符号图中的极化搜索：局部谱方法
Searching for polarization in signed graphs: a local spectral approach
摘要：
符号图已经被用来模拟社会网络中的交互，可以是积极的（友好的）或消极的（敌对的）。该模型已被用来研究社交网络中的两极分化和其他相关现象，这些现象可能对我们社会的民主审议进程有害。在这个应用领域中，一个有趣且具有挑战性的任务是在符号图中检测极化社区。已经为这项任务提出了许多不同的方法。然而，现有的方法旨在找到全局最优的解决方案。相反，在本文中，我们感兴趣的是找到极化的社区，这些社区与作为输入提供的一小部分种子节点有关。种子节点可以由两个集合组成，这两个集合构成极化结构的两侧。在本文中，我们制定的问题，找到当地的极化社区签署图作为一个局部偏置的特征问题。通过查看与拉普拉斯矩阵的最小特征值相关联的特征向量作为约束优化问题的解决方案，我们能够将局部信息作为附加约束。此外，我们表明，局部偏置向量可以用来找到社区的近似保证相对于一个本地模拟的Cheeger常数签署图。通过利用输入图中的稀疏性，可以在时间上线性地找到极化社区的指示向量。我们在真实网络上的实验验证了所提出的算法，并证明了它的有用性，在这种半监督的方式找到局部结构。
英文摘要：
Signed graphs have been used to model interactions in social net-works, which can be either positive (friendly) or negative (antagonistic). The model has been used to study polarization and other related phenomena in social networks, which can be harmful to the process of democratic deliberation in our society. An interesting and challenging task in this application domain is to detect polarized communities in signed graphs. A number of different methods have been proposed for this task. However, existing approaches aim at finding globally optimal solutions. Instead, in this paper we are interested in finding polarized communities that are related to a small set of seed nodes provided as input. Seed nodes may consist of two sets, which constitute the two sides of a polarized structure. In this paper we formulate the problem of finding local polarized communities in signed graphs as a locally-biased eigen-problem. By viewing the eigenvector associated with the smallest eigenvalue of the Laplacian matrix as the solution of a constrained optimization problem, we are able to incorporate the local information as an additional constraint. In addition, we show that the locally-biased vector can be used to find communities with approximation guarantee with respect to a local analogue of the Cheeger constant on signed graphs. By exploiting the sparsity in the input graph, an indicator vector for the polarized communities can be found in time linear to the graph size. Our experiments on real-world networks validate the proposed algorithm and demonstrate its usefulness in finding local structures in this semi-supervised manner.
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