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<p>Community detection via network embedding has received increasing interest in applications. However, existing approaches mainly focus on detecting the communities themselves, while the relationships between these detected communities remain underexplored. In this paper, we propose a novel regularization term - the cosine similarity penalty - to the negative log-likelihood function, which avoids grouping nodes with small degrees into the same community as most existing methods that heavily rely on clustering embedding vectors using the <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\ell _2\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ℓ</mi> <mn>2</mn> </msub> </math></EquationSource> </InlineEquation> regularized penalty, i.e., the Euclidean distance. The proposed method not only promotes the community structure but also is robust to the heterogeneity of the node degrees and can offer a clear interpretation of the relationships between the detected communities. This regularization term effectively brings together the embedding vectors with smaller angles, leading to consistent directions among embedding vectors within the same community. To resolve the resultant optimization task, a novel algorithm is developed to detect communities and estimate link probability. Moreover, the asymptotic properties of the proposed method are established in terms of network embedding. Numerical simulations demonstrate the performance of our method, and the illustrations of three real applications provide an interpretation for our model.</p>

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Learning social relationships: a network embedding-based approach for community detection via cosine-similarity

  • 期刊论文

  • 发表日期：

    2026年4月18日

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  • Yu Chen,
  • Lu Cheng,
  • Xiao Chen,
  • Jie Hu

摘要

Community detection via network embedding has received increasing interest in applications. However, existing approaches mainly focus on detecting the communities themselves, while the relationships between these detected communities remain underexplored. In this paper, we propose a novel regularization term - the cosine similarity penalty - to the negative log-likelihood function, which avoids grouping nodes with small degrees into the same community as most existing methods that heavily rely on clustering embedding vectors using the \(\ell _2\) ℓ 2 regularized penalty, i.e., the Euclidean distance. The proposed method not only promotes the community structure but also is robust to the heterogeneity of the node degrees and can offer a clear interpretation of the relationships between the detected communities. This regularization term effectively brings together the embedding vectors with smaller angles, leading to consistent directions among embedding vectors within the same community. To resolve the resultant optimization task, a novel algorithm is developed to detect communities and estimate link probability. Moreover, the asymptotic properties of the proposed method are established in terms of network embedding. Numerical simulations demonstrate the performance of our method, and the illustrations of three real applications provide an interpretation for our model.