论文标题
电压的结构
Structure from Voltage
论文作者
论文摘要
有效的电阻（ER）是审问图形结构的有吸引力的方法。它是计算图形laplacian的特征向量的替代方法。图形拉普拉斯人用于在高维数据中找到低维结构。在这里，基于ER的分析比基于EIGN-QUETORD的方法具有优势。不幸的是，冯·卢克斯堡（Von Luxburg）等人。 （2010年）表明，当顶点对应于公制空间上分布的样本时，遥远点之间的ER的极限会收敛到琐碎的数量，而该量没有关于图形结构的信息。我们表明，通过在图形中使用缩放电阻，$ n $顶点$ n^2 $，一个人获得了有意义的电压和有效电阻的限制。我们还表明，通过将“地面”节点添加到公制图中，一个简单自然的方法可以计算从所选点到所有其他点的所有距离。
Effective resistance (ER) is an attractive way to interrogate the structure of graphs. It is an alternative to computing the eigen-vectors of the graph Laplacian. Graph laplacians are used to find low dimensional structures in high dimensional data. Here too, ER based analysis has advantages over eign-vector based methods. Unfortunately Von Luxburg et al. (2010) show that, when vertices correspond to a sample from a distribution over a metric space, the limit of the ER between distant points converges to a trivial quantity that holds no information about the structure of the graph. We show that by using scaling resistances in a graph with $n$ vertices by $n^2$, one gets a meaningful limit of the voltages and of effective resistances. We also show that by adding a "ground" node to a metric graph one gets a simple and natural way to compute all of the distances from a chosen point to all other points.
