Biclustering via Sparse Singular Value Decomposition

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Abstract:

Summary. 

Sparse singular value decomposition (SSVD) is proposed as a new exploratory analysis tool for biclustering or identifying interpretable row–column associations within high-dimensional data matrices. SSVD seeks a low-rank, checkerboard structured matrix approximation to data matrices. The desired checkerboard structure is achieved by forcing both the left- and right-singular vectors to be sparse, that is, having many zero entries. By interpreting singular vectors as regression coefficient vectors for certain linear regressions, sparsity-inducing regularization penalties are imposed to the least squares regression to produce sparse singular vectors. An efficient iterative algorithm is proposed for computing the sparse singular vectors, along with some discussion of penalty parameter selection. A lung cancer microarray dataset and a food nutrition dataset are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated datasets.

Keywords: Adaptive lasso; Biclustering; Dimension reduction; High-dimension low sample size; Penalization; Principal component analysis

Document Type: Research Article

DOI: http://dx.doi.org/10.1111/j.1541-0420.2010.01392.x

Affiliations: 1: Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, U.S.A. 2: Department of Statistics, Texas A&M University, College Station, Texas 77843, U.S.A.

Publication date: December 1, 2010

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