Multi-Constrained Embedding for Accurate Community Detection on Undirected Networks

Abstract

A Symmetric Non-negative Matrix Factorization (SNMF)-based network embedding model adopts a unique Latent Factor (LF) matrix for describing the symmetry of an undirected network, which reduces its representation ability to the target network and thus resulting in accuracy loss when performing community detection. To address this issue, this paper proposes a new undirected network embedding model, i.e., Alternating Direction Method of Multipliers ( <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</u> DMM)-based, <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</u> odularity, <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</u> ymmetry and <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</u> onnegativity-constrained <underline xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</u> mbedding (AMSNE), which can be applicable to undirected, weighted or unweighted networks. It relies on two-fold ideas: a) Introducing the symmetry constraints into the model to correctly describe the symmetric of an undirected network without accuracy loss; and b) Adopting the ADMM principle to efficiently solve its constrained objective. Extensive experiments on eight real-world networks strongly evidence that the proposed AMSNE outperform several state-of-the-art models, making it suitable for real applications.