在复杂几何结构下，用深层谱特征实现更鲁棒的社区发现。
Spectral graph clustering with inhomogeneous latent geometry
- 基于积分算子分析邻接矩阵谱特性，定位关键特征值。
- 提出DBSPEC算法，仅需近似定位即可恢复社区结构。
- 适用于一般非均匀几何场景，比以往方法更通用可靠。
我们研究了存在混杂潜在几何结构时的谱聚类问题。此时主特征向量可能被潜在几何主导而非社区结构。但在块潜空间模型中，我们证明可通过谱系中较深位置的特征向量恢复社区结构。通过极限积分算子分析邻接矩阵的谱性质，利用其结构设计了DBSPEC——一种基于密度的谱聚类算法，只需近似定位信息特征值，对特征值分离不佳的情况也具鲁棒性。该方法可处理一般潜在几何，突破了以往工作对同质环面模型的限制。理论预测的信息特征值位置与真实世界实验观察高度吻合。
原文摘要 · Abstract (English)
We study spectral clustering in the presence of a confounding latent geometry. The leading eigenvectors may then be dominated by the latent geometry rather than by the communities. Nevertheless, we show in a block latent-space model that communities can be recovered from eigenvectors deeper in the spectrum. We analyze the spectral properties of the adjacency matrix through a limiting integral operator and use its structure to develop DBSPEC, a density-based spectral clustering algorithm that requires only approximate localization of the informative eigenvalue and is robust to poor eigenvalue separation. Crucially, this approach handles general latent geometries, overcoming restrictions to homogeneous toroidal models in prior works. Our theoretical predictions for the location of the informative eigenvalue notably align with observations in real-world experiments.
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