Graph-Time Convolutional Neural Networks

TL;DR

This paper introduces a novel graph-time convolutional neural network (GTCNN) that leverages product graphs to effectively learn from spatiotemporal data, capturing complex relationships through a principled convolutional approach.

Contribution

The paper proposes the first graph-time convolutional neural network using product graphs, with learnable spatiotemporal coupling and a zero-pad pooling method for efficient representation.

Findings

GTCNN outperforms baseline models on synthetic and real datasets.

The product graph approach effectively captures spatiotemporal dependencies.

Zero-pad pooling preserves spatial structure while reducing complexity.

Abstract

Spatiotemporal data can be represented as a process over a graph, which captures their spatial relationships either explicitly or implicitly. How to leverage such a structure for learning representations is one of the key challenges when working with graphs. In this paper, we represent the spatiotemporal relationships through product graphs and develop a first principle graph-time convolutional neural network (GTCNN). The GTCNN is a compositional architecture with each layer comprising a graph-time convolutional module, a graph-time pooling module, and a nonlinearity. We develop a graph-time convolutional filter by following the shift-and-sum principles of the convolutional operator to learn higher-level features over the product graph. The product graph itself is parametric so that we can learn also the spatiotemporal coupling from data. We develop a zero-pad pooling that preserves the spatial graph (the prior about the data) while reducing the number of active nodes and the parameters. Experimental results with synthetic and real data corroborate the different components and compare with baseline and state-of-the-art solutions.