Sparse Hyper-graph Non-negative Matrix Factorization by Maximizing Correntropy

Non-negative Matrix Factorization (NMF) as a powerful dimension reduction tool, which is widely used in the bioinformatics field. However, the loss function of conventional NMF is sensitive to non-Gaussian noise and outliers. In addition, NMF-based algorithm overlooks the geometric structure of high dimensional data. To improve the robustness of NMF, we propose a novel method called Sparse Hyper-graph regularized Non-negative Matrix Factorization by Maximizing Correntropy (SHNMF-MCC) in this paper. Specifically, the maximum correntropy criterion replaces the Euclidean distance in the loss term of SHNMF-MCC, which can filter out the noise with large outliers. Moreover, the high-order geometric structure in more sample points is completely preserved in the low-dimensional manifold through the hyper-graph regularization. Meanwhile, the sparse constraint is applied to the loss function to reduce matrix complexity and analysis difficulty. Then, the complex optimization problem can be solved by a half-quadratic (HQ) optimization approach. Before carrying out experiments, we analyze the convergence of SHNMF-MCC. Sample clustering experiments on The Cancer Genome Atlas (TCGA) data and single cell RNA-sequencing (scRNA-seq) data verify that the proposed method is more robust and effective than other similar robust approaches.