发表机构
Middlebury College（明德学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文综述了用凸函数度量多样性与隔离的方法，将隔离形式化为局部到全局的多样性比较，提出Jensen信息作为度量，并展示了三种纳入空间结构的方式。
AI 中文摘要
隔离度量问题旨在定量描述人口属性（如种族、民族、教育水平或收入）与区分性特征（如组织层级、学区或空间位置）之间的相互作用。本文主要是一篇说明性文章，对度量隔离的一种数学方法进行了主观性综述。我们首先介绍关于多样性的一些基本直觉，并通过概率单纯形上的凸函数框架将其统一。将隔离形式化为多样性度量的局部到全局比较，从而得到以Jensen信息作为隔离度量的一般类别。我们描述并计算性地展示了将空间结构纳入隔离度量的三种方式：空间平滑、聚合和局部Jensen信息。最后，我们为未来工作提出若干建议。
英文摘要
The problem of segregation measurement is to quantitatively describe the interaction of a population's attributes (such as race, ethnicity, education level, or income) with a separating distinction (such as organizational rank, school district, or spatial location). This primarily expository article gives an opinionated tour of one mathematical approach to measuring segregation. We begin with some basic intuitions about diversity and unify these through the framework of convex functions on the probability simplex. Formalizing segregation as a local-to-global comparison of diversity measures, resulting in the general class of Jensen informations as segregation measurements. We describe and computationally illustrate three ways to incorporate spatial structure into segregation measurements: spatial smoothing, aggregation, and local Jensen information. We close with several suggestions for future work.
