Consistent Estimation of the Number of Communities in Non‐uniform Hypergraph Model

ABSTRACT We propose an algorithm based on cross‐validation to estimate the number of communities in a general non‐uniform hypergraph model. The algorithm involves a three‐step process. Initially, it randomly divides the set of hyperedges into a training set and a testing set. Subsequently, for each candidate number of communities, we construct a spectral estimation of community labels and least square estimation of the hyperedge probabilities based on the training set. The final step involves the computation of cross‐validation scores using the testing set. The proposed algorithm is shown to be consistent when the number of vertices tends to infinity.