Signed networks, where edges are labeled as positive or negative to indicate friendly or antagonistic interactions, offer a natural framework for studying polarization, trust, and conflict in social systems. Detecting meaningful group structures in these networks is crucial for understanding online discourse, political division, and trust dynamics. A key challenge is to identify groups that are cohesive internally yet antagonistic externally, while allowing for neutral or unaligned vertices. In this paper, we address this problem by identifying $k$ polarized communities that are large, dense, and balanced in size. We develop an approach based on Frank-Wolfe optimization, leading to a local search procedure with provable convergence guarantees. Our method is both scalable and efficient, outperforming state-of-the-art baselines in solution quality while remaining competitive in terms of computational efficiency.

本文研究了签名网络中通过检测极化社区来应对社交系统中的敌对关系、信任和冲突问题。提出了一种基于Frank-Wolfe优化的局部搜索方法，能够识别内部紧密而外部敌对的$k$个极化社区，且具有可证明的收敛性和良好的计算效率。实验结果表明，该方法在解决质量上优于现有的最佳方法，同时在计算效率上也表现出竞争力。

有效的局部搜索方法用于签名网络中的极化社区发现