On the efficacy of higher-order spectral clustering under weighted stochastic block models

TL;DR

This paper analyzes the effectiveness of higher-order spectral clustering in community detection within weighted networks, demonstrating its advantages in dense, weak-signal scenarios through theoretical analysis and empirical validation.

Contribution

It provides a theoretical comparison of higher-order versus edge-based spectral clustering under weighted stochastic block models, highlighting conditions for superior performance.

Findings

Higher-order spectral clustering outperforms edge-based methods in dense, weak-signal networks.

Theoretical bounds show improved clustering accuracy with higher-order methods under certain conditions.

Simulations and real data confirm the practical benefits of higher-order spectral clustering.

Abstract

Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. There has been a few work studying the community detection problem -- a fundamental problem in network analysis, at the level of motifs. In particular, higher-order spectral clustering has been developed, where the notion of motif adjacency matrix is introduced as the input of the algorithm. However, it remains largely unknown that how higher-order spectral clustering works and when it performs better than its edge-based counterpart. To elucidate these problems, we investigate higher-order spectral clustering from a statistical perspective. In particular, we theoretically study the clustering performance of higher-order spectral clustering under a weighted stochastic block model and compare the resulting bounds with the corresponding results of edge-based spectral clustering. It turns out that when the network is dense with weak signal of weights, higher-order spectral clustering can really lead to the performance gain in clustering. We also use simulations and real data experiments to support the findings.