On The Effect of Hyperedge Weights On Hypergraph Learning

TL;DR

This paper investigates how hyperedge weights affect hypergraph learning performance, proposing three novel weighting schemes and demonstrating their effectiveness through extensive experiments on multiple datasets.

Contribution

It introduces three new hyperedge weighting methods based on geometry, statistical analysis, and linear regression, highlighting their impact on hypergraph learning.

Findings

Hyperedge weights significantly influence hypergraph learning outcomes.

Proposed weighting schemes improve classification and clustering performance.

Combining weighting schemes with hypergraph models yields state-of-the-art results.

Abstract

Hypergraph is a powerful representation in several computer vision, machine learning and pattern recognition problems. In the last decade, many researchers have been keen to develop different hypergraph models. In contrast, no much attention has been paid to the design of hyperedge weights. However, many studies on pairwise graphs show that the choice of edge weight can significantly influence the performances of such graph algorithms. We argue that this also applies to hypegraphs. In this paper, we empirically discuss the influence of hyperedge weight on hypegraph learning via proposing three novel hyperedge weights from the perspectives of geometry, multivariate statistical analysis and linear regression. Extensive experiments on ORL, COIL20, JAFFE, Sheffield, Scene15 and Caltech256 databases verify our hypothesis. Similar to graph learning, several representative hyperedge weighting schemes can be concluded by our experimental studies. Moreover, the experiments also demonstrate that the combinations of such weighting schemes and conventional hypergraph models can get very promising classification and clustering performances in comparison with some recent state-of-the-art algorithms.