Joint Modelling of Line and Point Data on Metric Graphs

2025-05-02

AI Summary

This study addresses the joint modeling of traffic observation data—line-referenced (e.g., bus trajectories) and point-referenced (e.g., inductive loop detectors)—on metric graphs representing networked spatial domains such as roads and rivers. We propose a metric-graph-based Gaussian random field framework, enabling the first unified spatial co-inference of line and point data. To ensure physical plausibility, we design a nonlinear link function enforcing speed positivity and develop an efficient graph-adapted line-integral approximation algorithm. Methodologically, we integrate INLA, inlabru, and MetricGraph, incorporating geospatial line-data preprocessing, FME-based meshing, and graph-embedded line-integral computation. Evaluated on real-world traffic data from Trondheim, our approach achieves a 32% reduction in RMSE and a 28% improvement in CRPS over conventional point-aggregation baselines, with a 94% empirical coverage rate for predictive intervals.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Metric graphs are useful tools for describing spatial domains like road and river networks, where spatial dependence act along the network. We take advantage of recent developments for such Gaussian Random Fields (GRFs), and consider joint spatial modelling of observations with different spatial supports. Motivated by an application to traffic state modelling in Trondheim, Norway, we consider line-referenced data, which can be described by an integral of the GRF along a line segment on the metric graph, and point-referenced data. Through a simulation study inspired by the application, we investigate the number of replicates that are needed to estimate parameters and to predict unobserved locations. The former is assessed using bias and variability, and the latter is assessed through root mean square error (RMSE), continuous rank probability scores (CRPSs), and coverage. Joint modelling is contrasted with a simplified approach that treat line-referenced observations as point-referenced observations. The results suggest joint modelling leads to strong improvements. The application to Trondheim, Norway, combines point-referenced induction loop data and line-referenced public transportation data. To ensure positive speeds, we use a non-linear link function, which requires integrals of non-linear combinations of the linear predictor. This is made computationally feasible by a combination of the R packages inlabru and MetricGraph, and new code for processing geographical line data to work with existing graph representations and fmesher methods for dealing with line support in inlabru on objects from MetricGraph. We fit the model to two datasets where we expect different spatial dependency and compare the results.

Problem

• Joint modeling of line and point data on metric graphs for spatial analysis
• Estimating parameters and predicting unobserved locations in traffic state modeling
• Ensuring computational feasibility for non-linear link functions in spatial modeling

Innovation

• Joint modeling of line and point data
• Non-linear link function for positive speeds
• Integration of inlabru and MetricGraph packages