A New Relaxation Approach to Normalized Hypergraph Cut

TL;DR

This paper introduces a novel relaxation method called RNHC for normalized hypergraph cut problems, effectively handling complex relationships in hypergraphs and outperforming existing methods in clustering and partitioning tasks.

Contribution

The paper presents a new relaxation approach for NHC, formulated as an optimization on the Stiefel manifold, with a Cayley transformation-based algorithm for improved performance.

Findings

RNHC outperforms state-of-the-art methods in hypergraph clustering.

Experimental results demonstrate RNHC's effectiveness on large VLSI hypergraph benchmarks.

The approach effectively handles complex hypergraph relationships beyond pairwise similarities.

Abstract

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.