Robust Hypergraph Clustering via Convex Relaxation of Truncated MLE
This work addresses hypergraph clustering for data with community structures, offering robust solutions for unbalanced sizes or outliers, but it is incremental as it builds on existing models and methods.
The authors tackled hypergraph clustering in a weighted stochastic block model by proposing the CRTMLE algorithm, which achieves order-wise optimal or best existing results for balanced communities and provides the first recovery guarantees for growing numbers of unbalanced clusters.
We study hypergraph clustering in the weighted $d$-uniform hypergraph stochastic block model ($d$\textsf{-WHSBM}), where each edge consisting of $d$ nodes from the same community has higher expected weight than the edges consisting of nodes from different communities. We propose a new hypergraph clustering algorithm, called \textsf{CRTMLE}, and provide its performance guarantee under the $d$\textsf{-WHSBM} for general parameter regimes. We show that the proposed method achieves the order-wise optimal or the best existing results for approximately balanced community sizes. Moreover, our results settle the first recovery guarantees for growing number of clusters of unbalanced sizes. Involving theoretical analysis and empirical results, we demonstrate the robustness of our algorithm against the unbalancedness of community sizes or the presence of outlier nodes.