# Periodic Residual Learning for Crowd Flow Forecasting

arXiv: https://arxiv.org/abs/2112.06132 · HTML: https://mlsanity.com/paper/2112.06132/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 43 references that are in the map.
- First posted on arXiv 8 Dec 2021.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Squeeze-and-Excitation Networks](https://mlsanity.com/paper/1709.01507/) (2017)
- [CBAM: Convolutional Block Attention Module](https://mlsanity.com/paper/1807.06521/) (2018)
- [WaveNet: A Generative Model for Raw Audio](https://mlsanity.com/paper/1609.03499/) (2016)
- [Convolutional LSTM Network: A Machine Learning Approach for Precipitation Nowcasting](https://mlsanity.com/paper/1506.04214/) (2015)
- [Dual Attention Network for Scene Segmentation](https://mlsanity.com/paper/1809.02983/) (2018)
- [Graph WaveNet for Deep Spatial-Temporal Graph Modeling](https://mlsanity.com/paper/1906.00121/) (2019)
- [GMAN: A Graph Multi-Attention Network for Traffic Prediction](https://mlsanity.com/paper/1911.08415/) (2019)
- [Deep Spatio-Temporal Residual Networks for Citywide Crowd Flows Prediction](https://mlsanity.com/paper/1610.00081/) (2016)
- [Coordinate Attention for Efficient Mobile Network Design](https://mlsanity.com/paper/2103.02907/) (2021)
- [Spatial-Temporal Transformer Networks for Traffic Flow Forecasting](https://mlsanity.com/paper/2001.02908/) (2020)
- [BAM: Bottleneck Attention Module](https://mlsanity.com/paper/1807.06514/) (2018)
- [Revisiting Spatial-Temporal Similarity: A Deep Learning Framework for Traffic Prediction](https://mlsanity.com/paper/1803.01254/) (2018)
- [Traffic Flow Forecasting with Spatial-Temporal Graph Diffusion Network](https://mlsanity.com/paper/2110.04038/) (2021)
- [Predicting Citywide Crowd Flows in Irregular Regions Using Multi-View Graph Convolutional Networks](https://mlsanity.com/paper/1903.07789/) (2019)
- [UrbanFM: Inferring Fine-Grained Urban Flows](https://mlsanity.com/paper/1902.05377/) (2019)
- [Fine-Grained Urban Flow Inference](https://mlsanity.com/paper/2002.02318/) (2020)

## Built on by (most cited first, 1 of 1)

- [MobilityDL: A Review of Deep Learning From Trajectory Data](https://mlsanity.com/paper/2402.00732/) (2024)

## Abstract (arXiv)

Crowd flow forecasting, which aims to predict the crowds entering or leaving certain regions, is a fundamental task in smart cities. One of the key properties of crowd flow data is periodicity: a pattern that occurs at regular time intervals, such as a weekly pattern. To capture such periodicity, existing studies either fuse the periodic hidden states into channels for networks to learn or apply extra periodic strategies to the network architecture. In this paper, we devise a novel periodic residual learning network (PRNet) for a better modeling of periodicity in crowd flow data. Unlike existing methods, PRNet frames the crowd flow forecasting as a periodic residual learning problem by modeling the variation between the inputs (the previous time period) and the outputs (the future time period). Compared to directly predicting crowd flows that are highly dynamic, learning more stationary deviation is much easier, which thus facilitates the model training. Besides, the learned variation enables the network to produce the residual between future conditions and its corresponding weekly observations at each time interval, and therefore contributes to substantially more accurate multi-step ahead predictions. Extensive experiments show that PRNet can be easily integrated into existing models to enhance their predictive performance.