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Predicting Citywide Crowd Flows in Irregular Regions Using Multi-View Graph Convolutional Networks

Junkai Sun, Junbo Zhang, Qiaofei Li, Xiuwen Yi, Yuxuan Liang, Yu Zheng

arXiv:1903.07789v2cs.CVcs.LG

TL;DR

Crowd-flow forecasting in irregular urban regions is difficult because spatial interactions and diverse temporal, external, and meta factors must be modeled together. The paper represents regions as a spatio-temporal graph and proposes MVGCN, which combines graph convolutions with multi-view fusion. Across four real-world mobility datasets, MVGCN outperforms several state-of-the-art baselines and supports an internal forecasting system.

  • Problem

    The paper targets forecasting inflow and outflow across irregular city regions, where spatial correlations, temporal dependencies, external factors, and meta features complicate prediction.

  • Method

    MVGCN uses multiple graph convolutional networks and fully connected networks to model spatial structure, temporal views, external factors, and meta information, then fuses their representations.

  • Results

    MVGCN achieves significantly better performance than eight baselines across four real-world datasets, including recurrent and graph-based approaches.

  • Takeaways & Limitations

    The framework supports citywide forecasting in irregular regions and has been implemented as an internal visualization system.

  • Takeaways & Limitations

    The framework allows different periods and trends to be configured according to the characteristics of the data.

Abstract

from arXiv · show

Being able to predict the crowd flows in each and every part of a city, especially in irregular regions, is strategically important for traffic control, risk assessment, and public safety. However, it is very challenging because of interactions and spatial correlations between different regions. In addition, it is affected by many factors: i) multiple temporal correlations among different time intervals: closeness, period, trend; ii) complex external influential factors: weather, events; iii) meta features: time of the day, day of the week, and so on. In this paper, we formulate crowd flow forecasting in irregular regions as a spatio-temporal graph (STG) prediction problem in which each node represents a region with time-varying flows. By extending graph convolution to handle the spatial information, we propose using spatial graph convolution to build a multi-view graph convolutional network (MVGCN) for the crowd flow forecasting problem, where different views can capture different factors as mentioned above. We evaluate MVGCN using four real-world datasets (taxicabs and bikes) and extensive experimental results show that our approach outperforms the adaptations of state-of-the-art methods. And we have developed a crowd flow forecasting system for irregular regions that can now be used internally.

1 INTRODUCTION

The paper addresses citywide crowd-flow forecasting in irregular regions by modeling spatial interactions and multiple temporal and external factors. It proposes MVGCN and evaluates it across four real-world mobility datasets.

  • Motivation: Accurate regional crowd-flow forecasts support traffic control, risk assessment, and public safety, including advance warnings or evacuations.The motivation cites the 2015 Shanghai New Year’s Eve stampede as an example of the stakes.
  • Motivation: Irregular city regions are separated by road networks, making grid-based crowd-flow prediction less faithful to urban structure.Prior work mainly focused on regular grids, although graph techniques have also modeled non-Euclidean correlations.
  • Problem formulation: The task predicts inflow and outflow for every irregular region, using transition flows to represent movement between regions.Inflow counts arrivals from other regions, while outflow counts departures to other regions during a time interval.
  • Problem formulation: Forecasting is difficult because regions interact spatially and flows depend on multiple temporal properties, external factors, and meta features.Examples include closeness, periods, trends, weather, events, and time-of-day information.
  • Approach: MVGCN fuses multiple views with gating and sum fusion to capture sudden and slight changes, respectively.Its graph convolutions model spatial correlations, while the multi-view design integrates distinct latent representations.
  • Approach: The proposed framework combines preprocessing, road-network map segmentation and clustering, transition-flow graph construction, and graph-convolutional forecasting.A demo system visualizes citywide forecasts for irregular regions.
  • Evaluation: Evaluation uses four real-world taxi and bike datasets, with results reported as outperforming adaptations of several state-of-the-art approaches.The comparisons include diffusion convolutional recurrent neural networks and a Gaussian Markov random field model.

2 PROBLEM DEFINITION

The paper partitions road-defined urban space into manageable irregular regions and represents their crowd flows as signals on a transition-flow graph. The prediction problem is forecasting future node attributes from historical observations.

