利用双模性重新审视有向网络中的社区检测
Community detection for directed networks revisited using bimodularity
AI总结：
本文提出双模性概念，通过凸松弛和奇异值分解优化有向网络中的社区检测，并在神经网络图谱中验证了其有效性。
摘要：
社区结构是现实世界网络数据中普遍存在的重要特征。已有大量方法被提出，用于利用诸如模块度指数等标准来揭示高度互联节点的子集。这些方法在无向图上取得了成功，但有向边信息尚未得到令人满意的处理。本文重新审视了有向社区的概念，将其视为发送社区与接收社区之间的映射。这转化为一种新的定义，我们称之为双模性。利用凸松弛，双模性可以通过有向模块度矩阵的奇异值分解进行优化。随后，我们提出了一种基于边的聚类方法，以揭示包含其映射的有向社区。新框架在合成模型上得到了验证，并进一步应用于秀丽隐杆线虫的神经网络图谱，其中它产生了有意义的头部和躯干运动系统的前馈循环。该框架为理解和检测有向网络中的社区结构奠定了基础。
英文摘要：
Community structure is a key feature omnipresent in real-world network data. Plethora of methods have been proposed to reveal subsets of densely interconnected nodes using criteria such as the modularity index. These approaches have been successful for undirected graphs, but directed edge information has not yet been dealt with in a satisfactory way. Here, we revisit the concept of directed communities as a mapping between sending and receiving communities. This translates into a new definition that we term bimodularity. Using convex relaxation, bimodularity can be optimized with the singular value decomposition of the directed modularity matrix. Subsequently, we propose an edge-based clustering approach to reveal the directed communities including their mappings. The feasibility of the new framework is illustrated on a synthetic model and further applied to the neuronal wiring diagram of the \textit{C. elegans}, for which it yields meaningful feedforward loops of the head and body motion systems. This framework sets the ground for the understanding and detection of community structures in directed networks.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
