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Signed networks are frequently observed in real life with additional signinformation associated with each edge, yet such information has been largelyignored in existing network models. This paper develops a unified embeddingmodel for signed networks to disentangle the intertwined balance structure andanomaly effect, which can greatly facilitate the downstream analysis, includingcommunity detection, anomaly detection, and network inference. The proposedmodel captures both balance structure and anomaly effect through a low rankplus sparse matrix decomposition, which are jointly estimated via a regularizedformulation. Its theoretical guarantees are established in terms of asymptoticconsistency and finite-sample probability bounds for network embedding,community detection and anomaly detection. The advantage of the proposedembedding model is also demonstrated through extensive numerical experiments onboth synthetic networks and an international relation network.

Signed Network Embedding with Application to Simultaneous Detection of Communities and Anomalies