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Strong consistency and optimality of spectral clustering in symmetric binary non-uniform Hypergraph Stochastic Block Model
Consider the unsupervised classification problem in random hypergraphs under the non-uniform \emph{Hypergraph Stochastic Block Model} (HSBM) with two equal-sized communities ($n/2$), where each edge appears independently with some probability depending only on the labels of its vertices.
Exact recovery for the non-uniform Hypergraph Stochastic Block Model
Consider the community detection problem in random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), where each hyperedge appears independently with some given probability depending only on the labels of its vertices.
Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Model
When the random hypergraph has bounded expected degrees, we provide a spectral algorithm that outputs a partition with at least a $\gamma$ fraction of the vertices classified correctly, where $\gamma\in (0. 5, 1)$ depends on the signal-to-noise ratio (SNR) of the model.
