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Title Sparse and orthogonal singular value decomposition
Publication Date
Date Accessioned
Degree MS
Discipline/Department Department of Statistics
Degree Level masters
University/Publisher Kansas State University
Abstract The singular value decomposition (SVD) is a commonly used matrix factorization technique in statistics, and it is very e ective in revealing many low-dimensional structures in a noisy data matrix or a coe cient matrix of a statistical model. In particular, it is often desirable to obtain a sparse SVD, i.e., only a few singular values are nonzero and their corresponding left and right singular vectors are also sparse. However, in several existing methods for sparse SVD estimation, the exact orthogonality among the singular vectors are often sacri ced due to the di culty in incorporating the non-convex orthogonality constraint in sparse estimation. Imposing orthogonality in addition to sparsity, albeit di cult, can be critical in restricting and guiding the search of the sparsity pattern and facilitating model interpretation. Combining the ideas of penalized regression and Bregman iterative methods, we propose two methods that strive to achieve the dual goal of sparse and orthogonal SVD estimation, in the general framework of high dimensional multivariate regression. We set up simulation studies to demonstrate the e cacy of the proposed methods.
Subjects/Keywords Bregman iteration; Multivariate regression; Orthogonality constraint; Singular value decomposition; Sparsity; Statistics (0463)
Contributors Kun Chen
Language en
Country of Publication us
Record ID handle:2097/15992
Repository ksu
Date Retrieved
Date Indexed 2018-01-03
Issued Date 2013-07-17 00:00:00
Note [degree] Master of Science; [level] Masters; [department] Department of Statistics; [advisor] Kun Chen;

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