时态图割的谱算法
Spectral Algorithms for Temporal Graph Cuts
摘要：
稀疏割问题包括确定一个小的边集，将图分解为平衡的顶点集。规范化切割问题平衡的是结果集的总度，而不是大小。图割的应用包括社区发现和计算机视觉。然而，切割问题最初是针对静态图提出的，这一假设在许多现代应用中并不成立，因为图是高度动态的。在本文中，我们介绍了时间图的稀疏性和规范化切割问题，通过强制执行切割随时间的光滑性来推广它们的标准定义。我们提出了新的配方和算法计算时间削减谱图理论，多重图，分而治之和低秩矩阵近似。此外，我们将我们的配方扩展到动态图形信号，其中切割也捕获节点值，作为图形小波。实验表明，我们的解决方案是准确的和可扩展的，使动态社区的发现和动态图过程的分析。
英文摘要：
The sparsest cut problem consists of identifying a small set of edges that breaks the graph into balanced sets of vertices. The normalized cut problem balances the total degree, instead of the size, of the resulting sets. Applications of graph cuts include community detection and computer vision. However, cut problems were originally proposed for static graphs, an assumption that does not hold in many modern applications where graphs are highly dynamic. In this paper, we introduce the sparsest and normalized cut problems in temporal graphs, which generalize their standard definitions by enforcing the smoothness of cuts over time. We propose novel formulations and algorithms for computing temporal cuts using spectral graph theory, multiplex graphs, divide-and-conquer and low-rank matrix approximation. Furthermore, we extend our formulation to dynamic graph signals, where cuts also capture node values, as graph wavelets. Experiments show that our solutions are accurate and scalable, enabling the discovery of dynamic communities and the analysis of dynamic graph processes.
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。
