Source-linked AI summary
Bike Flow Prediction with Multi-Graph Convolutional Networks
Di Chai, Leye Wang, Qiang Yang
TL;DR
Station-level bike flow prediction is difficult, while cluster-level methods cannot directly support precise station management. The paper proposes a multi-graph convolutional model with confidence intervals, reducing average prediction error by 25.1% in New York City and 17.0% in Chicago.
Problem
Single-station bike flow is difficult to predict, and cluster-level predictions cannot directly support precise management of individual stations.
Method
The model fuses distance, interaction, and correlation graphs, applies graph convolution and LSTM-based temporal modeling, and uses dropout to estimate confidence intervals.
Results
The model reduces average prediction error by 25.1% in New York City and 17.0% in Chicago compared with LSTM.
Takeaways & Limitations
The approach provides station-level flow estimates and confidence intervals for bike-sharing system managers’ decision making.
Takeaways & Limitations
The current model needs more than one year of historical bike flow records to obtain good prediction accuracy, leaving cold-start reduction as future work.
Abstract
from arXiv · showhide
One fundamental issue in managing bike sharing systems is the bike flow prediction. Due to the hardness of predicting the flow for a single station, recent research works often predict the bike flow at cluster-level. While such studies gain satisfactory prediction accuracy, they cannot directly guide some fine-grained bike sharing system management issues at station-level. In this paper, we revisit the problem of the station-level bike flow prediction, aiming to boost the prediction accuracy leveraging the breakthroughs of deep learning techniques. We propose a new multi-graph convolutional neural network model to predict the bike flow at station-level, where the key novelty is viewing the bike sharing system from the graph perspective. More specifically, we construct multiple inter-station graphs for a bike sharing system. In each graph, nodes are stations, and edges are a certain type of relations between stations. Then, multiple graphs are constructed to reflect heterogeneous relationships (e.g., distance, ride record correlation). Afterward, we fuse the multiple graphs and then apply the convolutional layers on the fused graph to predict station-level future bike flow. In addition to the estimated bike flow value, our model also gives the prediction confidence interval so as to help the bike sharing system managers make decisions. Using New York City and Chicago bike sharing data for experiments, our model can outperform state-of-the-art station-level prediction models by reducing 25.1% and 17.0% of prediction error in New York City and Chicago, respectively.
1 INTRODUCTION
Station-level bike flow is difficult to predict, motivating a model that captures inter-station spatial relationships alongside temporal patterns. The proposed approach also estimates prediction confidence and improves error over station-level baselines in New York City and Chicago.
- Single-station bike flow has complicated dynamics, so recent studies often predict flows at the cluster level.Cluster-level methods achieve higher accuracy but require grouping stations without ground truth for evaluating cluster appropriateness.
- Cluster-level predictions cannot directly support precise management decisions for individual stations.
- The proposed multi-graph convolutional network captures heterogeneous spatial relationships between stations and temporal patterns in historical flows.It uses multi-graph convolutional layers for spatial correlations and an LSTM encoder-decoder for temporal patterns.
- Dropout-based uncertainty modeling lets the model provide prediction confidence intervals in addition to estimated bike flow values.The simulations account for model uncertainty, model misspecification, and inherent noise.
2 RELATED WORK
Related work organizes bike flow prediction into cluster-based, area-based, and station-based approaches, while graph convolutional networks provide the relevant graph-learning foundation. Station-based prediction offers finer operational information but is more difficult.
- Existing bike flow prediction studies mainly use cluster-based, area-based, or station-based formulations.
- Cluster-based flow prediction: Cluster-based methods group stations and predict aggregate demand and cluster-level proportions, using station distance or usage information.
- Area-based flow prediction: Area-based methods segment city maps into grids and apply CNN, ResNet, or ConvLSTM models to predict flow by area.They do not directly fit single-station prediction because large grids contain multiple stations, whereas small grids may contain none.
- Station-based flow prediction: Station-based prediction is harder than cluster- or area-based prediction but provides more fine-grained information for system operation.Prior work includes simple baselines and time-series methods for predicting station availability or demand.
- Graph convolutional neural networks: Graph convolutional networks apply convolutional layers to graph data and were progressively extended toward faster localized convolutions and graph-based recurrent prediction.
3 DEFINITIONS AND PROBLEM
The paper represents a bike-sharing system as a weighted station graph and defines bike flow as station-level inflow and outflow over time. Given historical flows, the task is to predict the next interval’s flows.
- Definitions: A bike-sharing system graph contains stations as nodes and weighted edges representing inter-station relationships.Larger edge weights indicate stronger relationships; for example, an edge weight may be the reciprocal of station distance.
- Definitions: Bike flow consists of inflow and outflow vectors across the N stations during each time interval.
- Problem formulation: Given historical pairs of inflow and outflow vectors through time t−1, the task is to predict the next interval’s bike flow.
