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Predicting Station-level Hourly Demands in a Large-scale Bike-sharing Network: A Graph Convolutional Neural Network Approach

Lei Lin, Zhengbing He, Srinivas Peeta

arXiv:1712.04997v2stat.MLcs.LG

TL;DR

Station-level bike-sharing demand prediction must account for hidden correlations among stations and temporal demand dependencies. The paper proposes GCNN-DDGF, including an LSTM-enhanced recurrent architecture, and compares it with predefined-graph GCNNs and benchmark models. GCNNrec-DDGF performs best across the reported RMSE, MAE, and R2 measures, while learned-graph analysis reveals additional interstation correlations.

  • Problem

    Prior station-level models often fail to utilize hidden correlations between stations, while predefined graph structures constrain GCNN-based prediction.

  • Method

    GCNN-DDGF learns heterogeneous pairwise station correlations from data, with GCNNrec-DDGF adding an LSTM recurrent block to capture temporal demand dependencies.

  • Results

    GCNNrec-DDGF outperforms four predefined-adjacency GCNNs and seven benchmark models, with GCNNreg-DDGF following it.

  • Takeaways & Limitations

    The learned DDGF captures information similar to SD, DE, and DC matrices while uncovering additional hidden correlations between stations.

  • Takeaways & Limitations

    Future work should consider additional variables such as weather and extend GCNN-DDGF models to directed graphs.

Abstract

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This study proposes a novel Graph Convolutional Neural Network with Data-driven Graph Filter (GCNN-DDGF) model that can learn hidden heterogeneous pairwise correlations between stations to predict station-level hourly demand in a large-scale bike-sharing network. Two architectures of the GCNN-DDGF model are explored; GCNNreg-DDGF is a regular GCNN-DDGF model which contains the convolution and feedforward blocks, and GCNNrec-DDGF additionally contains a recurrent block from the Long Short-term Memory neural network architecture to capture temporal dependencies in the bike-sharing demand series. Furthermore, four types of GCNN models are proposed whose adjacency matrices are based on various bike-sharing system data, including Spatial Distance matrix (SD), Demand matrix (DE), Average Trip Duration matrix (ATD), and Demand Correlation matrix (DC). These six types of GCNN models and seven other benchmark models are built and compared on a Citi Bike dataset from New York City which includes 272 stations and over 28 million transactions from 2013 to 2016. Results show that the GCNNrec-DDGF performs the best in terms of the Root Mean Square Error, the Mean Absolute Error and the coefficient of determination (R2), followed by the GCNNreg-DDGF. They outperform the other models. Through a more detailed graph network analysis based on the learned DDGF, insights are obtained on the black box of the GCNN-DDGF model. It is found to capture some information similar to details embedded in the SD, DE and DC matrices. More importantly, it also uncovers hidden heterogeneous pairwise correlations between stations that are not revealed by any of those matrices.

1. Introduction

Station-level bike-sharing demand prediction is difficult because demand fluctuates across space and time, while prior station-specific models often fail to use hidden interstation correlations. The study proposes GCNN-DDGF to learn these correlations and improve hourly predictions.

  • Motivation: Fluctuating spatial and temporal demand makes accurate station-level prediction challenging for bike-sharing systems.Demand prediction supports operator rebalancing routes and schedules, helping address empty, full, or insufficiently supplied stations.
  • Research gap: Most previous station-level models predict each station separately and fail to exploit hidden correlations between stations.This separate-model strategy is also time consuming for networks with hundreds of stations.
  • Research gap: Traditional transportation approaches cannot reliably capture heterogeneous correlations because stations with similar demand need not share a road link or reachability relationship.A station’s reachability from another station during a period does not necessarily indicate high bike-sharing demand.
  • Research gap: CNN-based approaches are poorly suited to station-level prediction because large grids merge stations, whereas station-sized grids create huge sparse matrices with redundant zeros.These grid choices either lose station-level granularity or increase computational burden.
  • Contribution: GCNN-DDGF learns hidden heterogeneous pairwise station correlations without predefining an adjacency matrix.The study also introduces regular and recurrent architectures, with the recurrent version adding an LSTM block for temporal dependencies.
  • Contribution: GCNNrec-DDGF outperforms the four predefined-adjacency GCNNs and seven benchmark models, while learned-graph analysis reveals both known-matrix information and additional station correlations.The DDGF captures information similar to the SD, DE, and DC matrices and uncovers correlations not revealed by those matrices.

