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Spatiotemporal Multi-Graph Convolution for Ride-hailing Demand Forecasting
Yaguang Li*
Hong Kong University of Science and Technology,University of Southern California, Didi AI Labs, Didi Chuxing
AAAI2019
Joint work with
Xu Geng*, Leye Wang, Lingyu Zhang, Qiang Yang, Jieping Ye and Yan Liu
Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Introduction
More than 18 billion ride-hailing trips worldwide in 2018*– Twice as much as the world population.
Benefit of better ride-hailing demand forecasting
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Better Vehicle Dispatching
Early congestion warning
Higher vehicle utilization
* http://www.businessofapps.com/data/uber-statistics/, Nov 2018.
Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Region-level Ride-hailing Demand Forecasting
Input: past T observations of demands of all |𝑉| regions
Output: demands of all |𝑉| regions in the next time stamp
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Input Output
𝑓: ℝ𝑇×|𝑉| → ℝ|𝑉|
ℝ𝑇×|𝑉| ℝ|𝑉|
Complicated spatial and temporal correlations
Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Related Work
Spatiotemporal forecasting on grid– Classical settings for demand forecasting problem
– CNN-based approaches: region-wise relationship is Euclidean
• DeepST/STResNet: Crowd flow forecasting (Zhang et al., 2017)
• DMVST: Demand forecasting (Yao et al., 2018)
Spatiotemporal forecasting on graph– LinUOTD: handcrafted feature + LR for demand forecasting (Tong et al., 2017)
– DCRNN/ST-GCN: Graph convolution based traffic forecasting (Li et al., 2018a, Yu et al., 2018, Liet al., 2018b, Yan et al., 2018)
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Hard to capture the non-Euclidean correlations
Hard to capture the multimodal correlations
Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Multimodal Correlations among Regions
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Spatial proximity– Region 1 and 2
Functional similarity– Regions with similar context show
similar demand patterns
– Region 1 and 3
Road connectivity– High-speed transportation
facilitate correlation
– Region 1 and 4
Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Spatiotemporal Multi-Graph Convolution Network
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Reweight and aggregate temporal observations
RNN
Contextual Gated RNN
Contextual Gating
Encode pair-wise correlations using
graphs
Spatial proximity
Func. similarity
ConnectivityRegion
Correlation
Capture spatial correlations among regions with multi-
graph convolution
GCN
GCN
GCN
…
…
Graph convolution
Graph convolution
Graph convolution
…
Generate prediction
Aggregation
Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
CGRNN: Context-aware Temporal Aggregation
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T
T
𝑇 reweighted observations are aggregated with RNN
[𝑿 𝒕 , 𝑿(𝒕+𝟏), … ] ∈ ℝ𝑇× 𝑉 ×𝑃
𝑇 observations
𝑧 ∈ ℝ𝑇×1×𝑃𝐹𝑝𝑜𝑜𝑙(.)
• Summarize contextual information
• Calculate gates based on interdependencies between observations with self-attention
• Reweight observations with gates
• Aggregate reweighted observations with share-weight RNN
ContextualGating
෩𝑿 𝒕 , ෩𝑿 𝒕+𝟏 , … ∈ ℝ𝑇× 𝑉 ×𝑃
𝑇 reweighted observations
RNN RNN RNN. . .
Share-weight RNN
ℝ 𝑉 ×𝑃′
|V| re
gio
ns
𝑠 ∈ ℝ𝑇
Self-attention
Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Spatiotemporal Multi-Graph Convolution Network
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Generate predictionEncode pair-wise correlations using
graphs
Spatial proximity
Func. similarity
Connectivity
Reweight and aggregate observations
RNN
Contextual Gated RNN
Contextual Gating
Capture spatial correlations among regions with multi-
graph convolution
GCN
GCN
GCN
…
…
Graph convolution
Graph convolution
Graph convolution
…
Region
Correlation
Aggregation
Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Multi-graph Convolution
𝐻 = MGC 𝑋 = 𝜎 Agg 𝑓 𝐴𝑖; 𝜃𝑖 𝑋𝑊A𝑖 ∈ 𝔸
𝑋 ∈ ℝ 𝑉 ×𝑃𝐻 ∈ ℝ 𝑉 ×𝑃′
= 𝜎
𝑊 ∈ ℝ𝑃×𝑃′
Feature transformation
𝑓 𝐴𝑖; 𝜃𝑖 ∈ ℝ 𝑉 ×|𝑉|
Node aggregation
AggA𝑖 ∈ 𝔸
Aggregation function
𝑓 𝐴𝑖; 𝜃𝑖 : function of adjacency matrix 𝐴𝑖 with parameter 𝜃𝑖– Polynomial of graph Laplacian, graph attention etc.
