  Hypergraphs have gained increasing attention in the machine learning
community lately due to their superiority over graphs in capturing super-dyadic
interactions among entities. In this work, we propose a novel approach for the
partitioning of k-uniform hypergraphs. Most of the existing methods work by
reducing the hypergraph to a graph followed by applying standard graph
partitioning algorithms. The reduction step restricts the algorithms to
capturing only some weighted pairwise interactions and hence loses essential
information about the original hypergraph. We overcome this issue by utilizing
the tensor-based representation of hypergraphs, which enables us to capture
actual super-dyadic interactions. We prove that the hypergraph to graph
reduction is a special case of tensor contraction. We extend the notion of
minimum ratio-cut and normalized-cut from graphs to hypergraphs and show the
relaxed optimization problem is equivalent to tensor eigenvalue decomposition.
This novel formulation also enables us to capture different ways of cutting a
hyperedge, unlike the existing reduction approaches. We propose a hypergraph
partitioning algorithm inspired from spectral graph theory that can accommodate
this notion of hyperedge cuts. We also derive a tighter upper bound on the
minimum positive eigenvalue of even-order hypergraph Laplacian tensor in terms
of its conductance, which is utilized in the partitioning algorithm to
approximate the normalized cut. The efficacy of the proposed method is
demonstrated numerically on simple hypergraphs. We also show improvement for
the min-cut solution on 2-uniform hypergraphs (graphs) over the standard
spectral partitioning algorithm.
