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.
翻译:本文件专门论述几何图群集问题。虽然标准的光谱群集通常对几何图不起作用,但我们展示了一种有效的概括,我们称之为较高级的光谱群集。在概念上,它类似于古典光谱群集方法,但用于与较高级的等分解与高级的等离子值相关联的分解。我们为称为软几何区块模型的广大几何组图确定了这种算法的薄弱一致性。对算法的微小调整提供了很强的连贯性。我们还表明,我们的方法在数字实验中是有效的,即使对于大小不大的图表也是有效的。