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 graphs 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).

In this letter, we propose an algorithm for recovery of sparse and low rank components of matrices using an iterative method with adaptive thresholding. In each iteration, the low rank and sparse components are obtained using a thresholding operator. This algorithm is fast and can be implemented easily. We compare it with one of the most common fast methods in which the rank and sparsity are approximated by $\ell_1$ norm. We also apply it to some real applications where the noise is not so sparse. The simulation results show that it has a suitable performance with low run-time.