论文标题
基于光谱信息的大图集的样品特征平均值的理论分析和计算
Theoretical analysis and computation of the sample Frechet mean for sets of large graphs based on spectral information
论文作者
论文摘要
为了表征一组图的位置（平均值，中位数），需要一个适合度量空间的中心性概念，因为图集不是欧几里得空间。一种标准方法是考虑特征平均值。在这项工作中，我们为一组图表配备了由其各自邻接矩阵的特征值之间的规范定义的假数计。与编辑距离不同，该伪计揭示了多个尺度的结构变化，并且非常适合研究图值数据的各种统计问题。我们描述了一种算法，用于计算一组使用此伪计的固定尺寸的一组未取得的未加权图的样品特征平均值的近似值。
To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that is adapted to metric spaces, since graph sets are not Euclidean spaces. A standard approach is to consider the Frechet mean. In this work, we equip a set of graphs with the pseudometric defined by the norm between the eigenvalues of their respective adjacency matrix. Unlike the edit distance, this pseudometric reveals structural changes at multiple scales, and is well adapted to studying various statistical problems for graph-valued data. We describe an algorithm to compute an approximation to the sample Frechet mean of a set of undirected unweighted graphs with a fixed size using this pseudometric.
