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Learning Approach for Fast Approximate Matrix Factorizations.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Learning Approach for Fast Approximate Matrix Factorizations./
作者:	Yu, Haiyan.
面頁冊數:	1 online resource (53 pages)
附註:	Source: Masters Abstracts International, Volume: 84-01.
Contained By:	Masters Abstracts International84-01.
標題:	Electrical engineering. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=29211918click for full text (PQDT)
ISBN:	9798837550188

Learning Approach for Fast Approximate Matrix Factorizations.
Yu, Haiyan.

Learning Approach for Fast Approximate Matrix Factorizations. - 1 online resource (53 pages)

Source: Masters Abstracts International, Volume: 84-01.

Thesis (M.S.)--University of Denver, 2022.

Includes bibliographical references

Efficiently computing an (approximate) orthonormal basis and low-rank approximation for the input data X plays a crucial role in data analysis. One of the most efficient algorithms for such tasks is the randomized algorithm, which proceeds by computing a projection XA with a random projection matrix A of much smaller size, and then computing the orthonormal basis as well as low-rank factorizations of the tall matrix XA. While a random matrix A is the de facto choice, in this work, we improve upon its performance by utilizing a learning approach to find an adaptive projection matrix A from a set of training data. We derive a closed-form formulation for the gradient of the training problem, enabling us to use efficient gradient-based algorithms. Experiments show that the learned dense matrix trained by eight different objective functions achieves better performance than a random one. We also extend this approach for learning structured projection matrix, such as the sketching matrix that performs as selecting a few number of representative columns from the input data. Our experiments on both synthetical and real data show that both learned dense and sketch projection matrices outperform the random ones in finding the approximate orthonormal basis and low-rank approximations. We conclude the thesis by discussing possible approaches for generalization analysis.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2023

Mode of access: World Wide Web

ISBN: 9798837550188Subjects--Topical Terms:

649834
Electrical engineering.
Subjects--Index Terms:

Efficiently computingIndex Terms--Genre/Form:

542853
Electronic books.

Learning Approach for Fast Approximate Matrix Factorizations.
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500 $a Source: Masters Abstracts International, Volume: 84-01.
500 $a Advisor: Zhu, Zhihui.
502 $a Thesis (M.S.)--University of Denver, 2022.
504 $a Includes bibliographical references
520 $a Efficiently computing an (approximate) orthonormal basis and low-rank approximation for the input data X plays a crucial role in data analysis. One of the most efficient algorithms for such tasks is the randomized algorithm, which proceeds by computing a projection XA with a random projection matrix A of much smaller size, and then computing the orthonormal basis as well as low-rank factorizations of the tall matrix XA. While a random matrix A is the de facto choice, in this work, we improve upon its performance by utilizing a learning approach to find an adaptive projection matrix A from a set of training data. We derive a closed-form formulation for the gradient of the training problem, enabling us to use efficient gradient-based algorithms. Experiments show that the learned dense matrix trained by eight different objective functions achieves better performance than a random one. We also extend this approach for learning structured projection matrix, such as the sketching matrix that performs as selecting a few number of representative columns from the input data. Our experiments on both synthetical and real data show that both learned dense and sketch projection matrices outperform the random ones in finding the approximate orthonormal basis and low-rank approximations. We conclude the thesis by discussing possible approaches for generalization analysis.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2023
538 $a Mode of access: World Wide Web
650 4 $a Electrical engineering. $3 649834
653 $a Efficiently computing
653 $a Low-rank approximation
653 $a Approximate orthonormal basis
653 $a Sketch projection matrices
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