  • 2.1 Irregular Regions: Urban areas are naturally divided into irregular regions by road networks, and functional areas can exhibit different traffic-flow patterns.The text contrasts residential-to-work commuting patterns with return trips after work.
  • 2.1 Irregular Regions: Map segmentation uses grid-based morphological processing, including dilation to thicken roads and fill holes, followed by thinning to recover road skeletons.The map is partitioned into 2400×2400 grid-cells before road points are mapped into a binary image.
  • 2.1 Irregular Regions: Map clustering groups small low-level regions using Spearman rank correlation between their average crowd flows over a time period.The clustering produces higher-level regions that are more tractable for city-scale flow collection or prediction.
  • 2.1 Irregular Regions: The graph uses historical region-wise transition flows to capture dependencies between nearby and distant irregular regions.Transition flows reflect interactions arising from geographic adjacency and transportation links such as subways and taxis.
  • 2.2 Prediction Problem on Spatio-Temporal Graphs: An STG G = (V, E, A) contains N vertices and edges, with each vertex assigned a geospatial position and time-varying attributes.The adjacency matrix is binary and indicates whether two regions are correlated in traffic flow.
  • 2.2 Prediction Problem on Spatio-Temporal Graphs: Each graph signal X_t records node attributes such as inflow and outflow, while transition flows determine graph edges.For two flow attributes, the node feature dimension is C = 2.
  • 2.2 Prediction Problem on Spatio-Temporal Graphs: The formal forecasting task predicts the next-time-step node attributes from observed attributes {X_t | t = 1, 2, · · ·, T}.The target is X_T+1 for a given graph G = (V, E, A).

3 METHODOLOGY

MVGCN forecasts crowd flows over irregular-region spatio-temporal graphs by combining multiple temporal, external, and meta views. Its spatial graph convolution incorporates geographic distance, while fusion mechanisms address gradual and sudden external-factor changes.

  • 3 METHODOLOGY: The framework separates data preparation from model learning, selecting key timesteps and global information before forecasting with GCNs and FNNs.Temporal views use GCNs for spatial correlations, while global external and meta views use fully connected networks.
  • 3 METHODOLOGY: Multiple temporal views represent recent, daily, weekly, monthly, and quarterly dependencies and can be modeled in parallel.The selected input complexity is lr + ld + lw + lm + lq, whereas an RNN covering the full temporal dependencies can require O(lq ∗pq).
  • 3 METHODOLOGY: The spatial graph convolution modifies existing graph edges with distance-based weights derived from a thresholded Gaussian kernel.The method uses geographical distance between node positions, with parameters controlling adjacency scale and sparsity.
  • 3 METHODOLOGY: GCN-based residual units stack spatial graph convolutional layers to capture multi-hop spatial dependencies while supporting very deep networks.The layer propagation adds self-connections and uses trainable filter parameters; stacking residual units enables deeper architectures.
  • 3 METHODOLOGY: MVGCN fuses five temporal GCN outputs with external and meta representations using learnable weighting, concatenation, sum fusion, or gating.The temporal weights correspond to closeness, daily period, weekly period, monthly trend, and quarterly trend; sum fusion handles gradual changes and gating handles sudden changes such as rainstorms.
  • 3 METHODOLOGY: The model uses Huber loss, combining squared-error behavior near zero with absolute-error behavior when |x −ˆx| exceeds δ.The threshold δ is 1 by default.

4.1 Settings

The study evaluates MVGCN on four mobility datasets covering taxi and bike flows in irregular regions, using nine baselines and RMSE/MAE metrics.

  • Datasets: Four datasets cover taxi trajectories in Beijing and NYC and bike systems in NYC and Washington D.C.TaxiNYC2 uses 100 irregular regions; BikeDC3 and BikeNYC4 cluster stations into 120 regions.
  • Data split and graphs: The last four weeks are used for testing, with earlier data used for training.Graphs use geographical distance between stations or region centers, viewed as graph nodes.
  • Baselines: MVGCN is compared with nine baselines spanning time-series, tree-based, recurrent, graph-convolutional, and Gaussian Markov random-field models.The baselines include HA, VAR, GBRT, FC-LSTM, GCN, DCRNN, FCCF, FCCFnoTrans, and ST-MGCN.
  • Evaluation: Evaluation uses Root Mean Square Error (RMSE) and Mean Absolute Error (MAE), with smaller values indicating better performance.Models are selected using validation performance before test evaluation.

