to put provide a mathematically tractable graph-time convolutional network that highlights the role of spatiotemporal dependence. Following the duality in the graph spectral domain, I will also discuss the spectral response of these solutions as well as their ability to cope with uncertainties in the graph domain. Finally, I will touch upon some recent research on building model-based learning solutions for multivariate time series on networks that combine specific signal processing models with data-driven solutions to take the benefits of both worlds. Some numerical results with traffic and water networks will be used to illustrate the potential of this approach.