Multifractal Approach to the Analysis of Crime Dynamics: Results for Burglary in San Francisco

Abstract

This paper provides evidence of fractal, multifractal and chaotic behaviors in urban crime by computing key statistical attributes over a long data register of criminal activity. Fractal and multifractal analyses based on power spectrum, Hurst exponent computation, hierarchical power law detection and multifractal spectrum are considered ways to characterize and quantify the footprint of complexity of criminal activity. Moreover, observed chaos analysis is considered a second step to pinpoint the nature of the underlying crime dynamics. This approach is carried out on a long database of burglary activity reported by 10 police districts of San Francisco city. In general, interarrival time processes of criminal activity in San Francisco exhibit fractal and multifractal patterns. The behavior of some of these processes is close to 1/f noise. Therefore, a characterization as deterministic, high-dimensional, chaotic phenomena is viable. Thus, the nature of crime dynamics can be studied from geometric and chaotic perspectives. Our findings support that crime dynamics may be understood from complex systems theories like self-organized criticality or highly optimized tolerance.

Information Dynamics in Urban Crime

“…Other approaches related to the detection of chaos in time series may consulted in [ 61 ]. This analysis can be complemented from a statistical perspective with an indicator of self-similarity and predictability, such as the Hurst exponent [ 14 , 29 , 37 ]. Characteristic scales : In addition to the results produced from previous stages, spatio-temporal scales are suggested to approximate the understanding of the phenomenon.…”

“…Methods such as kernel density estimation (KDE) and self-exciting point processes (SPPs) among others have been considered in this context [ 13 ]. However, these tools usually base their assumptions on linearity, independence, stationarity, and ergodicity, which are not necessarily properties of criminal phenomena [ 14 ]. Additionally, statistical biases appear when using these approaches because of MAUP and CAP problems.…”

“…Two new approaches that refocus the crime patterning problem were proposed in [ 14 , 24 ]. The former considers an entropy analysis of crime regions across several cities, revealing that crime concentrates dynamically.…”

“…Other approaches related to the detection of chaos in time series may consulted in [61]. This analysis can be complemented from a statistical perspective with an indicator of self-similarity and predictability, such as the Hurst exponent [14,29,37].…”

Aportes al estudio de la dinámica espacio-temporal del crimen urbano desde una perspectiva de sistemas complejos

“…El análisis de estos patrones geométricos ha sido usual en la teoría de autómatas celulares [8], [91]. El autor ha introducido recientemente el termino de Patrón de producción informacional para referirse a estos patrones cuando se observan en el análisis de la información que produce un conjunto de variables de estado [92]. La caracterización estadística de la aparición de los patrones informacionales sobre el soporte se convierte en una posibilidad de trabajo que se dejará abierta.…”