  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 -- 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.
