The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It resembles in concept the classical spectral clustering method but uses for partitioning the eigenvector associated with a higher-order eigenvalue. We establish the weak consistency of this algorithm for a wide class of geometric graphs which we call Soft Geometric Block Model. A small adjustment of the algorithm provides strong consistency. We also show that our method is effective in numerical experiments even for graphs of modest size.

中文翻译：

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几何图形的高阶谱聚类

本论文致力于对几何图进行聚类。虽然标准谱聚类通常对几何图无效，但我们提出了一种有效的概括，我们称之为高阶谱聚类。它在概念上类似于经典的谱聚类方法，但用于分割与高阶特征值相关联的特征向量。我们为我们称为软几何块模型的一大类几何图形建立了该算法的弱一致性。算法的小调整提供了强一致性。我们还表明，即使对于中等大小的图形，我们的方法在数值实验中也是有效的。