Objectives: We introduce a new method for reducing crime in hot spots and across cities through ridge estimation. In doing so, our goal is to explore the application of density ridges to hot spots and patrol optimization, and to contribute to the policing literature in police patrolling and crime reduction strategies. Methods: We make use of the subspace-constrained mean shift algorithm, a recently introduced approach for ridge estimation further developed in cosmology, which we modify and extend for geospatial datasets and hot spot analysis. Our experiments extract density ridges of Part I crime incidents from the City of Chicago during the year 2018 and early 2019 to demonstrate the application to current data. Results: Our results demonstrate nonlinear mode-following ridges in agreement with broader kernel density estimates. Using early 2019 incidents with predictive ridges extracted from 2018 data, we create multi-run confidence intervals and show that our patrol templates cover around 94% of incidents for 0.1-mile envelopes around ridges, quickly rising to near-complete coverage. We also develop and provide researchers, as well as practitioners, with a user-friendly and open-source software for fast geospatial density ridge estimation. Conclusions: We show that ridges following crime report densities can be used to enhance patrolling capabilities. Our empirical tests show the stability of ridges based on past data, offering an accessible way of identifying routes within hot spots instead of patrolling epicenters. We suggest further research into the application and efficacy of density ridges for patrolling.

翻译：目标:我们采用一种新的方法减少热点和城市之间的犯罪。我们这样做的目的是探索将密度山脊应用于热点和巡逻优化,并在警察巡逻和减少犯罪战略中促进警务文献。方法:我们利用空间受限制的亚空间平均转移算法,这是最近在宇宙学中进一步发展的一种山脊估计方法,我们为地理空间数据集和热点分析而修改和扩展了这一方法。我们实验从芝加哥市2018年和2019年初提取了第一部分犯罪事件的密度山脊,以展示对当前数据的应用。结果:我们的航行效率显示非线性模式遵循的山脊与更广泛的内核密度估计数一致。我们利用2019年初的以2018年数据提取的预测性平均转移算法,我们创建了多运行的间隔,并表明我们的巡逻模板覆盖了大约94%的事件,用于地理空间数据集周围的0.1英里信封,迅速上升到接近完全的覆盖范围。我们还开发并向研究人员以及从业人员提供一个用户友好和开源的用于当前数据的软件,用以测量快速地理空间空间航行路线。我们用了一个基于历史脊测量的深度测量数据测算。我们可以进一步显示一个基于深度测测测测测测。