Anchored k-medoids: a novel adaptation of k-medoids further refined to measure long-term instability in the exposure to crime

Abstract

Longitudinal clustering techniques are widely deployed in computational social science to delineate groupings of subjects characterized by meaningful developmental trends. In criminology, such methods have been utilized to examine the extent to which micro places (such as streets) experience macro-level police-recorded crime trends in unison. This has largely been driven by a theoretical interest in the longitudinal stability of crime concentrations, a topic that has become particularly pertinent amidst a widespread decline in recorded crime. Recent studies have tended to rely on a generic implementation k-means to unpick this stability, with little consideration for its theoretical suitability. This study makes two methodological contributions. First, it demonstrates the application of k-medoids to study longitudinal crime concentrations, and second, it develops a novel ‘anchored k-medoids’ (ak-medoids), a bespoke clustering method specifically designed to meet the theoretical requirements of micro-place investigations into long-term stability. Using both simulated data and 15-years of police-recorded crime data from Birmingham, England, we compare the performances of k-medoids against ak-medoids. We find that both methods highlight instability in the exposure to crime over time, but the consistency and contribution of cluster solutions determined by ak-medoids provide insight overlooked by k-medoids, which is sensitive to short-term fluctuations and subject starting points. This has important implications for the theories said to explain longitudinal crime concentrations, and the law enforcement agencies seeking to offer an effective and equitable service to the public.