arXiv:2411.11074cs.SIcs.LG2024-11KDD被引 15

提出高效谱子空间聚类算法,更好分割带属性图的节点

Spectral Subspace Clustering for Attributed Graphs

  • 设计新目标函数与约束,融合图结构与属性数据
  • 线性时间求解器提升效率,8个数据集上性能全面领先
  • 理论揭示与导出率最小化关联,适合图聚类研究者

子空间聚类旨在将n个数据点划分为k个子空间(k<<n),在图像和视频分析中表现优异。近期研究将其应用于带属性图的顶点划分(即SCAG),但现有方法或计算开销大,或未能有效结合图拓扑与属性信息,影响聚类质量。本文提出两种高效算法S2CAG与M-S2CAG。S2CAG通过新目标函数、改进的顶点表示模型及两个非平凡约束实现高性能;基于理论转化与自适应策略,设计了线性时间优化求解器。深入分析揭示S2CAG与导出率最小化间的理论联系,进一步启发M-S2CAG以最大化模块度为目标。在8个基准数据集上对比17种基线方法的实验表明,所提方法在聚类质量上全面超越现有方法,同时保持高效率。

原文摘要 · Abstract (English)

Subspace clustering seeks to identify subspaces that segment a set of n data points into k (k<<n) groups, which has emerged as a powerful tool for analyzing data from various domains, especially images and videos. Recently, several studies have demonstrated the great potential of subspace clustering models for partitioning vertices in attributed graphs, referred to as SCAG. However, these works either demand significant computational overhead for constructing the nxn self-expressive matrix, or fail to incorporate graph topology and attribute data into the subspace clustering framework effectively, and thus, compromise result quality. Motivated by this, this paper presents two effective and efficient algorithms, S2CAG and M-S2CAG, for SCAG computation. Particularly, S2CAG obtains superb performance through three major contributions. First, we formulate a new objective function for SCAG with a refined representation model for vertices and two non-trivial constraints. On top of that, an efficient linear-time optimization solver is developed based on our theoretically grounded problem transformation and well-thought-out adaptive strategy. We then conduct an in-depth analysis to disclose the theoretical connection of S2CAG to conductance minimization, which further inspires the design of M-S2CAG that maximizes the modularity. Our extensive experiments, comparing S2CAG and M-S2CAG against 17 competitors over 8 benchmark datasets, exhibit that our solutions outperform all baselines in terms of clustering quality measured against the ground truth while delivering high efficiency

图聚类子空间聚类谱方法属性图

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