Partial recovery and weak consistency in the non-uniform hypergraph Stochastic Block Model. (arXiv:2112.11671v2 [math.ST] UPDATED)

We consider the community detection problem in sparse random hypergraphs
under the non-uniform hypergraph stochastic block model (HSBM), a general model
of random networks with community structure and higher-order interactions. 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. When the SNR grows slowly as the
number of vertices …

arxiv hypergraph math recovery stochastic uniform