Topological clustering of multilayer networks
Topological clustering of multilayer networks
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DOI：
10.1073/pnas.2019994118
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发表时间：
2021-05
期刊：
影响因子：
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通讯作者：
Monisha Yuvaraj;A. K. Dey;V. Lyubchich;Y. Gel;H. Poor
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文献类型：
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作者：
Monisha Yuvaraj;A. K. Dey;V. Lyubchich;Y. Gel;H. Poor
多层网络聚类应用于关键基础设施的优化孤岛、贸易协定分析和生态相互作用模式监测等不同领域。我们提出了一种基于形状概念的多层网络聚类的观点。通过调用拓扑数据分析的机制，我们首先研究每个节点邻域的形状，然后根据其局部邻域形状的相似程度对节点进行分组。这种方法的重要性可以通过房屋保险对气候风险的可持续性这一新兴问题来看待。拓扑学的观点为更高阶网络特性及其相互作用对复杂网络的分析提供了更系统、更强大、更严格的数学集成的可能性。多层网络继续在许多研究领域获得显著关注，特别是由于它们在模拟相互依赖的系统（如关键基础设施、人脑连接组和社会环境生态系统）方面的高实用性。然而，多层网络的聚类，特别是利用系统实体的高阶交互信息的聚类，仍然处于起步阶段。反过来，高阶连接通常是多层网络应用的关键，如开发关键基础设施的最佳划分，以便在网络物理威胁下隔离不健康的系统组件，以及同时识别受创伤或精神疾病影响的多个大脑区域。本文将拓扑数据分析的概念引入到复杂多层网络的研究中，提出了一种网络聚类的拓扑方法。关键的基本原理是对节点进行分组，而不是基于成对连接模式或在两个单独节点上记录的观察结果之间的关系，而是基于在不同分辨率尺度下其本地邻居的形状相似程度。由于局部节点邻域的形状是使用持久性图的拓扑摘要来量化的，因此我们将这种方法称为使用持久性图（CPD）进行聚类。CPD系统地解释了网络层内部和网络层之间节点交互的重要异构高阶特性，并集成了来自节点邻居的信息。我们通过将CPD应用于一个具有社会重要性的新问题来说明CPD的效用：在房屋保险索赔动态的背景下，住宅物业对天气和气候引起的风险的脆弱性分区。
Significance Multilayer network clustering is used in such diverse areas as optimal islanding of critical infrastructures, analysis of trade agreements, and monitoring ecological interaction patterns. We propose a perspective on multilayer network clustering based on the concept of shape. By invoking the machinery of topological data analysis, we first study a shape of each node neighborhood and then group nodes based on how similar shapes of their local neighborhoods are. The significance of this methodology can be viewed through an emerging problem of sustainability of house insurance to climate risks. The topological perspective opens possibilities for more systematic, robust, and mathematically rigorous integration of higher-order network properties and their interplay to the analysis of complex networks. Multilayer networks continue to gain significant attention in many areas of study, particularly due to their high utility in modeling interdependent systems such as critical infrastructures, human brain connectome, and socioenvironmental ecosystems. However, clustering of multilayer networks, especially using the information on higher-order interactions of the system entities, still remains in its infancy. In turn, higher-order connectivity is often the key in such multilayer network applications as developing optimal partitioning of critical infrastructures in order to isolate unhealthy system components under cyber-physical threats and simultaneous identification of multiple brain regions affected by trauma or mental illness. In this paper, we introduce the concepts of topological data analysis to studies of complex multilayer networks and propose a topological approach for network clustering. The key rationale is to group nodes based not on pairwise connectivity patterns or relationships between observations recorded at two individual nodes but based on how similar in shape their local neighborhoods are at various resolution scales. Since shapes of local node neighborhoods are quantified using a topological summary in terms of persistence diagrams, we refer to the approach as clustering using persistence diagrams (CPD). CPD systematically accounts for the important heterogeneous higher-order properties of node interactions within and in-between network layers and integrates information from the node neighbors. We illustrate the utility of CPD by applying it to an emerging problem of societal importance: vulnerability zoning of residential properties to weather- and climate-induced risks in the context of house insurance claim dynamics.