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Biclustering via sparse singular value decomposition. (English) Zbl 1233.62182

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 the 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 and a food nutrition data set are used to illustrate SSVD as a biclustering method. SSVD is also compared with some existing biclustering methods using simulated data sets.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62H30 Classification and discrimination; cluster analysis (statistical aspects)
65C60 Computational problems in statistics (MSC2010)
62J05 Linear regression; mixed models
92C50 Medical applications (general)

Software:

OSCAR; LAS
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References:

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