2. Literature Review

Prior bike-sharing demand studies operate at city, cluster, or station granularity, while graph convolutional methods address irregular domains but traditionally depend on manually specified graph structures. Station-level models have seldom combined spatial and temporal interstation correlations.

  • Prediction granularity: Bike-sharing demand prediction research is commonly divided into city-level, cluster-level, and station-level models.These groups differ primarily in the spatial granularity of their predictions.
  • City-level models: City-level studies predict total system demand but simplify rebalancing and often underuse detailed transaction variables.Such variables include trip duration, origin, destination, check-in and check-out time, and user information.
  • Cluster-level models: Cluster-level studies group stations using geographical, temporal, usage, or travel-pattern similarities before predicting aggregated demand.Methods include K-means, LDA, bipartite station clustering, geographically constrained clustering, community detection, and hierarchical clustering.
  • Station-level models: Station-level prediction is more challenging, and many prior models do not leverage spatial or temporal correlations between stations.Some station-level approaches instead fit separate models, including random forests, linear regressions, and linear mixed models.
  • Graph convolution: Graph convolutional neural networks extend convolution to irregular domains by using graph structures and adjacency matrices to encode relations among signals.Graph spectral filtering operates through graph transforms and localized filters.
  • Graph convolution: Conventional GCNNs require an artificially created graph and predefined adjacency matrix, whose quality strongly affects performance.This requirement is problematic when heterogeneous station relationships are difficult to specify in advance.

3. Methodology

The methodology reviews graph convolution and spectral filtering, considers several ways to define bike-sharing network adjacency, and then introduces a data-driven approach for learning the graph spectral filter.

  • GCNN framework: The methodology first describes GCNNs and graph spectral filtering.This establishes the graph-based convolution framework used for the demand prediction model.
  • Graph construction: It then discusses multiple approaches for defining an adjacency matrix in a bike-sharing network.These alternatives provide predefined graph structures for representing station relationships.
  • Data-driven filtering: Finally, the study introduces a data-driven method for learning the graph spectral filter.The learned filter avoids relying exclusively on manually specified graph relationships.

3.1. Graph Convolutional Neural Network

The GCNN represents station signals on a graph and uses localized spectral convolutions to combine information across connected vertices. Layer-wise graph propagation transforms these signals into station-level predictions.

  • A graph G=(V,x,E,A) represents stations as vertices, station signals as features, edges as connections, and A as the adjacency matrix.
  • The normalized graph Laplacian is constructed from the adjacency matrix and degree matrix, then decomposed into eigenvalues and orthonormal eigenvectors.
  • 3.1.1. Spectral Convolution on Graph: Spectral convolution applies a filter defined as a function of the Laplacian eigenvalues to graph signals.
  • 3.1.1. Spectral Convolution on Graph: Polynomial filters express convolution through powers of the Laplacian, producing a K-localized filter that combines signals within K graph steps.
  • 3.1.2. Layer-wise Calculation: The simplified first-order convolution adds self-connections, normalizes the adjacency matrix by vertex degrees, and applies trainable feature transformations.
  • 3.1.2. Layer-wise Calculation: Across layers, graph convolution and trainable weights with ReLU activations propagate features from input signals to output predictions for all stations.

3.2. GCNN with Pre-defined Adjacency Matrix

The pre-defined-adjacency GCNN constructs station graphs from four bike-sharing data relationships: spatial distance, demand, trip duration, and temporal demand correlation. Each relationship is thresholded to define binary station connections.

  • Four data matrices quantify station correlations and provide corresponding adjacency matrices for GCNN models.
  • Spatial Distance Matrix: The SD graph connects stations whose spherical distance, computed from latitude and longitude, is below a pre-defined threshold.
  • Demand Matrix: The DE graph connects station pairs whose total bidirectional demand exceeds a pre-defined threshold.
  • Average Trip Duration Matrix: The ATD graph connects stations when their average trip duration is below a pre-defined threshold, representing short average trips.
  • Demand Correlation Matrix: The DC graph uses Pearson correlations between hourly station-demand series and connects pairs whose correlation exceeds a threshold.

3.3. GCNN with Data-Driven Graph Filter

GCNN-DDGF replaces a fixed adjacency structure with a trainable symmetric graph filter that learns heterogeneous station correlations from data. Its recurrent variant adds an LSTM block to model temporal dependencies before predicting next-hour demand.

