A refined k-means clustering approach for optimizing urban police facility placement

This study investigates spatial crime patterns in the municipality of Matelândia, Brazil, with the aim of optimizing the placement of police facilities through an enhanced clustering approach. We use an unsupervised machine learning technique, and we introduce a refined k-Means methodology (called k-Means-c²), which identifies a centroid of centroids representing an optimal location derived from the central points of individual crime clusters. Contrary to the traditional clustering methods that treat all data points equally, our approach incorporates differentiated crime severity by assigning varying levels of importance to four distinct crime types: theft, robbery, domestic violence, and rape. Each crime category is analyzed independently, with tailored cluster counts selected to reflect both frequency and seriousness. A global centroid is then computed to prioritize regions with a higher concentration of severe crimes. We use post-pandemic crime data and empirically analyze whether the current military police base is optimally located. We then examine the potential need for an additional facility and assess the alignment between existing infrastructure and the spatial distribution of criminal activity. This research contributes to data-driven public safety planning by combining crime analytics with facility location optimization, offering a scalable and practical framework for urban law enforcement agencies.