Inhomogeneous Hypergraph Clustering with Applications

TL;DR

This paper introduces inhomogeneous hypergraph clustering, a novel method that assigns different costs to hyperedge cuts, improving performance in various applications by better capturing structural importance.

Contribution

It proposes a new hypergraph partitioning technique with theoretical guarantees and demonstrates its effectiveness in multiple real-world tasks.

Findings

Quadratic approximation to optimal solution under submodularity.

Significant performance improvements in structure learning, segmentation, and clustering.

Theoretical analysis of inhomogeneous hypergraph partitioning.

Abstract

Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different partitions of a hyperedge incur the same cost. However, this assumption fails to leverage the fact that different subsets of vertices within the same hyperedge may have different structural importance. We hence propose a new hypergraph clustering technique, termed inhomogeneous hypergraph partitioning, which assigns different costs to different hyperedge cuts. We prove that inhomogeneous partitioning produces a quadratic approximation to the optimal solution if the inhomogeneous costs satisfy submodularity constraints. Moreover, we demonstrate that inhomogenous partitioning offers significant performance improvements in applications such as structure learning of rankings, subspace segmentation and motif clustering.