arXiv:2411.09979cs.DScs.LG2024-11被引 3

提出高效动态抗对抗攻击的聚类算法,更新速度快且结果稳定。

Fully Dynamic Adversarially Robust Correlation Clustering in Polylogarithmic Update Time

  • 设计可快速响应边标签变化的动态聚类算法
  • 保持常数倍近似比,更新时间仅需对数平方级
  • 适合需要实时应对恶意干扰的图数据场景

研究具有自适应边标签翻转的动态相关性聚类问题。在相关性聚类中,给定一个包含 n 个顶点的完全图,其边被标记为 (+) 或 (-),目标是最小化跨集群的 (+) 边数量以及集群内部的 (-) 边数量。本文考虑具有对抗鲁棒性的动态设置,其中自适应对手可根据算法当前输出翻转边标签。主要成果是提出一个随机化算法,在任意时刻均能保持对最优解的 O(1) 近似,且均摊更新时间为 O(log²n)。此前,尚未有在对抗鲁棒设定下实现 O(1) 近似与 polylog(n) 更新时间的算法。我们通过合成及真实数据集上的实验验证了理论结果,表现出具有竞争力的实证性能。核心技术是维护稀疏-稠密分解的算法,可在 polylog(n) 时间内更新,可能具有独立应用价值。

原文摘要 · Abstract (English)

We study the dynamic correlation clustering problem with $\textit{adaptive}$ edge label flips. In correlation clustering, we are given a $n$-vertex complete graph whose edges are labeled either $(+)$ or $(-)$, and the goal is to minimize the total number of $(+)$ edges between clusters and the number of $(-)$ edges within clusters. We consider the dynamic setting with adversarial robustness, in which the $\textit{adaptive}$ adversary could flip the label of an edge based on the current output of the algorithm. Our main result is a randomized algorithm that always maintains an $O(1)$-approximation to the optimal correlation clustering with $O(\log^{2}{n})$ amortized update time. Prior to our work, no algorithm with $O(1)$-approximation and $\text{polylog}{(n)}$ update time for the adversarially robust setting was known. We further validate our theoretical results with experiments on synthetic and real-world datasets with competitive empirical performances. Our main technical ingredient is an algorithm that maintains $\textit{sparse-dense decomposition}$ with $\text{polylog}{(n)}$ update time, which could be of independent interest.

聚类算法动态图对抗鲁棒高效算法

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