In this study, we investigate the potential for optimizing hot spot patrol routes through density ridge estimation. We explore the application of an extended version of the subspace-constrained mean shift algorithm by using 2018 and 2019 Part I crime data from Chicago. Ultimately, the goal of mapping hot spots is to show concentrations of crime, thus targeting the epicenters only focuses on one problem area. For this reason, we refine patrol optimization to focus on the critical ridges in hot spots. In doing so, we extract density ridges of 2018 to early 2019 Part I crime incidents from Chicago to demonstrate that nonlinear mode-following ridges agree with broader kernel density estimations. We create multi-run confidence intervals and show that our patrol templates cover around 94% of incidents for 0.1-mile envelopes around ridges, and deliver evidence that ridges following crime densities enhances the efficiency of patrols. Our post-hoc tests show the stability of ridges, thus offering an alternative patrol route option that is effective and efficient.

在这项研究中，我们调查了通过密度脊估算来优化热点巡逻路线的潜力。我们使用来自芝加哥的2018年和2019年第I部分犯罪数据，探索了子空间约束均值漂移算法的扩展版本的应用。最终，绘制热点图的目标是显示犯罪的集中程度，因此，以震中为目标的焦点仅集中在一个问题领域。因此，我们优化巡逻优化以将重点放在热点的关键山脊上。在此过程中，我们从芝加哥提取了2018年至2019年初第I部分犯罪事件的密度脊，以证明遵循非线性模式的脊与更广泛的内核密度估计相符。我们创建了多次运行置信区间，并表明我们的巡逻模板涵盖了围绕脊线0.1英里的信封的约94％的事件，并提供证据表明犯罪密度后的山脊可提高巡逻效率。我们的事后测试显示了山脊的稳定性，因此提供了有效且高效的替代巡逻路线选择。