Matrix Factorization Framework for Community Detection under the Degree-Corrected Block Model

TL;DR

This paper introduces a scalable matrix factorization approach for community detection under the degree-corrected block model, improving efficiency and initialization for inference algorithms.

Contribution

It reformulates DCBM inference as a constrained nonnegative matrix factorization and proposes a theoretically grounded initialization strategy applicable to any DCBM-structured graph.

Findings

Detects communities comparable to traditional methods but faster on large networks

Initialization strategy improves solution quality and reduces inference iterations

Processes large graphs (100,000 nodes, 1 million edges) in about 4 minutes

Abstract

Community detection is a fundamental task in data analysis, and block models provide an approach for identifying a wide variety of community structures while offering high interpretability. The degree-corrected block model (DCBM) is an established model that accounts for the heterogeneity of node degrees. However, inference methods are computationally costly and highly sensitive to initialization, while cheaper alternatives, such as spectral or modularity-based approaches, are restricted to detecting specific structures, typically assortative. In this work, we show that DCBM inference can be reformulated as a constrained nonnegative matrix factorization problem. Leveraging this insight, we propose a novel method for community detection and a theoretically well-grounded initialization strategy that provides an initial estimate of communities for inference algorithms. Our approach is agnostic to any specific network structure and applies to graphs with any structure representable by a DCBM. Experiments on synthetic and real benchmark networks show that our method detects communities comparable to those found by DCBM inference while being faster; for instance, it processes a graph with 100,000 nodes and 1,000,000 edges in approximately 4 minutes. Moreover, the proposed initialization strategy significantly improves solution quality and reduces the number of iterations required by all tested inference algorithms. Overall, this work provides a scalable and robust framework for community detection and highlights the benefits of a matrix-factorization perspective for the DCBM.