# Graph-Time Convolutional Neural Networks

arXiv: https://arxiv.org/abs/2103.01730 · HTML: https://mlsanity.com/paper/2103.01730/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 35 references that are in the map.
- First posted on arXiv 2 Mar 2021.

## Builds on (most cited first, 28 of 28)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Relational inductive biases, deep learning, and graph networks](https://mlsanity.com/paper/1806.01261/) (2018)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting](https://mlsanity.com/paper/1709.04875/) (2017)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [Representation Learning on Graphs: Methods and Applications](https://mlsanity.com/paper/1709.05584/) (2017)
- [Self-Attention Graph Pooling](https://mlsanity.com/paper/1904.08082/) (2019)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Structured Sequence Modeling with Graph Convolutional Recurrent Networks](https://mlsanity.com/paper/1612.07659/) (2016)
- [Deep Learning for Spatio-Temporal Data Mining: A Survey](https://mlsanity.com/paper/1906.04928/) (2019)
- [An Attention Enhanced Graph Convolutional LSTM Network for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1902.09130/) (2019)
- [Convolutional Neural Network Architectures for Signals Supported on Graphs](https://mlsanity.com/paper/1805.00165/) (2018)
- [Dynamic Graph Convolutional Networks](https://mlsanity.com/paper/1704.06199/) (2017)
- [Graphs, Convolutions, and Neural Networks: From Graph Filters to Graph Neural Networks](https://mlsanity.com/paper/2003.03777/) (2020)
- [Gated Graph Recurrent Neural Networks](https://mlsanity.com/paper/2002.01038/) (2020)
- [Bike Flow Prediction with Multi-Graph Convolutional Networks](https://mlsanity.com/paper/1807.10934/) (2018)
- [EdgeNets:Edge Varying Graph Neural Networks](https://mlsanity.com/paper/2001.07620/) (2020)
- [Autoregressive Moving Average Graph Filtering](https://mlsanity.com/paper/1602.04436/) (2016)
- [Forecasting Time Series with VARMA Recursions on Graphs](https://mlsanity.com/paper/1810.08581/) (2018)
- [A Time-Vertex Signal Processing Framework](https://mlsanity.com/paper/1705.02307/) (2017)
- [Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs](https://mlsanity.com/paper/1612.03615/) (2016)
- [Forecasting Multi-Dimensional Processes over Graphs](https://mlsanity.com/paper/2004.08260/) (2020)
- [Constructing Geographic and Long-term Temporal Graph for Traffic Forecasting](https://mlsanity.com/paper/2004.10958/) (2020)
- [Sampling and Reconstruction of Signals on Product Graphs](https://mlsanity.com/paper/1807.00145/) (2018)
- [Graph-Adaptive Activation Functions for Graph Neural Networks](https://mlsanity.com/paper/2009.06723/) (2020)

## Built on by (most cited first, 8 of 8)

- [Graph Pooling for Graph Neural Networks: Progress, Challenges, and Opportunities](https://mlsanity.com/paper/2204.07321/) (2022)
- [TraverseNet: Unifying Space and Time in Message Passing for Traffic Forecasting](https://mlsanity.com/paper/2109.02474/) (2021)
- [Space-Time Graph Neural Networks](https://mlsanity.com/paper/2110.02880/) (2021)
- [Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis](https://mlsanity.com/paper/2206.15174/) (2022)
- [Continuous Product Graph Neural Networks](https://mlsanity.com/paper/2405.18877/) (2024)
- [Uncertainty in Graph Contrastive Learning with Bayesian Neural Networks](https://mlsanity.com/paper/2312.00232/) (2023)
- [Second-Order Tensorial Partial Differential Equations on Graphs](https://mlsanity.com/paper/2509.02015/) (2025)
- [Graph Variate Neural Networks](https://mlsanity.com/paper/2509.20311/) (2025)

## Abstract (arXiv)

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.