Spatiotemporal Multi-Graph Convolution for Ride-hailing ...yaguang/papers/aaai19_multi_graph... ·...

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.

http://www.businessofapps.com/data/uber-statistics/


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


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


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


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


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


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


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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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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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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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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6.0

8.0

10.0

12.0

14.0

16.0

18.0

Ro

ot

Mea

n S

qu

are

Erro

r

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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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

11.0

12.0

13.0

Ro

ot

Mea

n S

qu

are

Erro

r

w/o Spatial Proximity w/o Functionalw/o Transportation ST-MGCN

10.0

10.5

11.0

11.5

12.0

12.5

13.0

Ro

ot

Mea

n S

qu

are

Erro

r

Average Pooling CG

RNN CG + RNN

Effect of spatial correlation modeling Effect of temporal correlation modeling

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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


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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Thank You!

Q & A

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