Sparse Graph Regularization Non-Negative Matrix Factorization Based on Huber Loss Model for Cancer Data Analysis

Non-negative matrix factorization (NMF) is a matrix decomposition method based on the square loss function. To exploit cancer information, cancer gene expression data often uses the NMF method to reduce dimensionality. Gene expression data usually have some noise and outliers, while the original NMF loss function is very sensitive to non-Gaussian noise. To improve the robustness and clustering performance of the algorithm, we propose a sparse graph regularization NMF based on Huber loss model for cancer data analysis (Huber-SGNMF). Huber loss is a function between L1-norm and L2-norm that can effectively handle non-Gaussian noise and outliers. Taking into account the sparsity matrix and data geometry information, sparse penalty and graph regularization terms are introduced into the model to enhance matrix sparsity and capture data manifold structure. Before the experiment, we first analyzed the robustness of Huber-SGNMF and other models. Experiments on The Cancer Genome Atlas (TCGA) data have shown that Huber-SGNMF performs better than other most advanced methods in sample clustering and differentially expressed gene selection.