A Doubled Adjacency Spectral Embedding Approach to Graph Clustering

TL;DR

This paper introduces Doubled Adjacency Spectral Embedding (DASE), a novel spectral clustering method that improves community detection in sparse and dense networks with core-periphery structures.

Contribution

The paper proposes DASE, a new spectral clustering approach leveraging squared adjacency matrices, with theoretical guarantees and demonstrated effectiveness on real-world data.

Findings

DASE outperforms classical ASE in sparse network clustering.

Theoretical analysis confirms consistency of DASE in core-periphery detection.

Empirical results show improved clustering accuracy on real-world datasets.

Abstract

Spectral clustering is a popular tool in network data analysis, with applications in a variety of scientific application areas. However, many studies have shown that classical spectral clustering does not perform well on certain network structures, particularly core-periphery networks. To improve clustering performance in core-periphery structures, Adjacency Spectral Embedding (ASE) has been introduced, which performs clustering via a network's adjacency matrix instead of the graph Laplacian. Despite its advantages in this setting, the optimal performance of ASE is limited to dense networks, whilst network data observed in practice is often sparse in nature. To address this limitation, we propose a new approach which we term Doubled Adjacency Spectral Embedding (DASE), motivated by the observation that the squared adjacency matrix will leverage the fewer connections in sparse structures more efficiently in clustering applications. Theoretical results establish that the resulting clustering algorithm enjoys good consistency properties when determining sparse community structure. The performance and general applicability of the proposed method is evaluated using extensive simulations on both directed and undirected networks. Our results highlight the improved clustering performance on both sparse and dense networks in the presence of core-periphery structures. We illustrate our proposed technique on real-world employment and transportation datasets.