刚性图形对齐
Rigid Graph Alignment
摘要：
图形数据库一直是重要研究和开发的主题。模块化、中心化、对齐和集群等问题已经在各种应用环境中得到了形式化和解决。在本文中，我们专注于数据库的应用程序中，图形有一个空间的基础，我们称之为刚性图。这样的图中的节点具有相对于它们的图邻居的优选位置。这种图的示例包括大生物分子、人脑的功能连接体和移动终端/传感器通信日志的抽象。当分析这样的网络时，重要的是要考虑边的长度;例如，当通过图形对齐来识别保守模式时，除了拓扑相似性之外，重要的是保守边具有相关的长度。与拓扑图对齐的大量工作相比，刚性图对齐同时对齐网络以及以边长为特征的底层结构。我们制定的问题，并提出了一个元算法的基础上期望最大化，交替对齐网络和结构。我们证明，我们的元算法显着提高了在目标应用程序的比对质量，相比单独的拓扑或结构对齐。我们应用刚性图形对齐功能的大脑网络来自20个主题从人类连接组计划（HCP）数据库，并显示出超过两倍的质量增加的对齐状态的最先进的拓扑对齐。我们通过对合成图的研究来评估与输入数据集相关的各种参数的影响，在合成图中我们充分表征了我们方法的性能。我们的结果广泛适用于其他应用程序和抽象网络，可以嵌入度量空间-例如，通过光谱嵌入
英文摘要：
Graph databases have been the subject of significant research and development. Problems such as modularity, centrality, alignment, and clustering have been formalized and solved in various application contexts. In this paper, we focus on databases for applications in which graphs have a spatial basis, which we refer to as rigid graphs. Nodes in such graphs have preferred positions relative to their graph neighbors. Examples of such graphs include abstractions of large biomolecules, functional connectomes of the human brain, and mobile device/ sensor communication logs. When analyzing such networks it is important to consider edge lengths; e.g., when identifying conserved patterns through graph alignment, it is important for conserved edges to have correlated lengths, in addition to topological similarity. In contrast to a large body of work on topological graph alignment, rigid graph alignment simultaneously aligns the network, as well as the underlying structure as characterized by edge lengths. We formulate the problem and present a meta-algorithm based on expectation-maximization that alternately aligns the network and the structure. We demonstrate that our meta-algorithm significantly improves the quality of alignments in target applications, compared to topological or structural aligners alone. We apply rigid graph alignment to functional brain networks derived from 20 subjects drawn from the Human Connectome Project (HCP) database, and show over a two-fold increase in quality of alignment over state of the art topological aligners. We evaluate the impact of various parameters associated with input datasets through a study on synthetic graphs, where we fully characterize the performance of our method. Our results are broadly applicable to other applications and abstracted networks that can be embedded in metric spaces -- e.g., through spectral embeddings.
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