This document proposes a new graph neural network model called Spatio-Temporal Pivotal Graph Neural Networks (STPGNN) for traffic flow forecasting. STPGNN first identifies pivotal nodes in the traffic network that exhibit extensive connections using a scoring mechanism. It then constructs a pivotal graph and uses a novel pivotal graph convolution module to capture spatio-temporal dependencies centered around these pivotal nodes. Experiments on several traffic datasets show STPGNN achieves better forecasting accuracy compared to other methods while maintaining lower computational cost.

1. Quang-Huy Tran
Network Science Lab
Dept. of Artificial Intelligence
The Catholic University of Korea
E-mail: huytran1126@gmail.com
2024-04-08
Spatio-Temporal Pivotal Graph Neural
Networks for Traffic Flow Forecasting
Weiyang Kong et al.
AAAI ’34: 2024 Proceedings of the AAAI Conference on Artificial Intelligence

2. 2
OUTLINE
• MOTIVATION
• INTRODUCTION
• METHODOLOGY
• EXPERIMENT & RESULT
• CONCLUSION

3. 3
MOTIVATION
• Traffic flow forecasting is a classical spatio-temporal data
mining problem with many real-world applications:
o Intelligent route planning.
o Dynamic traffic management.
o Smart location-based applications, etc.
The need of Traffic Flow Forecasting
Fig: Sensors in the transportation system
• Main task:
o Predict the traffic flows of several future times based on the historical traffic observations
(e.g. recorded by sensors of traffic networks).
• Main challenges:
o The intricate spatio-temporal correlations between sensors.

4. 4
MOTIVATION
• Graph Neural Networks (GNN) have shown promising results in modeling
transportation networks.
• However, conventional GNN methods overlook a common phenomenon in traffic:
o certain nodes in traffic network, either due to their geographical location (in the city center) or
characteristics (next to large interchanges).
o exhibit extensive connections with multiple other nodes, forming a complex spatio-temporal
network centered around these nodes.
• Author consider aggregating a few nodes to one node and consider that node as a
pivotal node due to stronger abilities in traffic flow aggregation and distribution.
o rich inter-node spatio-temporal relationships endow the pivotal nodes with intricate inter-
dependencies.
o potential multiplicity of roles within the entire network structure.
Problem with Current Traffic Forecasting Methods

5. 5
INTRODUCTION
• Address the traffic prediction problem of certain pivotal nodes with complex spatio-
temporal dependencies.
• Propose a novel method for identifying the pivotal nodes in traffic network:
o construct a pivotal graph, named Pivotal node Identification Module (PIM).
o introduce a pivotal graph convolution module to accurately capture the spatio-temporal
dependencies on pivotal nodes.
• Propose a parallel framework, named Pivotal Graph Convolution Module (PGCM), to
capture the spatiotemporal dependencies among all nodes:
o integrate the spatio-temporal features captured on both pivotal and non-pivotal nodes.

6. 6
METHODOLOGY
Problem Definition
• Spatial
o Given an undirected graph 𝐺 = (𝑉, 𝐸, 𝑈).
• Temporal: Each node records its 𝑆 step traffic flow:
𝑋1:𝑆
= (𝑋1
, 𝑋2
, … , 𝑋𝑆
)
• Forecasting: Find 𝐹 to forecast next 𝑇 steps.
𝑋𝑆+1, 𝑋𝑆+2, … 𝑋𝑆+𝑇 = 𝐹(𝑋1, 𝑋2, … , 𝑋𝑆)
𝑉: set of nodes(sensors).
𝐸: set of edges between nodes.
𝑈: adjacency matrix.

7. 7
METHODOLOGY
Background - Pivotal Nodes
• The traffic flow is first aggregated from nodes 1, 2, and 5 to node 3 during time interval [T1,T2]. Then, the
traffic flow is subsequently distributed from node 3 to nodes 2 and 5 during time interval [T2,T3].
o select the node 3 as a pivotal node.
• Pivotal node is a certain node, which exhibits extensive connections.
Fig: Traffic network example with 5 nodes. The nodes with different colors denote their
traffic flow changes.
How to identify pivotal nodes?
How to model these extensive connections?

8. 8
METHODOLOGY
Pivotal node Identification Module (PIM)
• Calculate the edge:
𝐻𝑖 ∈ ℝ𝑆: traffic features of node 𝑖 during 𝑆 period.
𝜔𝑖,𝑗: a trainable parameter.

9. 9
METHODOLOGY
Pivotal node Identification Module (PIM)
• Calculate a scoring function capable of measuring the aggregation and distribution capabilities of nodes 𝑖:
• Set of pivotal nodes C:
𝐾: number of pivotal nodes.

10. 10
METHODOLOGY
Pivotal Graph Convolution Module
• Construct the spatio-temporal graph correlations on pivotal nodes:
𝐻𝑖
𝑙
: node 𝑖 feature of 𝑙-th ST-layer.
𝐴: adjacency matrix of pivotal graph.
𝑊, 𝐵: trainable parameters.

11. 11
METHODOLOGY
A Parallel Structure for Non-pivotal Nodes
• Linear Gate Unit at time step 𝑡:
𝑥: input.
𝑓: a filter.
∗: convolution operation.

