A Doubled Adjacency Spectral Embedding Approach to Graph Clustering

2025-12-12

AI Summary

Spectral clustering suffers significant performance degradation on core-periphery structured networks—particularly under sparsity—due to inadequate modeling of sparse inter-layer connections by existing adjacency spectral embedding (ASE) methods. To address this, we propose Double Adjacency Spectral Embedding (DASE), the first method to construct the embedding space using the square of the adjacency matrix, thereby enhancing representation fidelity for sparse cross-core-periphery links. We establish theoretical consistency of DASE under the degree-corrected stochastic block model (DCSBM) with varying sparsity levels. Empirical evaluation on synthetic benchmarks and real-world employment and transportation networks demonstrates that DASE consistently outperforms both ASE and Laplacian spectral clustering: it achieves average accuracy improvements of 12–28% on core-periphery structures, while exhibiting superior robustness to sparsity and strong generalization across diverse network domains.

Technology Category

• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Search and Optimization: Distributed Search
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Social Networks and Social Media: Computational social science
• Security and Privacy: Large-scale security measurements

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 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 DASE 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.

Problem

• Improves spectral clustering for core-periphery networks
• Addresses limitations of ASE in sparse network data
• Proposes DASE to enhance clustering in sparse structures

Innovation

• Doubled Adjacency Spectral Embedding for sparse networks
• Uses squared adjacency matrix to leverage sparse connections
• Improves clustering in core-periphery structures on sparse data