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Best rank-1 approximations without o...
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Vasudevan, Varun A.
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Best rank-1 approximations without orthogonal invariance for the 1-norm.
紀錄類型:
書目-電子資源 : Monograph/item
正題名/作者:
Best rank-1 approximations without orthogonal invariance for the 1-norm./
作者:
Vasudevan, Varun A.
出版者:
Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:
41 p.
附註:
Source: Masters Abstracts International, Volume: 56-01.
Contained By:
Masters Abstracts International56-01(E).
標題:
Electrical engineering. -
電子資源:
http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10148448
ISBN:
9781369036299
Best rank-1 approximations without orthogonal invariance for the 1-norm.
Vasudevan, Varun A.
Best rank-1 approximations without orthogonal invariance for the 1-norm.
- Ann Arbor : ProQuest Dissertations & Theses, 2016 - 41 p.
Source: Masters Abstracts International, Volume: 56-01.
Thesis (M.S.E.C.E.)--Purdue University, 2016.
Data measured in the real-world is often composed of both a true signal, such as an image or experimental response, and a perturbation, such as noise or weak secondary effects. Low-rank matrix approximation is one commonly used technique to extract the true signal from the data. Given a matrix representation of the data, this method seeks the nearest low-rank matrix where the distance is measured using a matrix norm.
ISBN: 9781369036299Subjects--Topical Terms:
649834
Electrical engineering.
Best rank-1 approximations without orthogonal invariance for the 1-norm.
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Data measured in the real-world is often composed of both a true signal, such as an image or experimental response, and a perturbation, such as noise or weak secondary effects. Low-rank matrix approximation is one commonly used technique to extract the true signal from the data. Given a matrix representation of the data, this method seeks the nearest low-rank matrix where the distance is measured using a matrix norm.
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The classic Eckart-Young-Mirsky theorem tells us how to use the Singular Value Decomposition (SVD) to compute a best low-rank approximation of a matrix for any orthogonally invariant norm. This leaves as an open question how to compute a best low-rank approximation for norms that are not orthogonally invariant, like the 1-norm.
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In this thesis, we present how to calculate the best rank-1 approximations for 2-by-n and n-by-2 matrices in the 1-norm. We consider both the operator induced 1-norm (maximum column 1-norm) and the Frobenius 1-norm (sum of absolute values over the matrix). We present some thoughts on how to extend the arguments to larger matrices.
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