A New Relaxation Approach to Normalized Hypergraph Cut
This work addresses the challenge of handling complex relationships beyond pairwise similarities in hypergraphs, which is incremental but improves performance in specific domains like VLSI design.
The paper tackles the normalized hypergraph cut problem by proposing a novel relaxation approach called RNHC, which outperforms state-of-the-art methods on large hypergraph benchmarks for clustering and VLSI partitioning.
Normalized graph cut (NGC) has become a popular research topic due to its wide applications in a large variety of areas like machine learning and very large scale integration (VLSI) circuit design. Most of traditional NGC methods are based on pairwise relationships (similarities). However, in real-world applications relationships among the vertices (objects) may be more complex than pairwise, which are typically represented as hyperedges in hypergraphs. Thus, normalized hypergraph cut (NHC) has attracted more and more attention. Existing NHC methods cannot achieve satisfactory performance in real applications. In this paper, we propose a novel relaxation approach, which is called relaxed NHC (RNHC), to solve the NHC problem. Our model is defined as an optimization problem on the Stiefel manifold. To solve this problem, we resort to the Cayley transformation to devise a feasible learning algorithm. Experimental results on a set of large hypergraph benchmarks for clustering and partitioning in VLSI domain show that RNHC can outperform the state-of-the-art methods.