4 MULTI-GRAPH CONVOLUTIONAL NEURAL NETWORK MODEL
The model represents bike-sharing stations as multiple heterogeneous inter-station graphs, fuses them, and applies graph convolution before temporal prediction. An LSTM encoder-decoder predicts station-level flow while the model also estimates prediction confidence.
- (i) Graph Generation: The framework builds weighted distance, interaction, and correlation graphs whose nodes are stations and whose edges encode heterogeneous inter-station relationships.The graph-generation stage uses spatial distance, historical ride records, and historical usage correlations to represent relationship strength.
- (ii) Multi-graph Convolution: The multi-graph convolution layer performs graph convolution on the fused graph to encode station-node features and heterogeneous spatial correlations.Graph structure makes the operation approximately local because interaction graphs are sparse or distance-graph edge weights are often near zero.
- (iii) Prediction Network: The prediction network estimates station-level bike flow and prediction confidence by modeling model uncertainty, model misspecification, and inherent noise.The paper describes dropout-based simulations for inferring the prediction confidence interval.
- (ii) Multi-graph Convolution: Graph fusion normalizes each adjacency matrix and combines the graphs through weighted element-wise summation into one fused graph.A softmax operation keeps fusion weights normalized, and the fused graph is then used for graph convolution.
- (iii) Prediction Network: An encoder-decoder network with LSTM units captures temporal patterns in historical bike-flow records after multi-graph convolution.The model can use the encoder’s final state and external context features such as temperature, wind speed, and weekday/weekend information.
5 EVALUATION
Experiments on New York City and Chicago bike-sharing data evaluate prediction error, graph fusion, confidence intervals, training-data length, and computational efficiency. The multi-graph method improves prediction over baselines and single-graph variants, while confidence estimation and training-data analyses clarify its practical use and boundaries.
- 5.1 Experiment Setting: The evaluation uses four years of New York City and Chicago riding records, with the last 80 days for testing, the preceding 40 days for validation, and one-hour prediction granularity.Weather data is sourced from the National Centers for Environmental Information.
- Prediction Error: RMSE results show that the multi-graph model reduces average station-level prediction error by 25.1% in New York City and 17.0% in Chicago versus LSTM.LSTM performs best among the listed baselines, while the multi-graph method still outperforms it significantly.
- Prediction Error: 30.2% and 25.2% lower error are achieved than LSTM for New York City’s top 5 and top 10 busiest stations, respectively.These stations are emphasized because over-demand problems may occur where usage is highest.
- Effectiveness of Multi-Graph Fusion: 5.6–9.2% lower error is obtained by the multi-graph model than single-graph models for New York City’s top 5 busy stations.Across cities, the best single-graph choice depends on the evaluated stations, whereas fusion avoids selecting one graph manually.
- Confidence Interval Estimation: The proposed confidence intervals achieve the closest coverage ratio to 95% compared with dropout-only or validation-variance alternatives.The method models model uncertainty, model misspecification, and inherent noise, using a 95% interval target.
- Tuning the Training Data Length: Training data shorter than 6 months performs poorly in Chicago, while errors decrease significantly beyond 12 months; at least one year is suggested for robust accuracy.Training data is used both to construct inter-station graphs and to train the neural network parameters.
- Computation Efficiency: Training takes about 2 to 3 hours offline, while inference takes a few seconds, which the authors regard as sufficient for real-life prediction systems.The reported experiments use a server with an Intel Xeon E5-2690 CPU, 56 GB memory, and an Nvidia Tesla K80 GPU.
6 CONCLUSION AND FUTURE WORK
The proposed model combines heterogeneous inter-station graphs with uncertainty estimation for station-level bike flow prediction. Future work includes broader traffic applications, anomaly detection, cold-start reduction, and improved temporal modeling.
- Conclusion: The model represents stations through distance, interaction, and correlation graphs, fuses them, and applies graph convolution alongside temporal modeling.An encoder-decoder structure with LSTM units captures temporal patterns in historical bike flow records.
- Conclusion: The model also estimates prediction confidence intervals using dropout to obtain robust uncertainty estimates.These intervals are intended to support decision-making under fluctuating station demand.
- Future Work: Future work extends the model toward a general urban traffic prediction methodology for systems such as subways.The authors describe this as an ongoing extension of the bike flow prediction model.
- Future Work: Confidence intervals may also support anomaly detection by identifying unusually large uncertainty for stations during particular time slots.The authors plan to test this use in real-life bike sharing systems.
- Future Work: The current model requires more than one year of historical bike flow records for good accuracy, motivating work on the cold-start problem.The stated goal is to reduce the required training-data length.
- Future Work: The authors will investigate replacing LSTM units with attention units to determine whether temporal prediction performance improves.Recent studies are cited as suggesting that attention may be more effective.