A truncated nuclear norm and graph-Laplacian regularized low-rank representation method for tumor clustering and gene selection

BACKGROUND: Clustering and feature selection act major roles in many communities. As a matrix factorization, Low-Rank Representation (LRR) has attracted lots of attentions in clustering and feature selection, but sometimes its performance is frustrated when the data samples are insufficient or contain a lot of noise. RESULTS: To address this drawback, a novel LRR model named TGLRR is proposed by integrating the truncated nuclear norm with graph-Laplacian. Different from the nuclear norm minimizing all singular values, the truncated nuclear norm only minimizes some smallest singular values, which can dispel the harm of shrinkage of the leading singular values. Finally, an efficient algorithm based on Linearized Alternating Direction with Adaptive Penalty is applied to resolving the optimization problem. CONCLUSIONS: The results show that the TGLRR method exceeds the existing state-of-the-art methods in aspect of tumor clustering and gene selection on integrated gene expression data.