Labeled Graph Clustering via Projected Gradient Descent

Advances in recovering low-rank matrices from noisy observations have led to tractable algorithms for clustering from general pair-wise labels with provable performance guarantees. Based on convex relaxation, it has been shown that the ground truth clusters can be recovered with high probability under a generalized stochastic block model by solving a semidefinite program. Although tractable, the algorithm is typically too slow for sufficiently large problems in practice. Inspired by recent advances in non-convex approaches to low-rank recovery problems, we propose an algorithm based on projected gradient descent that enjoys similar provable guarantees as the convex counterpart, but can be orders of magnitude faster. Our theoretical results are further supported by encouraging empirical results.