  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 (GL1-SVD) and group L0-norm penalty
(GL0-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 (OGL1-SVD) and overlapping group L0-norm penalty
(OGL0-SVD). We first adopt an alternating iterative strategy to solve GL1-SVD
based on a block coordinate descent method, and GL0-SVD based on a projection
method. The key of solving OGL1-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 OGL0-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.
