# Modeling Spatial Nonstationarity via Deformable Convolutions for Deep Traffic Flow Prediction

arXiv: https://arxiv.org/abs/2101.12010 · HTML: https://mlsanity.com/paper/2101.12010/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 58 references that are in the map.
- First posted on arXiv 8 Jan 2021.

## Builds on (most cited first, 16 of 16)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [DeepLab: Semantic Image Segmentation with Deep Convolutional Nets, Atrous Convolution, and Fully Connected CRFs](https://mlsanity.com/paper/1606.00915/) (2016)
- [Rethinking Atrous Convolution for Semantic Image Segmentation](https://mlsanity.com/paper/1706.05587/) (2017)
- [Deformable Convolutional Networks](https://mlsanity.com/paper/1703.06211/) (2017)
- [Spatial Temporal Graph Convolutional Networks for Skeleton-Based Action Recognition](https://mlsanity.com/paper/1801.07455/) (2018)
- [Universal adversarial perturbations](https://mlsanity.com/paper/1610.08401/) (2016)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [T-GCN: A Temporal Graph ConvolutionalNetwork for Traffic Prediction](https://mlsanity.com/paper/1811.05320/) (2018)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Understanding Convolution for Semantic Segmentation](https://mlsanity.com/paper/1702.08502/) (2017)
- [Deep Multi-View Spatial-Temporal Network for Taxi Demand Prediction](https://mlsanity.com/paper/1802.08714/) (2018)
- [Improving the Robustness of Deep Neural Networks via Stability Training](https://mlsanity.com/paper/1604.04326/) (2016)
- [How to Build a Graph-Based Deep Learning Architecture in Traffic Domain: A Survey](https://mlsanity.com/paper/2005.11691/) (2020)
- [Topology Density Map for Urban Data Visualization and Analysis](https://mlsanity.com/paper/2007.15828/) (2020)
- [Revisiting the Modifiable Areal Unit Problem in Deep Traffic Prediction with Visual Analytics](https://mlsanity.com/paper/2007.15486/) (2020)
- [Deformable Kernel Convolutional Network for Video Extreme Super-Resolution](https://mlsanity.com/paper/2010.00154/) (2020)

## Built on by (most cited first, 4 of 4)

- [Spatiotemporal-Augmented Graph Neural Networks for Human Mobility Simulation](https://mlsanity.com/paper/2306.09381/) (2023)
- [Parameterized Decision-making with Multi-modal Perception for Autonomous Driving](https://mlsanity.com/paper/2312.11935/) (2023)
- [ODMixer: Fine-grained Spatial-temporal MLP for Metro Origin-Destination Prediction](https://mlsanity.com/paper/2404.15734/) (2024)
- [Adaptive Convolutional Forecasting Network Based on Time Series Feature-Driven](https://mlsanity.com/paper/2405.12038/) (2024)

## Abstract (arXiv)

Deep neural networks are being increasingly used for short-term traffic flow prediction, which can be generally categorized as convolutional (CNNs) or graph neural networks (GNNs). CNNs are preferable for region-wise traffic prediction by taking advantage of localized spatial correlations, whilst GNNs achieves better performance for graph-structured traffic data. When applied to region-wise traffic prediction, CNNs typically partition an underlying territory into grid-like spatial units, and employ standard convolutions to learn spatial dependence among the units. However, standard convolutions with fixed geometric structures cannot fully model the nonstationary characteristics of local traffic flows. To overcome the deficiency, we introduce deformable convolution that augments the spatial sampling locations with additional offsets, to enhance the modeling capability of spatial nonstationarity. On this basis, we design a deep deformable convolutional residual network, namely DeFlow-Net, that can effectively model global spatial dependence, local spatial nonstationarity, and temporal periodicity of traffic flows. Furthermore, to better fit with convolutions, we suggest to first aggregate traffic flows according to pre-conceived regions or self-organized regions based on traffic flows, then dispose to sequentially organized raster images for network input. Extensive experiments on real-world traffic flows demonstrate that DeFlow-Net outperforms GNNs and existing CNNs using standard convolutions, and spatial partition by pre-conceived regions or self-organized regions further enhances the performance. We also demonstrate the advantage of DeFlow-Net in maintaining spatial autocorrelation, and reveal the impacts of partition shapes and scales on deep traffic flow prediction.