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Best rank-1 approximations without o...

Purdue University.

Best rank-1 approximations without orthogonal invariance for the 1-norm.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Best rank-1 approximations without orthogonal invariance for the 1-norm./
Author:	Vasudevan, Varun A.
Description:	1 online resource (41 pages)
Notes:	Source: Masters Abstracts International, Volume: 56-01.
Contained By:	Masters Abstracts International56-01(E).
Subject:	Electrical engineering. -
Online resource:	click for full text (PQDT)
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. - 1 online resource (41 pages)

Source: Masters Abstracts International, Volume: 56-01.

Thesis (M.S.E.C.E.)

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9781369036299Subjects--Topical Terms:

596380
Electrical engineering.
Index Terms--Genre/Form:

554714
Electronic books.

Best rank-1 approximations without orthogonal invariance for the 1-norm.
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099 $a TUL $f hyy $c available through World Wide Web
100 1 $a Vasudevan, Varun A. $3 1180506
245 1 0 $a Best rank-1 approximations without orthogonal invariance for the 1-norm.
264 0 $c 2016
300 $a 1 online resource (41 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
500 $a Source: Masters Abstracts International, Volume: 56-01.
500 $a Adviser: David F. Gleich.
502 $a Thesis (M.S.E.C.E.) $c Purdue University $d 2016.
504 $a Includes bibliographical references
520 $a 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.
520 $a 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.
520 $a 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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Electrical engineering. $3 596380
650 4 $a Mathematics. $3 527692
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0544
690 $a 0405
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Purdue University. $b Electrical and Computer Engineering. $3 1148521
773 0 $t Masters Abstracts International $g 56-01(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10148448 $z click for full text (PQDT)

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