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

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.