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Reliable and Efficient Algorithms for Spectrum-Revealing Low-Rank Data Analysis.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Reliable and Efficient Algorithms for Spectrum-Revealing Low-Rank Data Analysis./
作者:	Anderson, David Gaylord.
面頁冊數:	1 online resource (131 pages)
附註:	Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
Contained By:	Dissertation Abstracts International78-10B(E).
標題:	Applied mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9781369842784

Reliable and Efficient Algorithms for Spectrum-Revealing Low-Rank Data Analysis.
Anderson, David Gaylord.

Reliable and Efficient Algorithms for Spectrum-Revealing Low-Rank Data Analysis. - 1 online resource (131 pages)

Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.

Thesis (Ph.D.)

Includes bibliographical references

As the amount of data collected in our world increases, reliable compression algorithms are needed when datasets become too large for practical analysis, when significant noise is present in the data, or when the strongest signals in the data are needed. In this work, two data compression algorithms are presented. The main result is a low-rank approximation algorithm (a type of compression algorithm) that uses modern techniques in randomization to repurpose a classic algorithm in the field of linear algebra called the LU decomposition to perform data compression. The resulting algorithm is called Spectrum-Revealing LU (SRLU).

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

Mode of access: World Wide Web

ISBN: 9781369842784Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Reliable and Efficient Algorithms for Spectrum-Revealing Low-Rank Data Analysis.
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100 1 $a Anderson, David Gaylord. $3 1180581
245 1 0 $a Reliable and Efficient Algorithms for Spectrum-Revealing Low-Rank Data Analysis.
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300 $a 1 online resource (131 pages)
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500 $a Source: Dissertation Abstracts International, Volume: 78-10(E), Section: B.
500 $a Advisers: Ming Gu; Per-Olof Persson.
502 $a Thesis (Ph.D.) $c University of California, Berkeley $d 2016.
504 $a Includes bibliographical references
520 $a As the amount of data collected in our world increases, reliable compression algorithms are needed when datasets become too large for practical analysis, when significant noise is present in the data, or when the strongest signals in the data are needed. In this work, two data compression algorithms are presented. The main result is a low-rank approximation algorithm (a type of compression algorithm) that uses modern techniques in randomization to repurpose a classic algorithm in the field of linear algebra called the LU decomposition to perform data compression. The resulting algorithm is called Spectrum-Revealing LU (SRLU).
520 $a Both rigorous theory and numeric experiments demonstrate the effectiveness of SRLU. The theoretical work presented also develops a framework with which other low-rank approximation algorithms can be analyzed. As the name implies, Spectrum-Revealing LU seeks to capture the entire spectrum of the data (i.e. to capture all signals present in the data).
520 $a A second compression algorithm is also introduced, which seeks to compression graphs. Called a sparsification algorithm, this algorithm can accept a weighted or unweighted graph and produce an approximation without changing the weights (or introducing weights in the case of an unweighted graph). Theoretical results provide a bound on the quality of the results, and a numeric example is also explored.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
650 4 $a Statistics. $3 556824
655 7 $a Electronic books. $2 local $3 554714
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690 $a 0463
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a University of California, Berkeley. $b Mathematics. $3 1180510
773 0 $t Dissertation Abstracts International $g 78-10B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10252046 $z click for full text (PQDT)