On The Effect of Hyperedge Weights On Hypergraph Learning
This work addresses the under-explored problem of hyperedge weight design in hypergraph learning for researchers in computer vision and machine learning, though it is incremental as it extends known graph weighting concepts to hypergraphs.
The paper investigates how hyperedge weight design affects hypergraph learning performance, proposing three novel weighting schemes and showing through experiments on multiple datasets that these combinations with conventional models achieve promising classification and clustering results compared to recent state-of-the-art algorithms.
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.