发表机构
Inria Sophia Antipolis; Federal University of Rio Grande do Sul; University of Münster（索菲亚·安蒂波利斯国立计算机与自动化研究所; 南里奥格兰德联邦大学; 明斯特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对混杂潜在几何下谱聚类的问题，提出DBSPEC算法，可从深层特征向量恢复社区，能处理一般潜在几何，其理论预测与真实实验结果一致。
AI 中文摘要
我们研究存在混杂潜在几何时的谱聚类问题，此时主导特征向量可能受潜在几何而非社区主导。但我们在块潜在空间模型中证明，可从频谱中更深层的特征向量恢复社区。我们通过极限积分算子分析邻接矩阵的谱性质，利用其结构开发了DBSPEC算法——一种基于密度的谱聚类算法，仅需对信息特征值进行近似定位，且对特征值分离度差的情况具有鲁棒性。关键在于，该方法可处理一般潜在几何，克服了现有工作对均匀环形模型的限制。我们对信息特征值位置的理论预测与真实实验中的观察结果显著一致。
英文摘要
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.
Comments28 pages, 11 figures