Agg: Aggregation function– Sum, average, attention-based aggregation
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Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Multi-graph Convolution
node aggregation
node aggregation
Graph 𝐴1
Example node 𝑣𝑖
Graph 𝐴2
Graph 𝐴3
ℎ𝑖1 = 𝑓 𝐴1; 𝜃1 𝑋𝑊 𝑖,:
ℎ𝑖2 = 𝑓 𝐴2; 𝜃2 𝑋𝑊 𝑖,:
ℎ𝑖3 = 𝑓 𝐴3; 𝜃3 𝑋𝑊 𝑖,:
ℎ𝑖Agg .
node aggregation
Neighborhood node
𝐻 = 𝜎 Agg 𝑓 𝐴𝑖; 𝜃𝑖 𝑋𝑊
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Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Datasets
Beijing:– 1296 regions, 19M samples
– 10 months in 2017
Shanghai– 896 regions, 13M samples
– 10 months in 2017
POI/Road network– OpenStreetMap
Beijing
Shanghai
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Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Experiments
Baselines– Historical Average (HA)
– Linear Regression (LASSO, Ridge)
– Vector Auto-Regression (VAR)
– Spatiotemporal Auto-Regressive Model (STAR)
– Gradient Boosted Machine (GBM)
– Spatiotemporal Residual Network (ST-ResNet), with Euclidean grid
– Spatiotemporal graph convolutional network (ST-GCN), with road network graph
– Deep Multi-view Spatiotemporal Network (DMVST-Net), with Euclidean grid, SOTA for ride-hailing demand forecasting
Task– One step ahead ride-hailing demand forecasting
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Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
6.0
8.0
10.0
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18.0
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HA LASSO Ridge VAR STAR
GBM STResNet DMVST-Net ST-GCN ST-MGCN
Experimental Results
ST-MGCN achieves the best performance on both datasets– 10+% improvement*.
Beijing Shanghai
* In terms of relative error reduction of RMSE.
`
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Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Experimental Results
Both spatial and temporal correlations modeling are necessary– Removing either graph component leads to significantly worse performance.
– With CGRNN, ST-MGCN achieves the best performance.
10.0
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w/o Spatial Proximity w/o Functionalw/o Transportation ST-MGCN
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Average Pooling CG
RNN CG + RNN
Effect of spatial correlation modeling Effect of temporal correlation modeling
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Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Summary
Spatial: encode pairwise correlations into multiple graphs
Temporal: reweight (self-attention) and aggregate (RNN)
Result: 10+% improvement on real-world large-scale datasets
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Scan to download the poster
Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Reference
1. Defferrard, M., Bresson, X., & Vandergheynst, P. (2016). Convolutional neural networks on graphs with fast localized spectral filtering. In NIPS (pp. 3844-3852)
2. Li, Y., Yu, R., Shahabi, C., & Liu, Y. (2018). Diffusion convolutional recurrent neural network: Data-driven traffic forecasting. ICLR.
3. Tong, Y., Chen, Y., Zhou, Z., Chen, L., Wang, J., Yang, Q., ...& Lv, W. (2017). The simpler the better: a unified approach to predicting original taxi demands based on large-scale online platforms. KDD (pp. 1653-1662). ACM.
4. Yao, H., Wu, F., Ke, J., Tang, X., Jia, Y., Lu, S., ... & Ye, J. (2018). Deep multi-view spatial-temporal network for taxi demand prediction. arXiv preprint arXiv:1802.08714.
5. Yu, B., Yin, H., & Zhu, Z. Spatio-Temporal Graph Convolutional Networks: A Deep Learning Framework for Traffic Forecasting. IJCAI 2018
6. Zhang, J., Zheng, Y., Qi, D., Li, R., Yi, X., & Li, T. (2018). Predicting citywide crowd flows using deep spatio-temporal residual networks. Artificial Intelligence, 259, 147-166.
7. Zhang, X., He, L., Chen, K., Luo, Y., Zhou, J., & Wang, F. (2018). Multi-View Graph Convolutional Network and Its Applications on Neuroimage Analysis for Parkinson's Disease. arXiv preprint arXiv:1805.08801.
8. Yan, S., Xiong, Y., & Lin, D. (2018). Spatial temporal graph convolutional networks for skeleton-based action recognition. AAAI
9. Li, C., Cui, Z., Zheng, W., Xu, C., & Yang, J. (2018). Spatio-Temporal Graph Convolution for Skeleton Based Action Recognition. AAAI
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Yaguang Li Spatiotemporal Multi-Graph Convolution Network for Ride-hailing Demand Forecasting
Thank You!
Q & A
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