On the effect of hyperedge weights on hypergraph learning

Abstract

Hypergraph is a powerful representation for 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 weighting schemes. However, many studies on pairwise graphs showed that the choice of edge weight can significantly influence the performances of such graph algorithms. We argue that this also applies to hypergraphs. In this paper, we empirically study the influence of hyperedge weights on hypergraph learning via proposing three novel hyperedge weighting schemes from the perspectives of geometry, multivariate statistical analysis, and linear regression. Extensive experiments on ORL, COIL20, JAFFE, Sheffield, Scene15 and Caltech256 datasets verified our hypothesis for both classification and clustering problems. For each of these classes of problems, our empirical study concludes with suggesting a suitable hypergraph weighting scheme. Moreover, the experiments also demonstrate that the combinations of such weighting schemes and conventional hypergraph models can achieve competitive classification and clustering performances in comparison with some recent state-of-the-art algorithms.