Robust ℓ2−Hypergraph and Its Applications

Hypergraph, an important learning tool to modulate high-order data correlations, has a wide range of applications in machine learning and computer vision. The key issue of the hypergraph-based applications is to construct an informative hypergraph, in which the hyperedges effectively represent the high-order data correlations. In practice, the real-world data is usually sampled from a union of non-linear manifolds. Due to the issues of noise and data corruptions, many data samples deviate from the underlying data manifolds. To construct an informative hypergraph that represents real-world data distribution well, we propose a hypergraph model (ℓ2-Hypergraph). Our model generates each hyperedge by solving an affine subspace ridge regression problem, where the samples with non-zero representation coefficients are used for hyperege generation. Specifically, to be robust to sparse noise and corruptions, a sparse constraint is imposed on data errors. We have conducted image clustering and classification experiments on real-world datasets. The experimental results demonstrate that our hypergraph model is superior to the existing hypergraph construction methods in both accuracy and robustness to sparse noise.