A Quotient Space Formulation for Generative Statistical Analysis of Graphical Data
A Quotient Space Formulation for Generative Statistical Analysis of Graphical Data
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DOI：
10.1007/s10851-021-01027-1
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发表时间：
2021-03
影响因子：
2
通讯作者：
Xiaoyang Guo;A. Srivastava;S. Sarkar
中科院分区：
文献类型：
--
作者：
Xiaoyang Guo;A. Srivastava;S. Sarkar
涉及多个相关随机变量的复杂分析通常会产生图形模型--一组节点表示感兴趣的变量，相应的边表示节点之间的统计交互作用。为了开发图形数据的统计分析，特别是向生成式建模，人们需要用于匹配和比较图形的数学表示和度量，以及随后的工具，如测地线、均值和协方差。本文利用商结构来开发计算这些量的有效算法，从而产生有用的统计工具，包括主成分分析、统计检验和建模。我们使用来自几个问题领域的数据集来证明这个框架的有效性，这些领域包括字母、生化结构和社会网络。
Complex analyses involving multiple, dependent random quantities often lead to graphical models—a set of nodes denoting variables of interest, and corresponding edges denoting statistical interactions between nodes. To develop statistical analyses for graphical data, especially towards generative modeling, one needs mathematical representations and metrics for matching and comparing graphs, and subsequent tools, such as geodesics, means, and covariances. This paper utilizes a quotient structure to develop efficient algorithms for computing these quantities, leading to useful statistical tools, including principal component analysis, statistical testing, and modeling. We demonstrate the efficacy of this framework using datasets taken from several problem areas, including letters, biochemical structures, and social networks.