Lee Hyekyoung, Chung Moo K, Kang Hyejin, Kim Boong-Nyun, Lee Dong Soo
Department of Nuclear Medicine, Seoul National University, College of Medicine, Seoul, Korea.
Med Image Comput Comput Assist Interv. 2011;14(Pt 2):302-9. doi: 10.1007/978-3-642-23629-7_37.
The difference between networks has been often assessed by the difference of global topological measures such as the clustering coefficient, degree distribution and modularity. In this paper, we introduce a new framework for measuring the network difference using the Gromov-Hausdorff (GH) distance, which is often used in shape analysis. In order to apply the GH distance, we define the shape of the brain network by piecing together the patches of locally connected nearest neighbors using the graph filtration. The shape of the network is then transformed to an algebraic form called the single linkage matrix. The single linkage matrix is subsequently used in measuring network differences using the GH distance. As an illustration, we apply the proposed framework to compare the FDG-PET based functional brain networks out of 24 attention deficit hyperactivity disorder (ADHD) children, 26 autism spectrum disorder (ASD) children and 11 pediatric control subjects.
网络之间的差异通常通过全局拓扑度量的差异来评估，例如聚类系数、度分布和模块性。在本文中，我们引入了一个使用格罗莫夫 - 豪斯多夫（GH）距离来测量网络差异的新框架，该距离常用于形状分析。为了应用GH距离，我们通过使用图滤波将局部连接的最近邻补丁拼接在一起，定义脑网络的形状。然后将网络的形状转换为一种称为单链矩阵的代数形式。随后，单链矩阵用于使用GH距离测量网络差异。作为示例，我们应用所提出的框架来比较24名注意力缺陷多动障碍（ADHD）儿童、26名自闭症谱系障碍（ASD）儿童和11名儿科对照受试者的基于FDG - PET的功能性脑网络。
