Sparse robust graph-regularized non-negative matrix factorization based on correntropy

Non-negative Matrix Factorization (NMF) is a popular data dimension reduction method in recent years. The traditional NMF method has high sensitivity to data noise. In the paper, we propose a model called Sparse Robust Graph-regularized Non-negative Matrix Factorization based on Correntropy (SGNMFC). The maximized correntropy replaces the traditional minimized Euclidean distance to improve the robustness of the algorithm. Through the kernel function, correntropy can give less weight to outliers and noise in data but give greater weight to meaningful data. Meanwhile, the geometry structure of the high-dimensional data is completely preserved in the low-dimensional manifold through the graph regularization. Feature selection and sample clustering are commonly used methods for analyzing genes. Sparse constraints are applied to the loss function to reduce matrix complexity and analysis difficulty. Comparing the other five similar methods, the effectiveness of the SGNMFC model is proved by selection of differentially expressed genes and sample clustering experiments in three The Cancer Genome Atlas (TCGA) datasets.