Link-aware semi-supervised hypergraph.

Hypergraph learning has been widely applied to various learning tasks. To ensure learning accuracy, it is essential to construct an informative hypergraph structure that effectively modulates data correlations. However, existing hypergraph construction methods essentially resort to an unsupervised learning paradigm, which ignores supervisory information, such as pairwise links/non-links. In this article, to exploit the supervisory information, we propose a novel link-aware hypergraph learning model, which modulates high-order correlations of data samples in a semi-supervised manner. To construct a hypergraph, a coefficients matrix of the entire dataset is first calculated by solving a linear regression problem. Then, pairwise link constraints are exploited and propagated to the unconstrained samples, upon which the coefficients matrix is adjusted accordingly. Finally, the adjusted coefficients are used to generate a set of the hyperedges, as well as calculate the corresponding weights. We have validated the proposed link-aware semi-supervised hypergraph model on the problem of image clustering. Superior performance over the state-of-the-art methods demonstrates the effectiveness of the proposed hypergraph model.