Theoretical analysis and computation of the sample Fréchet mean of sets of large graphs for various metrics

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-03-28 DOI:10.1093/imaiai/iaad002

Daniel Ferguson, F. G. Meyer

引用次数: 0

Abstract

To characterize the location (mean, median) of a set of graphs, one needs a notion of centrality that has been adapted to metric spaces. A standard approach is to consider the Fréchet mean. In practice, computing the Fréchet mean for sets of large graphs presents many computational issues. In this work, we suggest a method that may be used to compute the Fréchet mean for sets of graphs which is metric independent. We show that the technique proposed can be used to determine the Fréchet mean when considering the Hamming distance or a distance defined by the difference between the spectra of the adjacency matrices of the graphs.

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各种指标的大图集样本均值的理论分析与计算

为了描述一组图的位置(平均值，中位数)，我们需要一个适用于度量空间的中心性概念。一种标准的方法是考虑fr切特平均值。在实践中，计算大型图集的fr平均值会出现许多计算问题。在这项工作中，我们提出了一种方法，可用于计算与度量无关的图集的fr平均值。我们证明，当考虑汉明距离或由图的邻接矩阵的谱之间的差定义的距离时，所提出的技术可以用来确定fr平均。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.