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This work considers clustering nodes of a largely incomplete graph. Under the problem setting, only a small amount of queries about the edges can be made, but the entire graph is not observable. This problem finds applications in large-scale data clustering using limited annotations, community detection under restricted survey resources, and graph topology inference under hidden/removed node interactions. Prior works tackled this problem from various perspectives, e.g., convex programming-based low-rank matrix completion and active query-based clique finding. Nonetheless, many existing methods are designed for estimating the single-cluster membership of the nodes, but nodes may often have mixed (i.e., multi-cluster) membership in practice. Some query and computational paradigms, e.g., the random query patterns and nuclear norm-based optimization advocated in the convex approaches, may give rise to scalability and implementation challenges. This work aims at learning mixed membership of nodes using queried edges. The proposed method is developed together with a systematic query principle that can be controlled and adjusted by the system designers to accommodate implementation challenges&#x2014;e.g., to avoid querying edges that are physically hard to acquire. Our framework also features a lightweight and scalable algorithm with membership learning guarantees. Real-data experiments on crowdclustering and community detection are used to showcase the effectiveness of our method.

Mixed Membership Graph Clustering via Systematic Edge Query