A Hybrid Inductive-Transductive Network for Traffic Flow Imputation on Unsampled Locations

TL;DR

<3-5 sentence high-level summary> Problem: imputing traffic flow at unobserved locations is difficult due to sparse sensing and heterophily. Approach: HINT combines transductive speed modeling with inductive flow imputation using a Transformer-based inductive spatial module, FiLM-conditioned GCN, static/dynamic features from OSM and simulations, and a novel INDU-TRANSDUCTIVE training strategy with hard-node mining and noise injection. Findings: across MOW, Torino, and Essen, HINT consistently outperforms existing inductive baselines, with notable gains when using simulated and external features, and robustness on heterophilous networks. Impact: enables accurate, scalable flow imputation for dynamic urban networks and supports better planning and sensing strategies in smart cities.

Abstract

Accurately imputing traffic flow at unsensed locations is difficult: loop detectors provide precise but sparse measurements, speed from probe vehicles is widely available yet only weakly correlated with flow, and nearby links often exhibit strong heterophily in the scale of traffic flow (e.g., ramps vs. mainline), which breaks standard GNN assumptions. We propose HINT, a Hybrid INductive-Transductive Network, and an INDU-TRANSDUCTIVE training strategy that treats speed as a transductive, network-wide signal while learning flow inductively to generalize to unseen locations. HINT couples (i) an inductive spatial transformer that learns similarity-driven, long-range interactions from node features with (ii) a diffusion GCN conditioned by FiLM on rich static context (OSM-derived attributes and traffic simulation), and (iii) a node-wise calibration layer that corrects scale biases per segment. Training uses masked reconstruction with epoch-wise node sampling, hard-node mining to emphasize difficult sensors, and noise injection on visible flows to prevent identity mapping, while graph structure is built from driving distances. Across three real-world datasets, MOW (Antwerp, Belgium), UTD19-Torino, and UTD19-Essen, HINT consistently surpasses state-of-the-art inductive baselines. Relative to KITS, HINT reduces MAE on MOW by $\approx42$% with basic simulation and $\approx50$% with calibrated simulation; on Torino by $\approx22$%, and on Essen by $\approx12$%. Even without simulation, HINT remains superior on MOW and Torino, while simulation is crucial on Essen. These results show that combining inductive flow imputation with transductive speed, traffic simulations and external geospatial improves accuracy for the task described above.

Figures (7)

• Figure 1:
• Figure 2: Pearson correlation values boxplot
• Figure 3: Speed-Flow Diagrams: Comparison between a motorway (Location ID 721) and a motorway link (Location ID 122). They demonstrate high speed stability even at higher traffic flows. These diagrams are plotted based on the whole duration of the dataset.
• Figure 4: Traffic flow plot on two nearby sections. Even though the traffic flow mostly follows a similar trend, the scale varies significantly between the two.
• Figure 5: UTD19-Torino loop detector locations used in this study.