离散集作为连续度量空间的概率嵌入
Probabilistic Embedding Of Discrete Sets As Continuous Metric Spaces
摘要：
定义在离散集$V$上的任何对称仿射函数$w: V\times V \to \mathbb{R}_+$都导出$V$上的欧氏空间结构。特别地，由亲和（或邻接）矩阵指定的无向图可以被认为是度量拓扑空间。我们已经计算了一个链，一个多面体，和一个有限的二维晶格的概率轨迹的视觉表示。
英文摘要：
Any symmetric affinity function $w: V\times V \to \mathbb{R}_+$ defined on a discrete set $V$ induces Euclidean space structure on $V$. In particular, an undirected graph specified by an affinity (or adjacency) matrix can be considered as a metric topological space. We have calculated the visual representations of the probabilistic locus for a chain, a polyhedron, and a finite 2-dimensional lattice.
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。
