论文标题
几何图的高阶光谱聚类
Higher-Order Spectral Clustering for Geometric Graphs
论文作者
论文摘要
本文专门用于聚类几何图。尽管标准光谱聚类通常对于几何图不有效，但我们提出了有效的概括，我们称之为高阶光谱聚类。它类似于概念的经典光谱聚类方法，但用于划分与高阶特征值相关的特征向量。我们为宽类的几何图建立了该算法的弱一致性，我们称之为软几何块模型。该算法的少量调整提供了强大的一致性。我们还表明，即使对于适度大小的图形，我们的方法在数值实验中也有效。
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.
