Compressive graph clustering from random sketches

Graph clustering, where the goal is to cluster the nodes in a graph into disjoint clusters, arises from applications such as community detection, network monitoring, and bioinformatics. This paper describes an approach for graph clustering based on a small number of linear measurements, i.e. sketches, of the adjacency matrix, where each sketch corresponds to the number of edges in a randomly selected subgraph. Under the stochastic block model, we propose a computationally tractable algorithm based on semidefinite programming to recover the underlying clustering structure, by motivating the low-dimensional parsimonious structure of the clustering matrix. Numerical examples are presented to validate the excellent performance of the proposed algorithm, which allows exact recovery of the clustering matrix under favorable trade-offs between the number of sketches and the edge density gap under the stochastic block model.