Randomized Robust Matrix Completion for the Community Detection Problem

This paper focuses on the unsupervised clustering of large partially observed graphs. We propose a provable randomized framework in which a clustering algorithm is applied to a graph's adjacency matrix generated from a stochastic block model. A sub-matrix is constructed using random sampling, and the low rank component is found using a convex-optimization-based matrix completion algorithm. The clusters are then identified based on this low rank component using a correlation-based retrieval step. Additionally, a new random node sampling algorithm is presented which significantly improves upon the performance of the clustering algorithm with unbalanced data. Given a partially observed graph with adjacency matrix A \in R^{N \times N}, the proposed approach can reduce the computational complexity from O(N^2) to O(N).