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AbstractSparse 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. © 2010, The International Biometric Society.
CitationLee M, Shen H, Huang JZ, Marron JS (2010) Biclustering via Sparse Singular Value Decomposition. Biometrics 66: 1087–1095. Available: http://dx.doi.org/10.1111/j.1541-0420.2010.01392.x.
SponsorsThe authors extend grateful thanks to one coeditor, one associate editor, and three reviewers for their constructive comments. ML, HS, and JSM are partially supported by NSF grant DMS-0606577. JZH is partially supported by NSF grants DMS-0606580, DMS-0907170, NCI grant CA57030, and award KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST).
CollectionsPublications Acknowledging KAUST Support
- Robust biclustering by sparse singular value decomposition incorporating stability selection.
- Authors: Sill M, Kaiser S, Benner A, Kopp-Schneider A
- Issue date: 2011 Aug 1
- Sparse non-negative matrix factorizations via alternating non-negativity-constrained least squares for microarray data analysis.
- Authors: Kim H, Park H
- Issue date: 2007 Jun 15
- Biclustering of microarray data with MOSPO based on crowding distance.
- Authors: Liu J, Li Z, Hu X, Chen Y
- Issue date: 2009 Apr 29
- Joint analysis of multiple high-dimensional data types using sparse matrix approximations of rank-1 with applications to ovarian and liver cancer.
- Authors: Okimoto G, Zeinalzadeh A, Wenska T, Loomis M, Nation JB, Fabre T, Tiirikainen M, Hernandez B, Chan O, Wong L, Kwee S
- Issue date: 2016
- Gene selection in cancer classification using sparse logistic regression with Bayesian regularization.
- Authors: Cawley GC, Talbot NL
- Issue date: 2006 Oct 1