Signed networks are frequently observed in real life with additional sign information associated with each edge, yet such information has been largely ignored in existing network models. This paper develops a unified embedding model for signed networks to disentangle the intertwined balance structure and anomaly effect, which can greatly facilitate the downstream analysis, including community detection, anomaly detection, and network inference. The proposed model captures both balance structure and anomaly effect through a low rank plus sparse matrix decomposition, which are jointly estimated via a regularized formulation. Its theoretical guarantees are established in terms of asymptotic consistency and finite-sample probability bounds for network embedding, community detection and anomaly detection. The advantage of the proposed embedding model is also demonstrated through extensive numerical experiments on both synthetic networks and an international relation network.

翻译：符号网络在现实生活中频繁出现，其每条边均带有额外的符号信息，然而现有网络模型对此类信息大多未予考虑。本文针对符号网络提出一种统一嵌入模型，以解耦相互交织的平衡结构与异常效应，从而极大促进下游分析任务，包括社区检测、异常检测及网络推理。该模型通过低秩加稀疏矩阵分解同时捕捉平衡结构与异常效应，并借助正则化方法实现两者的联合估计。本文从渐近一致性与有限样本概率界两方面建立了网络嵌入、社区检测及异常检测的理论保证。通过在合成网络与国际关系网络上的大量数值实验，进一步验证了所提嵌入模型的优势。