# Length- and Usage-Weighted Indices for Representative Route Extraction from Trajectory Data

## TL;DR

This paper introduces new weighted indices to improve the extraction of representative routes from vehicle trajectory data, reducing bias from short links and enhancing route grouping stability.

## Contribution

The novel weighted indices (Lw, ALw, Ow) recalibrate route similarity metrics to reduce short-link bias and improve stability in heterogeneous urban networks.

## Key findings

- Weighted indices reduce structural variance by 20–30% and enhance route grouping stability.
- The weighted framework improves VKT estimation, congestion diagnostics, and large-scale trajectory analytics.
- Refined trajectory similarity metrics support accurate analysis and decision-making in urban mobility management.

## Abstract

What are the main findings?
Three weighted indices (Lw, ALw, Ow) mitigate short-link bias and recalibrate overlap effects.Weighted indices reduce structural variance by 20–30% and enhance route grouping stability, and Spearman correlations (ρ = 0.863, 0.071, 0.189) confirm robust calibration without distortion.

Three weighted indices (Lw, ALw, Ow) mitigate short-link bias and recalibrate overlap effects.

Weighted indices reduce structural variance by 20–30% and enhance route grouping stability, and Spearman correlations (ρ = 0.863, 0.071, 0.189) confirm robust calibration without distortion.

What is the implication of the main finding?
More reliable representative links/paths can improve VKT estimation, congestion diagnostics, and large-scale trajectory analytics in heterogeneous urban networks.The weighted framework is practical and reproducible, supporting integration into ITS and navigation services for data-driven planning and policy.

More reliable representative links/paths can improve VKT estimation, congestion diagnostics, and large-scale trajectory analytics in heterogeneous urban networks.

The weighted framework is practical and reproducible, supporting integration into ITS and navigation services for data-driven planning and policy.

This paper introduces weighted indices—link passing ratio adjusted by length, average link usage ratio weighted by frequency and length, and path overlap weighted by length and usage—to improve representative path extraction from large-scale vehicle trajectory data. Conventional indices often overstate the representativeness of short links, leading to biased path similarity and unstable grouping. The proposed indices explicitly down-weight short segments such that routes with many small links no longer appear falsely similar. Using data from 18,205 real-world urban trajectories, the weighted indices reduced short-link bias by 20–30% and increased the stability of representative path grouping by 15–30% compared with conventional metrics. Distribution of comparisons confirmed that the weighted indices consistently capture the structural characteristics of real-world GPS-based trajectories, reflecting stable link usage and overlap patterns. These improvements were evaluated on a refined subset comprising 12,540 link-level observations and 8320 route pair comparisons, ensuring statistical robustness and consistency. These improvements are expected to enhance downstream applications such as estimations of vehicle kilometers traveled, congestion diagnostics, and sensor-based mobility services. The findings demonstrate that refining trajectory similarity metrics at the link level has direct implications for intelligent transportation systems, supporting accurate analysis and practical decision-making in large-scale urban mobility management.