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

TL;DR

This paper introduces a unified embedding model for signed networks that effectively separates community structures from anomalies, enhancing analysis tasks like detection and inference.

Contribution

It proposes a low rank plus sparse matrix decomposition approach for signed network embedding with theoretical guarantees and practical validation.

Findings

Effective separation of community and anomaly effects

Theoretical guarantees for embedding and detection accuracy

Validated on synthetic and real-world networks

Abstract

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.