Learning flexible representations of stochastic processes on graphs

TL;DR

This paper introduces a new class of linear operations for stochastic processes on graphs, enabling more flexible and expressive graph convolutional networks for time-varying data.

Contribution

It proposes a novel parameterization of linear operations using functional calculus for stochastic processes on directed and undirected graphs, enhancing modeling flexibility.

Findings

Models richer behaviors than existing methods.

Displays greater flexibility in learning representations.

Achieves low learning complexity.

Abstract

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.