4.2 Comprehensive Results

MVGCN performs strongly across the four datasets and remains effective under sudden changes and multi-step forecasting, while competing sequence models lack several temporal and external factors.

  • Comprehensive comparison: MVGCN performs best on all four datasets under both metrics except MAE on TaxiNYC.The comparison covers nine baselines using RMSE and MAE.
  • Comprehensive comparison: MVGCN outperforms ST-MGCN on two taxi datasets for both RMSE and MAE.ST-MGCN results are reported only for taxi datasets because graph data are unavailable for the bike datasets.
  • Dataset and feature effects: TaxiBJ shows MVGCN’s greatest improvement among the four datasets, while removing FCCF transition features slightly increases both RMSE and MAE.The passage attributes TaxiBJ’s improvement to its richer external information and links the FCCF degradation to transition-feature removal.
  • Sudden changes: Sudden-change evaluations define the top 5% of timeslots by absolute flow differences as anomalous cases and compare MVGCN with five baselines.The sudden changes may be caused by anomalous weather or traffic events.
  • Multi-step prediction: MVGCN achieves the best results for all six BikeDC prediction steps, with only small RMSE and MAE increases as the horizon grows from 1 to 6.The original GCN is not robust as the timestep increases, and DCRNN does not capture period, trend, or external factors.

4.3 Effects of Different Components

Ablations show that temporal views, geospatial information, and external or meta features contribute to MVGCN performance, while five GCN layers give the best TaxiNYC result.

  • Temporal view: Adding daily temporal information greatly improves performance over the recent view alone, and additional daily, weekly, monthly, and quarterly views improve it further.The experiments evaluate RMSE and MAE across five temporal views.
  • Spatial graph convolution: Removing geospatial position increases RMSE from 23.15 to 23.64, demonstrating the effectiveness of spatial graph convolution.The spatial layer incorporates geospatial position into graph convolution.
  • External and meta features: Removing external factors increases RMSE from 23.15 to 24.41, while removing meta data increases it to 23.23.These results are reported on the TaxiNYC test set.
  • GCN depth and loss: Performance with RMSE, MAE, or Huber loss first decreases and then increases as GCN layers increase, with the best results at five layers.The ablation is conducted on TaxiNYC using RMSE as the plotted metric.

5 CROWD FLOW FORECASTING SYSTEM IN IRREG-

The authors developed UrbanFlow, an internal crowd-flow forecasting demo for irregular regions and deployed it in Beijing.

  • UrbanFlow system: UrbanFlow visualizes predicted and ground-truth inflow and outflow for selected irregular regions in Beijing.The system is accessible internally and is shown in Figure 13(a).

6 RELATED WORK

Related work spans time-series, recurrent, graph-based, and city-scale traffic prediction, but existing approaches often miss either spatial correlations or irregular urban regions.

  • Road-traffic prediction commonly targets single or multiple road segments, while newer work addresses city-scale traffic flow.
  • The paper positions irregular urban-area forecasting as distinct from prior grid-based and road-segment prediction settings.
  • Multi-graph graph convolution models non-Euclidean correlations but evaluates experiments in regular grid-based regions.
  • Time-series models such as ARIMA and vector autoregression capture temporal dependencies but fail to capture spatial correlations.
  • RNNs, LSTMs, and GRUs support sequence learning and long-term temporal dependencies, but these models do not capture both spatial and temporal information.

7 CONCLUSION

MVGCN predicts inflow and outflow across irregular city regions by combining graph convolutions with multiple temporal, external, and meta-information views. Across four real-world datasets, it performs significantly better than eight baselines.

  • MVGCN uses several graph convolutional networks to predict inflow and outflow in every irregular city region.
  • The model captures adjacent and multi-hop spatial correlations, interactions, and geospatial position through spatial graph convolutions.
  • MVGCN integrates closeness, daily and weekly periods, longer-term trends, weather, events, and time-of-day metadata.
  • Across four real-world datasets, MVGCN performs significantly better than eight baselines, including recurrent neural networks and Gaussian Markov random field-based models.
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