Group-Sparse SVD Models via L1- and L0-norm Penalties and their Applications in Biological Data

被引:9
作者
Min, Wenwen [1 ,2 ]
Liu, Juan [3 ]
Zhang, Shihua [4 ,5 ,6 ]
机构
[1] Chinese Univ Hong Kong, Sch Sci & Engn, Shenzhen 518172, Peoples R China
[2] Shenzhen Res Inst Big Data, Shenzhen 518172, Peoples R China
[3] Wuhan Univ, Sch Comp Sci, Wuhan 430072, Peoples R China
[4] Chinese Acad Sci, Acad Math & Syst Sci, NCMIS, CEMS,RCSDS, Beijing 100190, Peoples R China
[5] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
[6] Chinese Acad Sci, Ctr Excellence Anim Evolut & Genet, Kunming 650223, Yunnan, Peoples R China
基金
中国国家自然科学基金;
关键词
Sparse SVD; low-rank matrix decomposition; group-sparse penalty; overlapping group-sparse penalty; coordinate descent method; alternating direction method of multipliers (ADMM); data mining; SINGULAR-VALUE DECOMPOSITION; ALTERNATING LINEARIZED MINIMIZATION; REGRESSION SHRINKAGE; SELECTION; NONCONVEX; CONVERGENCE; ALGORITHM; LASSO;
D O I
10.1109/TKDE.2019.2932063
中图分类号
TP18 [人工智能理论];
学科分类号
081104 ; 0812 ; 0835 ; 1405 ;
摘要
Sparse Singular Value Decomposition (SVD) models have been proposed for biclustering high dimensional gene expression data to identify block patterns with similar expressions. However, these models do not take into account prior group effects upon variable selection. To this end, we first propose group-sparse SVD models with group Lasso (GL(1)-SVD) and group L-0-norm penalty (GL(0)-SVD) for non-overlapping group structure of variables. However, such group-sparse SVD models limit their applicability in some problems with overlapping structure. Thus, we also propose two group-sparse SVD models with overlapping group Lasso (OGL(1)-SVD) and overlapping group L-0-norm penalty (OGL(0)-SVD). We first adopt an alternating iterative strategy to solve GL(1)-SVD based on a block coordinate descent method, and GL(0)-SVD based on a projection method. The key of solving OGL(1)-SVD is a proximal operator with overlapping group Lasso penalty. We employ an alternating direction method of multipliers (ADMM) to solve the proximal operator. Similarly, we develop an approximate method to solve OGL(0)-SVD. Applications of these methods and comparison with competing ones using simulated data demonstrate their effectiveness. Extensive applications of them onto several real gene expression data with gene prior group knowledge identify some biologically interpretable gene modules.
引用
收藏
页码:536 / 550
页数:15
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