Learning flexible representations of stochastic processes on graphs
This work addresses a domain-specific limitation in graph neural networks for time-varying data on graphs, representing an incremental improvement over existing methods.
The authors tackled the problem of learning representations for stochastic processes on directed or undirected graphs by proposing a class of linear operations for graph convolutional networks, achieving arbitrarily low learning complexity and demonstrating richer modeling behaviors and greater flexibility compared to product graph methods.
Graph convolutional networks adapt the architecture of convolutional neural networks to learn rich representations of data supported on arbitrary graphs by replacing the convolution operations of convolutional neural networks with graph-dependent linear operations. However, these graph-dependent linear operations are developed for scalar functions supported on undirected graphs. We propose a class of linear operations for stochastic (time-varying) processes on directed (or undirected) graphs to be used in graph convolutional networks. We propose a parameterization of such linear operations using functional calculus to achieve arbitrarily low learning complexity. The proposed approach is shown to model richer behaviors and display greater flexibility in learning representations than product graph methods.