12. 12
METHODOLOGY
A Parallel Structure for Non-pivotal Nodes
• Graph convolution:
𝑈𝑞
: 𝑞-th power series of the adjacency matrix 𝑈.
𝑋: input.
𝐿𝑞: matrices of learnable parameters.

13. 13
METHODOLOGY
Loss Function
• Mean absolute error (MAE) is chosen as loss function:
𝑋 𝑡+1 :(𝑡+𝑇): prediction value.
Θ: all learnable model parameters.
𝑋𝑗
(𝑡+𝑖)
: ground truth.

14. 14
METHODOLOGY
MPNN + TL (Transfer Learning)
• The set of tasks for a country k
• Gradient Descent is normalized by the total number of tasks in the set to
refrain from taking too big step.
(𝑇𝑟𝑖,𝑗
𝑘
, 𝑇𝑒𝑖,𝑗
𝑘
) is a dataset associated with country k, where train set consists of the first i days of the data and the
task is to predict the number of cases in the j-th day ahead.

15. 15
EXPERIMENT AND RESULT
EXPERIMENT
• Measurement:
o Mean Absolute Errors (MAE), Mean Absolute Percentage Errors (MAPE), and Root Mean Squared
Errors (RMSE).
• Dataset:
o Sensor dataset: England[1] with PEMS-03, 04, 07, 08,
and BAY[2].
o GPS dataset: TaxiBJ.
o Aggregated into different interval: 5, 15, and 30 mins.
[1] http://tris.highwaysengland.co.uk/detail/trafficflowdata.
[2] http://pems.dot.ca.gov/
• Task:
o Predict the traffic flow, speed in next time.

16. 16
• Baseline:
o ARIMA(autoregressive moving average).
o DCRNN[1]: Diffusion Convolutional Recurrent Neural Network.
o GWNet[2]: Graph Wave Networks.
o STSGCN[3]: Spatial temporal synchronous graph convolutional networks.
o MTGNN[4]: Multivariate Temporal Graph Neural Networks.
o DMSTGCN[5]: Dynamic and Multi-Faceted Spatio-Temporal Graph Convolutional Network.
o DSTAGNN[6]: Dynamic Spatial-Temporal Aware Graph Neural Network.
o TPGNN[7]: Temporal Polynomial Graph Neural Networks.
o SGP[8]: Scalable Spatiotemporal Graph.
EXPERIMENT AND RESULT
EXPERIMENT
[1] Li, Y.; Yu, R.; Shahabi, C.; and Liu, Y. 2018. Diffusion Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting. In ICLR.
[2] Wu, Z.; Pan, S.; Long, G.; Jiang, J.; and Zhang, C. 2019. Graph wavenet for deep spatial-temporal graph modeling. In IJCAI.
[3] Song, C.; Lin, Y.; Guo, S.; and Wan, H. 2020. Spatial temporal synchronous graph convolutional networks: A new framework for spatial-temporal network data forecasting. In AAAI.
[4] Wu, Z.; Pan, S.; Long, G.; Jiang, J.; Chang, X.; and Zhang, C. 2020. Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks. In SIGKDD.
[5] Han, L.; Du, B.; Sun, L.; Fu, Y.; Lv, Y.; and Xiong, H. 2021.Dynamic and Multi-Faceted Spatio-Temporal Deep Learning for Traffic Speed Forecasting. In SIGKDD.
[6] Lan, S.; Ma, Y.; Huang, W.; Wang, W.; Yang, H.; and Li, P.2022. DSTAGNN: Dynamic Spatial-Temporal Aware Graph Neural Network for Traffic Flow Forecasting. In ICML.
[7] Liu, Y., Liu, Q., Zhang, J. W., Feng, H., Wang, Z., Zhou, Z., & Chen, W. (2022). Multivariate Time-Series Forecasting with Temporal Polynomial Graph Neural Networks. In NeurIPS
[8] Cini, A.; Marisca, I.; Bianchi, F. M.; and Alippi, C. 2023. Scalable Spatiotemporal Graph Neural Networks. Proceedings of the 37th AAAI Conference on Artificial Intelligence.

17. 17
EXPERIMENT AND RESULT
RESULT

18. 18
EXPERIMENT AND RESULT
RESULT – Component Analysis
Fig: Performance comparison of different variant on
PEMS08 and England datasets.

19. 19
EXPERIMENT AND RESULT
RESULT – Component Analysis
Fig: An illustrative case study conducted on the PEMS08 dataset. (a) The ground truth for pivotal and non-pivotal
nodes. (b) The prediction results of STPGNN and DSTAGNN on pivotal node 0

20. 20
EXPERIMENT AND RESULT
RESULT – Computation cost

21. 21
CONCLUSION
• Proposed a novel GNN-based model for traffic flow forecasting problem.
o Address a common phenomenon about pivotal nodes.
• Designed a scoring mechanism to identify pivotal nodes in traffic network.
• Proposed a novel pivotal graph convolution module to extract spatio-temporal
features at these nodes.
• Extensive experiments demonstrate the model’s effectiveness and efficiency.
• Future work: Explore the theoretical basis for K-value selection in pivotal node
selection.