Consistency of Spectral Hypergraph Partitioning under Planted Partition Model

Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. A number of algorithms exist in the literature that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received attention in the literature as compared to the extensive studies on the guarantees of graph partitioning. For instance, consistency results of spectral clustering under the planted partition or stochastic blockmodel are well-known (Rohe et al., 2011; Lei and Rinaldo, 2015). In this paper, we present a planted partition model for sparse random non-uniform hypergraphs that generalizes the stochastic blockmodels for graphs and uniform hypergraphs. We derive an asymptotic error bound of a spectral hypergraph partitioning algorithm under this model using matrix Bernstein inequality. To the best of our knowledge, this is the first consistency result related to partitioning non-uniform hypergraphs.