2001
DOI: 10.1137/s0895479899357875
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Structure and Perturbation Analysis of Truncated SVDs for Column-Partitioned Matrices

Abstract: We present a detailed study of truncated SVD for column-partitioned matrices. In particular, we analyze the relation between the truncated SVD. of a matrix and the truncated SVDs of its submatrices. We give necessary and sufficient conditions under which truncated SVD of a matrix can be constructed from those of its submatrices. We also present perturbation analysis to •show that an approximate truncated SVD can still be computed even if the given necessary and sufficient conditions are only approximately sati… Show more

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Cited by 12 publications
(7 citation statements)
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“…In a similar setting, Zhang and Zha [33] consider structural and perturbation analysis of truncated SVDs for column partitioned matrices. Necessary and sufficient conditions are given in order to reconstruct the truncated SVD of the original data matrix A from the truncated SVDs of its block-column-wise partitioning.…”
Section: Related Workmentioning
confidence: 99%
See 1 more Smart Citation
“…In a similar setting, Zhang and Zha [33] consider structural and perturbation analysis of truncated SVDs for column partitioned matrices. Necessary and sufficient conditions are given in order to reconstruct the truncated SVD of the original data matrix A from the truncated SVDs of its block-column-wise partitioning.…”
Section: Related Workmentioning
confidence: 99%
“…U T U = I and V T V = I. In the blockcolumn-wise approximations used in [9,7,13,33,6] the left singular vectors U i are obtained by approximating the block-columns A i , then the approximation of A is obtained in terms ofŨ = [U 1 , · · · , U c ], which is not orthonormal and has to be dealt with explicitly in order to compute the core matrix in the approximation. A difference compared to the column subset selection methods, which use only part of the data to compute the low rank approximation, is that we use the entire matrix A to compute the clustered low rank approximation.…”
Section: Related Workmentioning
confidence: 99%
“…An orthonormal basis is computed using these representatives in order to approximate A. In a similar setting, Zhang and Zha [45] consider structural and perturbation analysis of truncated SVDs for column partitioned matrices. Necessary and sufficient conditions are given in order to reconstruct the truncated SVD of the original data matrix A from the truncated SVDs of its block-column-wise partitioning.…”
Section: Principal Angles Assume We Have a Truncated Svd Approximatimentioning
confidence: 99%
“…An important difference of our method, in comparison with the approximations in [14,9,41,45,8], is that we cluster rows and columns simultaneously. In addition U = diag(U 1 , .…”
Section: Principal Angles Assume We Have a Truncated Svd Approximatimentioning
confidence: 99%
“…Reference [21] addresses the following important issue. If we possess truncated SVD approximations for blocks of A, how does this information help us to approximate A?…”
Section: Low Rank Matrix Approximationsmentioning
confidence: 99%