[Paper Review] Modularity-Based Clustering for Network-Constrained Trajectories

Mohamed Khalil El Mahrsi, Fabrice Rossi|arXiv (Cornell University)|May 10, 2012

Data Management and Algorithms7 references3 citations

TL;DR

This paper proposes a modularity-based graph clustering approach for network-constrained trajectories, modeling trajectories as bags of weighted road segments using TF-IDF-inspired spatial weights and cosine similarity. The method constructs a similarity graph and applies modularity-optimization hierarchical clustering, achieving significantly higher intraclass overlap (up to 4,823) than classic hierarchical clustering, indicating more cohesive and meaningful trajectory clusters.

ABSTRACT

We present a novel clustering approach for moving object trajectories that are constrained by an underlying road network. The approach builds a similarity graph based on these trajectories then uses modularity-optimization hiearchical graph clustering to regroup trajectories with similar profiles. Our experimental study shows the superiority of the proposed approach over classic hierarchical clustering and gives a brief insight to visualization of the clustering results.

Motivation & Objective

• Address the challenge of clustering trajectories constrained by road networks to uncover global movement patterns.
• Overcome limitations of existing density-based and Euclidean-space clustering methods that do not account for network constraints.
• Develop a method that groups entire trajectories based on shared road segments, preserving trajectory integrity.
• Improve clustering quality by leveraging graph modularity to detect communities of similar trajectories.
• Enable better traffic analysis and decision-making through more coherent and semantically meaningful trajectory clusters.

Proposed method

• Model trajectories as ordered sequences of timestamped road segments on a directed graph representing the road network.
• Assign spatial weights to road segments within each trajectory using a TF-IDF-inspired formula: $\omega_{e,T} = \frac{\mbox{length}(e)}{\sum_{e'\in T}\mbox{length}(e')} \cdot \log\frac{|\mathcal{T}|}{|\{T' : e\in T'\}|}$.
• Compute cosine similarity between trajectories based on their weighted segment profiles: $\mbox{Similarity}(T_i,T_j) = \frac{\sum_e \omega_{e,T_i}\omega_{e,T_j}}{\sqrt{\sum_e \omega_{e,T_i}^2} \sqrt{\sum_e \omega_{e,T_j}^2}}$.
• Construct a weighted, undirected similarity graph $G_{\mbox{Sim}} = (\mathcal{T}, E', W)$, where nodes are trajectories and edges exist only if similarity > 0.
• Apply hierarchical modularity-optimization clustering on the similarity graph to detect communities of similar trajectories.
• Use modularity maximization to guide the hierarchical merging process, favoring clusters with dense internal connections and sparse external links.

Experimental results

Research questions

• RQ1 Can modularity-based graph clustering effectively group network-constrained trajectories into meaningful communities?
• RQ2 How does modularity-optimization clustering compare to classic hierarchical clustering (single, average, full linkage) in terms of cluster cohesion and separation?
• RQ3 To what extent does the proposed method preserve trajectory integrity and detect shared movement patterns across road segments?
• RQ4 How do the clustering results perform in terms of intraclass and interclass overlap of shared road segments?
• RQ5 Can the method detect congestion patterns and movement tendencies that are not visible at the individual trajectory level?

Key findings

• The proposed modularity-optimization clustering achieved the highest intraclass overlap (4,823) among all tested methods when clustering into 648 clusters.
• At 648 clusters, modularity-based clustering achieved an intraclass overlap of 4,823, significantly outperforming average linkage (4,106), full linkage (4,491), and single linkage (881).
• Single linkage hierarchical clustering produced the lowest interclass overlap (35.4) but this was due to highly unbalanced clusters, indicating poor cluster quality.
• As the number of clusters increased, modularity-based clustering maintained stable and superior performance in intraclass overlap compared to other hierarchical methods.
• The method demonstrated consistent superiority in intraclass overlap across all tested cluster counts, indicating more cohesive and semantically meaningful clusters.
• The results suggest that modularity-optimization clustering better captures shared movement patterns and is more suitable for traffic analysis and rerouting decisions.