Spatio-Temporal Graph Neural Network for Urban Spaces: Interpolating Citywide Traffic Volume

TL;DR

GNNUI introduces a spatio-temporal graph neural network tailored for urban traffic interpolation under sparse sensor coverage, using a masking-based training regime, node features, and a zero-inflated negative binomial loss to model zero-heavy urban distributions. It systematically compares fixed adjacency matrices and demonstrates that a binary adjacency structure yields the strongest performance across two large urban benchmarks (Berlin Strava and NYC taxi), while maintaining robustness as sensor coverage drops from 90% to 1%. The work shows that incorporating rich urban features and careful loss design improves interpolation quality (low KL divergence; accurate zero handling) and remains competitive with substantially less training data than baselines like IGNNK and XGBoost. These findings support practical deployment in real-world cities and highlight strategic sensor placement and urban feature integration as key design choices for scalable, citywide traffic estimation.

Abstract

Graph Neural Networks have shown strong performance in traffic volume forecasting, particularly on highways and major arterial networks. Applying them to urban settings, however, presents unique challenges: urban networks exhibit greater structural diversity, traffic volumes are highly overdispersed with many zeros, the best way to account for spatial dependencies remains unclear, and sensor coverage is often very sparse. We introduce the Graph Neural Network for Urban Interpolation (GNNUI), a novel urban traffic volume estimation approach. GNNUI employs a masking algorithm to learn interpolation, integrates node features to capture functional roles, and uses a loss function tailored to zero-inflated traffic distributions. In addition to the model, we introduce two new open, large-scale urban traffic volume benchmarks, covering different transportation modes: Strava cycling data from Berlin and New York City taxi data. GNNUI outperforms recent, some graph-based, interpolation methods across metrics (MAE, RMSE, true-zero rate, Kullback-Leibler divergence) and remains robust from 90% to 1% sensor coverage. For example, on the Strava dataset, the MAE increases only from 7.1 to 10.5, and on the Taxi dataset, from 23.0 to 40.4. These results demonstrate that GNNUI maintains strong performance despite extreme data scarcity, a common condition in real-world urban settings. We also examine how graph connectivity choices influence model accuracy.

Figures (8)

• Figure 1: Urban street networks (left) and corresponding distributions of street-level traffic volume (right). Street segments used for training and validation are shown in one color, and test segments in another, illustrating the spatial split applied in our experiments. Dots indicate the locations of the currently employed traffic and cycling sensors, which are displayed for reference only. Our analyses do not rely on these sensors; instead, we use trajectory-based data from taxi trips (New York) and Strava cycling records (Berlin). The sensors are shown solely to illustrate the sparsity of conventional urban monitoring infrastructure.
• Figure 2: The figure illustrates how the interpolation is performed, whether the entire graph is leveraged in training. Across both figures, the seen locations are street segments $\{1,\cdots, 7\}$, and the unseen locations are street segments $\{8, 9\}$. Depicted are further the node feature training data $X$, the target variable training data $T$, the time window starting at $t$ of size $h$, as well as the node features of the unseen nodes $X_t^u$, the node features of the seen nodes $X_t^s$ and the corresponding target variables $T_t^u$ and $T_t^s$.
• Figure 3: The graph and weight matrix are constructed based on the underlying street network, where each street segment is represented by a sensor location. The sensor locations form the nodes of the graph. Nodes are either fully connected (left), with edge weights representing distance or similarity (see Equations \ref{['eq:graphweights_distance']} and \ref{['eq:graphweights_similarity']}), or connected only to neighbouring nodes (right), using a binary adjacency matrix where weights are 1 for neighboring segments and 0 otherwise (see Equation \ref{['eq:graphweights_binary']}).
• Figure 4: Performance of GNNUI, IGNNK, and XGBoost under varying levels of data scarcity. Notice that there is a structural break on the x-axis at 10%.
• Figure 5: The figure corresponds to Figure \ref{['fig:explanaion_interpolation']} in the main text - but here in a setup, where the prediction step lies in the future of the training.