2-dimensional singular value decomposition for 2D maps and images

Chris Ding; Jieping Ye

2-dimensional singular value decomposition for 2D maps and images

Chris Ding, Jieping Ye

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

For a set of 1D vectors, standard singular value decomposition (SVD) is frequently applied. For a set of 2D objects such as images or weather maps, we form 2dSVD, which computes principal eigenvectors of row-row and column-column covariance matrices, exactly as in the standard SVD. We study optimality properties of 2dSVD as low-rank approximation and show that it provides a framework unifying two recent approaches. Experiments on images and weather maps illustrate the usefulness of 2dSVD.

Original language	English (US)
Title of host publication	Proceedings of the 2005 SIAM International Conference on Data Mining, SDM 2005
Pages	32-43
Number of pages	12
State	Published - 2005
Externally published	Yes
Event	5th SIAM International Conference on Data Mining, SDM 2005 - Newport Beach, CA, United States Duration: Apr 21 2005 → Apr 23 2005

Other

Other	5th SIAM International Conference on Data Mining, SDM 2005
Country/Territory	United States
City	Newport Beach, CA
Period	4/21/05 → 4/23/05

ASJC Scopus subject areas

Software

Cite this

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title = "2-dimensional singular value decomposition for 2D maps and images",

abstract = "For a set of 1D vectors, standard singular value decomposition (SVD) is frequently applied. For a set of 2D objects such as images or weather maps, we form 2dSVD, which computes principal eigenvectors of row-row and column-column covariance matrices, exactly as in the standard SVD. We study optimality properties of 2dSVD as low-rank approximation and show that it provides a framework unifying two recent approaches. Experiments on images and weather maps illustrate the usefulness of 2dSVD.",

author = "Chris Ding and Jieping Ye",

year = "2005",

language = "English (US)",

pages = "32--43",

booktitle = "Proceedings of the 2005 SIAM International Conference on Data Mining, SDM 2005",

note = "5th SIAM International Conference on Data Mining, SDM 2005 ; Conference date: 21-04-2005 Through 23-04-2005",

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T1 - 2-dimensional singular value decomposition for 2D maps and images

AU - Ding, Chris

AU - Ye, Jieping

PY - 2005

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N2 - For a set of 1D vectors, standard singular value decomposition (SVD) is frequently applied. For a set of 2D objects such as images or weather maps, we form 2dSVD, which computes principal eigenvectors of row-row and column-column covariance matrices, exactly as in the standard SVD. We study optimality properties of 2dSVD as low-rank approximation and show that it provides a framework unifying two recent approaches. Experiments on images and weather maps illustrate the usefulness of 2dSVD.

AB - For a set of 1D vectors, standard singular value decomposition (SVD) is frequently applied. For a set of 2D objects such as images or weather maps, we form 2dSVD, which computes principal eigenvectors of row-row and column-column covariance matrices, exactly as in the standard SVD. We study optimality properties of 2dSVD as low-rank approximation and show that it provides a framework unifying two recent approaches. Experiments on images and weather maps illustrate the usefulness of 2dSVD.

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M3 - Conference contribution

AN - SCOPUS:84880116864

SP - 32

EP - 43

BT - Proceedings of the 2005 SIAM International Conference on Data Mining, SDM 2005

T2 - 5th SIAM International Conference on Data Mining, SDM 2005

Y2 - 21 April 2005 through 23 April 2005

ER -

2-dimensional singular value decomposition for 2D maps and images

Abstract

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ASJC Scopus subject areas

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