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

by   Jeonghwan Lee, et al.

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.


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