Time-Conditioned Dances with Simplicial Complexes: Zigzag Filtration Curve based Supra-Hodge Convolution Networks for Time-series Forecasting

Yuzhou Chen, Yulia R. Gel, H. Vincent Poor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

Graph neural networks (GNNs) offer a new powerful alternative for multivariate time series forecasting, demonstrating remarkable success in a variety of spatio-temporal applications, from urban flow monitoring systems to health care informatics to financial analytics. Yet, such GNN models pre-dominantly capture only lower order interactions, that is, pairwise relations among nodes, and also largely ignore intrinsic time-conditioned information on the underlying topology of multivariate time series. To address these limitations, we propose a new time-aware GNN architecture which amplifies the power of the recently emerged simplicial neural networks with a time-conditioned topological knowledge representation in a form of zigzag persistence. That is, our new approach, Zigzag Filtration Curve based Supra-Hodge Convolution Networks (ZFC-SHCN) is built upon the two main components: (i) a new highly computationally efficient zigzag persistence curve which allows us to systematically encode time-conditioned topological information, and (ii) a new temporal multiplex graph representation module for learning higher-order network interactions. We discuss theoretical properties of the proposed time-conditioned topological knowledge representation and extensively validate the new time-aware ZFC-SHCN model in conjunction with time series forecasting on a broad range of synthetic and real-world datasets: traffic flows, COVID-19 biosurveillance, Ethereum blockchain, surface air temperature, wind energy, and vector autoregressions. Our experiments demonstrate that the ZFC-SHCN achieves the state-of-the-art performance with lower requirements on computational costs.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 35 - 36th Conference on Neural Information Processing Systems, NeurIPS 2022
EditorsS. Koyejo, S. Mohamed, A. Agarwal, D. Belgrave, K. Cho, A. Oh
PublisherNeural information processing systems foundation
ISBN (Electronic)9781713871088
StatePublished - 2022
Externally publishedYes
Event36th Conference on Neural Information Processing Systems, NeurIPS 2022 - New Orleans, United States
Duration: Nov 28 2022Dec 9 2022

Publication series

NameAdvances in Neural Information Processing Systems
Volume35
ISSN (Print)1049-5258

Conference

Conference36th Conference on Neural Information Processing Systems, NeurIPS 2022
Country/TerritoryUnited States
CityNew Orleans
Period11/28/2212/9/22

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Information Systems
  • Signal Processing

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