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We study the problem of efficient exact partitioning of the hypergraphsgenerated by high-order planted models. A high-order planted model assumes someunderlying cluster structures, and simulates high-order interactions by placinghyperedges among nodes. Example models include the disjoint hypercliques, thedensest subhypergraphs, and the hypergraph stochastic block models. We showthat exact partitioning of high-order planted models (a NP-hard problem ingeneral) is achievable through solving a computationally efficient convexoptimization problem with a tensor nuclear norm constraint. Our analysisprovides the conditions for our approach to succeed on recovering the trueunderlying cluster structures, with high probability.

Exact Partitioning of High-order Planted Models with a Tensor Nuclear Norm Constraint