A Unified Graph Theory Approach: Clustering and Learning in Criminal Data

Crime report clustering plays a critical role in modern law enforcement, enabling the identification of patterns and trends essential for proactive policing. However, traditional clustering approaches face significant challenges with the complex, unstructured nature of crime reports and their inherent sparse relationships. While graph-based clustering shows promise, issues of noise sensitivity and data sparsity persist. This study introduces a unified approach integrating spectral graph-based clustering with Graph Convolutional Networks (GCN) to address these challenges. The proposed approach encompasses data collection, preprocessing, linguistic feature extraction, vectorization, graph construction, graph learning, and clustering to effectively capture the intricate similarities between crime reports. The proposed approach achieved significant improvements over existing methods: a Silhouette Score of 0.77, a Davies–Bouldin Index of 0.51, and consistent performance across varying dataset sizes (100–1000 nodes). These results demonstrate the potential for enhanced crime pattern detection in law enforcement operations.