A Novel Sparse Graph-Regularized Singular Value Decomposition Model and Its Application to Genomic Data Analysis

Learning the gene coexpression pattern is a central challenge for high-dimensional gene expression analysis. Recently, sparse singular value decomposition (SVD) has been used to achieve this goal. However, this model ignores the structural information between variables (e.g., a gene network). The typical graph-regularized penalty can be used to incorporate such prior graph information to achieve more accurate discovery and better interpretability. However, the existing approach fails to consider the opposite effect of variables with negative correlations. In this article, we propose a novel sparse graph-regularized SVD model with absolute operator (AGSVD) for high-dimensional gene expression pattern discovery. The key of AGSVD is to impose a novel graph-regularized penalty (|u|TL|u|). However, such a penalty is a nonconvex and nonsmooth function, so it brings new challenges to model solving. We show that the nonconvex problem can be efficiently handled in a convex fashion by adopting an alternating optimization strategy. The simulation results on synthetic data show that our method is more effective than the existing SVD-based ones. In addition, the results on several real gene expression data sets show that the proposed methods can discover more biologically interpretable expression patterns by incorporating the prior gene network.

Automated summary

In this article, a novel sparse graph-regularized SVD model with absolute operator (AGSVD) is proposed for discovering high-dimensional gene expression patterns. The model effectively handles the structural information between variables and incorporates prior graph information through a graph-regularized penalty, leading to improved interpretability and accuracy. The nonconvex problem introduced by the novel penalty function is efficiently solved using an alternating optimization strategy, and the simulation results demonstrate the effectiveness of the proposed method over existing SVD-based approaches for gene expression analysis.