Robust non-negative matrix factorization with multiple correntropy-induced hypergraph regularizer

Abstract Non-negative matrix factorization (NMF) is a popular learning tool, which has widely used in computer vision and image processing. Many variants and extensions of NMF have been proposed, where the manifold regularized NMF methods have achieved promising performance due to the preservation of the geometric structures of the data. However, for many applications, the data is usually contaminated by complex noise. The noise leads the data to deviate from the intrinsic manifold, resulting in the degenerate performance. To make the NMF methods reflect the underlying manifold structure well, we propose a novel robust non-negative matrix factorization model. Our model proposes a novel ensemble manifold regularizer, which combines multiple robust hypergraphs to estimate the underlying manifold. Specifically, the correntropy-induced hypergraph is used as the initial manifold estimation. By incorporating the proposed regularizer into the original NMF framework, two novel manifold regularized NMF methods are proposed. The clustering results on the noisy image datasets demonstrate that our model is effective, which achieves the state-of-the-art performance.