发表机构
Texas A&M University（德克萨斯农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出DISCCO贝叶斯框架，仅用距离矩阵和空间邻接图对复杂对象进行空间聚类，通过节点脆弱性参数提供中心性摘要，模拟和实际数据验证了其优于现有方法。
AI 中文摘要
聚类问题日益涉及在空间上观测到的复杂对象，例如分布、矩阵、函数、图像或多变量数据，对于这些对象，对象之间具有科学意义的不相似性通常比对象-响应似然模型更容易指定，并且在计算上更易处理。我们提出DISCCO，一个贝叶斯框架，用于仅使用成对距离矩阵和空间邻接图对空间索引的复杂对象进行聚类，具有广泛的适用性和极少的用户建模要求。该模型将分层的基于距离的似然（考虑簇内紧致性和簇间分离性）与随机空间图划分先验相结合，确保后验簇在空间上是连续的。一个关键的模型特征是节点特定的脆弱性参数集，这些参数诱导重叠的簇内距离之间的依赖性，并在每个推断的簇内提供对象级中心性或边缘性的后验摘要。我们开发了一种部分折叠的马尔可夫链蒙特卡洛算法用于后验推断。使用分布值和矩阵值响应的模拟表明，与现有的距离聚类方法相比，所提出的空间距离聚类框架改善了区域恢复，而脆弱性层提供了可解释的中心性摘要。对休斯顿人口普查区块组种族构成分布和美国西部县级癌症死亡率矩阵的实际应用说明了该方法如何恢复可解释的连续簇和基于脆弱性的中心性地图。
英文摘要
Clustering problems increasingly involve complex objects observed over space, such as distributions, matrices, functions, images, or multivariate data, for which a scientifically meaningful dissimilarity between objects is often easier to specify and computationally more tractable than an object-response likelihood model. We propose DISCCO, a Bayesian framework for clustering spatially indexed complex objects using only a pairwise distance matrix and a spatial adjacency graph, with broad applicability and minimal user modeling requirements. The model combines a hierarchical distance-based likelihood accounting for within-cluster compactness and between-cluster separation with a random spatial graph partition prior, ensuring that posterior clusters are spatially contiguous. A key model feature is a set of node-specific frailty parameters that induce dependence among overlapping within-cluster distances and provide posterior summaries of object-level centrality or peripherality within each inferred cluster. We develop a partially collapsed Markov chain Monte Carlo algorithm for posterior inference. Simulations with distribution- and matrix-valued responses show that the proposed spatial distance-clustering framework improves region recovery relative to existing distance-clustering methods, while the frailty layer provides interpretable centrality summaries. Real applications to Houston Census Block Group racial-composition distributions and Western US county-level cancer mortality matrices illustrate how the method recovers interpretable contiguous clusters and frailty-based centrality maps.