  • A single pre-defined metric may not encode heterogeneous station correlations, motivating a trainable data-driven graph filter.
  • Data-driven Graph Filter: The DDGF is a symmetric matrix of trainable filter parameters learned during model training.
  • Data-driven Graph Filter: GCNN-DDGF uses the learned filter to capture hidden heterogeneous pairwise station correlations and improve demand prediction performance.
  • Model Architectures: GCNNreg-DDGF contains convolution and feedforward blocks, while its recurrent counterpart adds an LSTM-based recurrent block.
  • GCNNrec-DDGF: In GCNNrec-DDGF, each historical signal is multiplied by the learned filter, passed through recurrent cells, and mapped by a feedforward block to next-step station demands.
  • GCNNrec-DDGF: The recurrent architecture is controlled by the number of time steps T and hidden units d in each LSTM cell.

4. Citi Bike-Sharing Demand Dataset

The study uses a filtered New York City Citi Bike dataset covering 272 persistent stations and more than 28 million transactions from 2013 to 2016. Hourly demand varies substantially across stations, while spatial distance, trip duration, and demand correlations reveal distinct network patterns.

  • Dataset and preprocessing: The dataset contains over 28 million Citi Bike transactions from 07/01/2013 through 06/30/2016 across 272 stations.
  • Dataset and preprocessing: Stations were retained only if they existed throughout all three years and had at least 26,304 total three-year trips.
  • Dataset and preprocessing: Each station contributes 26,304 hourly demand values, split into 22,304 training, 2,000 validation, and 2,000 testing observations.
  • Demand characteristics: Some stations average more than ten bikes per hour, and higher average demand generally corresponds to greater standard deviation.
  • Spatial and trip-duration patterns: Average trip duration is about 10 minutes within 1 mile and exceeds 45 minutes beyond 5 miles, using station-coordinate distances rather than actual trip distances.
  • Demand correlations: Hourly station demands are highly correlated, with no negative coefficients, a correlation mean of 0.50, and 0.5% of coefficients near 1.

5. Model Development and Results

The study develops GCNN models for next-hour station-level demand using recent station-demand histories and compares learned and predefined graph structures. GCNNrec-DDGF performs best on the testing criteria, while graph analysis shows that the learned filter captures both known and hidden station relationships.

  • Data and input construction: The input uses demand from recent hours to predict the next hour’s demand vector across 272 stations.Records are normalized between 0 and 1, and demand periodicity is not considered.
  • Model development: Six GCNN variants use spatial distance, demand, average trip duration, demand correlation, or learned data-driven adjacency structures.The two DDGF architectures differ by whether they include a recurrent LSTM block.
  • Validation results: 2.97 and 2.46 are the validation RMSEs of the two GCNN-DDGF models, compared with 3.39 for GCNN-SD and 3.36 for GCNN-DE.The DDGF models learn the optimal graph filter directly from the data.
  • Testing results: 2.12 RMSE, 1.26 MAE, and 0.75 R2 make GCNNrec-DDGF the best testing model, with GCNNreg-DDGF second best.GCNNrec-DDGF also has RMSE of 2.58 during 7:00 AM–9:00 PM.
  • Testing results: 3.44 RMSE, 2.21 MAE, and 0.35 R2 make GCNN-ATD the poorest model, showing that adjacency-matrix quality strongly affects GCNN performance.The benchmark models also perform poorly when they omit station correlations or temporal dependencies.
  • Graph analysis: The learned DDGF resembles spatial, demand, and correlation matrices while also encoding heterogeneous connections unexplained by those matrices.It assigns substantial weights to some distant stations, extending beyond purely spatial proximity.

6. Conclusions and Future Research Directions

The paper introduces GCNN-DDGF architectures that learn hidden heterogeneous station correlations, with GCNNrec-DDGF adding recurrent modeling of temporal demand dependencies. GCNNrec-DDGF outperforms the tested alternatives, while graph analysis reveals both known and previously hidden station relationships.

  • The paper proposes GCNNreg-DDGF and GCNNrec-DDGF for station-level hourly demand prediction in large-scale bike-sharing networks.
  • GCNN-DDGF addresses the limitation that GCNN performance relies on a pre-defined graph structure by automatically capturing heterogeneous pairwise station correlations.
  • GCNNrec-DDGF adds an LSTM recurrent block to capture temporal dependencies in bike-sharing demand series.
  • GCNNrec-DDGF outperforms four GCNNs with predefined adjacency matrices and seven benchmark models.
  • Analysis of the learned DDGF shows information similar to the SD, DE, and DC matrices alongside hidden station correlations absent from those matrices.
  • Future work includes adding weather and social-event variables, developing online hyperparameter adaptation, modeling uncertainty, and extending the graph filter to sparse directed graphs.
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