Exact Partitioning of High-order Planted Models with a Tensor Nuclear Norm Constraint
This work addresses efficient clustering in hypergraph data, which is incremental as it extends convex optimization techniques to high-order models.
The paper tackles the NP-hard problem of exact partitioning in high-order planted models, such as hypergraph stochastic block models, by proposing a convex optimization method with a tensor nuclear norm constraint, achieving exact recovery with high probability under certain conditions.
We study the problem of efficient exact partitioning of the hypergraphs generated by high-order planted models. A high-order planted model assumes some underlying cluster structures, and simulates high-order interactions by placing hyperedges among nodes. Example models include the disjoint hypercliques, the densest subhypergraphs, and the hypergraph stochastic block models. We show that exact partitioning of high-order planted models (a NP-hard problem in general) is achievable through solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint. Our analysis provides the conditions for our approach to succeed on recovering the true underlying cluster structures, with high probability.