Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecasting

TL;DR

This paper introduces Z-GCNETs, a novel deep learning architecture that incorporates time-conditioned topological features via zigzag persistence into graph convolutional networks, improving time series forecasting accuracy.

Contribution

It develops a new topological summary called zigzag persistence image and integrates it into GCNs, providing theoretical stability guarantees and demonstrating superior performance.

Findings

Outperforms 13 state-of-the-art methods on 4 datasets

Effectively captures topological features over time

Enhances robustness and accuracy of time series forecasting

Abstract

There recently has been a surge of interest in developing a new class of deep learning (DL) architectures that integrate an explicit time dimension as a fundamental building block of learning and representation mechanisms. In turn, many recent results show that topological descriptors of the observed data, encoding information on the shape of the dataset in a topological space at different scales, that is, persistent homology of the data, may contain important complementary information, improving both performance and robustness of DL. As convergence of these two emerging ideas, we propose to enhance DL architectures with the most salient time-conditioned topological information of the data and introduce the concept of zigzag persistence into time-aware graph convolutional networks (GCNs). Zigzag persistence provides a systematic and mathematically rigorous framework to track the most important topological features of the observed data that tend to manifest themselves over time. To integrate the extracted time-conditioned topological descriptors into DL, we develop a new topological summary, zigzag persistence image, and derive its theoretical stability guarantees. We validate the new GCNs with a time-aware zigzag topological layer (Z-GCNETs), in application to traffic forecasting and Ethereum blockchain price prediction. Our results indicate that Z-GCNET outperforms 13 state-of-the-art methods on 4 time series datasets.