发表机构
Memorial Sloan Kettering Cancer Center; DigITs AI/ML Solutions（纪念斯隆-凯特琳癌症中心; DigITs AI/ML 解决方案）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于Voronoi盆地和马尔可夫链的稠密盆地熵，用于点模式分析，可敏感检测聚类，并在组织病理学中提供互补于传统熵的判别度量。
AI 中文摘要
本文重新审视空间背景下的熵概念，旨在为组织病理学等领域中的点模式分析推导出可计算且可解释的度量。我们讨论了随机点过程假设，如泊松均匀性和简单顺序抑制（SSI），并回顾了点集的Voronoi和Delaunay剖分的既有结果，以评估其为严格的实证假设检验提供零分布的可能性。我们提出（1）一种新颖的“稠密盆地熵”，基于Voronoi盆地上的Ord分布定义，并证明其对聚类敏感；（2）一种相关的马尔可夫链，设计为底层平面域中布朗运动的简化或近似。我们研究了SSI机制和实证数据中稠密盆地熵的界限，并表明马尔可夫链的熵率和谱间隙可产生锐利的判别度量。最后，我们展示了通过将一个集合在另一个集合的马尔可夫不变测度上聚合来实现多集合分析的推广。组织病理学中的模拟和实验表明，我们提出的度量提供了与空间分析中其他熵实例互补的见解。代码可在我们的SMProfiler GitHub上找到：此https URL。
英文摘要
In this paper, we revisit the concept of entropy in the spatial context with the aim of deriving computable and interpretable metrics for point pattern analysis in domains such as histopathology. We discuss stochastic point process assumptions like Poisson homogeneity and Simple Sequential Inhibition (SSI) and review established results for Voronoi and Delaunay tilings of point sets for their potential to provide null distributions for rigorous empirical hypothesis testing. We present (1) a novel "dense basin entropy" defined in terms of the Ord distribution supported on Voronoi basins, which is shown to be sensitive to clustering, and (2) a related Markov chain designed as a simplification or approximation of Brownian motion in the underlying planar domain. We investigate bounds on the dense basin entropy in the SSI regime and in empirical data, and show that the entropy rate and spectral gap of the Markov chain lead to sharp discrimination metrics. Finally, we demonstrate a generalization to multiple-set analysis via aggregation of one set over the Markov invariant measure for another. Simulations and experiments in histopathology show that our proposed metrics offer insights complementary to other instantiations of entropy in spatial analysis. The code can be found on our SMProfiler GitHub: https://github.com/nadeemlab/SMProfiler.
CommentsNeurIPS'26 Main Conference (Accepted)
