  We prove strong consistency of spectral clustering under the degree-corrected
hypergraph stochastic block model in the sparse regime where the maximum
expected hyperdegree is as small as $\Omega(\log n)$ with $n$ denoting the
number of nodes. We show that the basic spectral clustering without
preprocessing or postprocessing is strongly consistent in an even wider range
of the model parameters, in contrast to previous studies that either trim
high-degree nodes or perform local refinement. At the heart of our analysis is
the entry-wise eigenvector perturbation bound derived by the leave-one-out
technique. To the best of our knowledge, this is the first entry-wise error
bound for degree-corrected hypergraph models, resulting in the strong
consistency for clustering non-uniform hypergraphs with heterogeneous
hyperdegrees.
