2026-09-19T00:19:47Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1571452024-10-10T03:04:26Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Shah, Devavrat
Zhao, Freddie
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2024-10-09T18:24:15Z
2024-10-09T18:24:15Z
2024-09
2024-10-07T14:34:34.925Z
https://hdl.handle.net/1721.1/157145
Singular value decomposition (SVD) is an essential matrix factorization technique that decomposes a matrix into singular values and corresponding singular vectors that form orthonormal bases. SVD has wide-ranging applications from principal component analysis (PCA) to matrix completion and approximation. Methods for computing the SVD of a matrix are extensive and involve optimization algorithms with some theoretical guarantees, though many of these techniques are not scalable in nature. We show the efficacy of a distributed stochastic gradient descent algorithm by implementing parallelized alternating least squares and prove theoretical guarantees for its convergence and empirical results, which allow for the development of a simple framework for solving SVD in a correct, scalable, and easily optimizable manner.
M.Eng.
Massachusetts Institute of Technology
Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
Copyright retained by author(s)
https://creativecommons.org/licenses/by-nc-nd/4.0/
Distributed Singular Value Decomposition Through
Least Squares
Thesis
application/pdf
Master
Master of Engineering in Electrical Engineering and Computer Science
Publication
unknown
unknown
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<Abstract>Singular value decomposition (SVD) is an essential matrix factorization technique that decomposes a matrix into singular values and corresponding singular vectors that form orthonormal bases. SVD has wide-ranging applications from principal component analysis (PCA) to matrix completion and approximation. Methods for computing the SVD of a matrix are extensive and involve optimization algorithms with some theoretical guarantees, though many of these techniques are not scalable in nature. We show the efficacy of a distributed stochastic gradient descent algorithm by implementing parallelized alternating least squares and prove theoretical guarantees for its convergence and empirical results, which allow for the development of a simple framework for solving SVD in a correct, scalable, and easily optimizable manner.</Abstract>
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