随机块体模型是离散表面张力
Stochastic Block Models are a Discrete Surface Tension
摘要：
网络，代表代理人和他们之间的相互作用，出现在无数的应用在整个科学，工程，甚至人文学科。为了理解网络中的大规模结构，一个常见的任务是将网络的节点聚类成称为“社区”的集合，这样社区内的连接密集，但社区之间的连接稀疏。一种流行的和统计学原理的方法来执行这样的聚类是使用一个家庭的生成模型称为随机块模型（SBM）。在本文中，我们表明，最大似然估计在SBM是一个著名的连续表面张力问题，在冶金中的应用所产生的网络模拟。为了说明这种关系的效用，我们实现了三个表面张力算法的网络模拟，我们成功地恢复了人工合成网络中的种植社区结构，并对我们从高光谱视频构建的经验网络产生了迷人的见解。
英文摘要：
Networks, which represent agents and interactions between them, arise in myriad applications throughout the sciences, engineering, and even the humanities. To understand large-scale structure in a network, a common task is to cluster a network's nodes into sets called "communities", such that there are dense connections within communities but sparse connections between them. A popular and statistically principled method to perform such clustering is to use a family of generative models known as stochastic block models (SBMs). In this paper, we show that maximum likelihood estimation in an SBM is a network analog of a well-known continuum surface-tension problem that arises from an application in metallurgy. To illustrate the utility of this relationship, we implement network analogs of three surface-tension algorithms, with which we successfully recover planted community structure in synthetic networks and which yield fascinating insights on empirical networks that we construct from hyperspectral videos.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
