Hypergraph Clustering in the Weighted Stochastic Block Model via Convex Relaxation of Truncated MLE

We study hypergraph clustering under the weighted $d$-uniform hypergraph stochastic block model ($d$-WHSBM), where each edge consisting of $d$ nodes has higher expected weight if $d$ nodes are from the same community compared to edges consisting of nodes from different communities. We propose a new hypergraph clustering algorithm, which is a convex relaxation of truncated maximum likelihood estimator (CRTMLE), that can handle the relatively sparse, high-dimensional regime of the $d$-WHSBM with community sizes of different orders. We provide performance guarantees of this algorithm under a unified framework for different parameter regimes, and show that it achieves the order-wise optimal or the best existing results for approximately balanced community sizes. We also demonstrate the first recovery guarantees for the setting with growing number of communities of unbalanced sizes.