{"id":{"repo_id":"mit","oai_identifier":"oai:dspace.mit.edu:1721.1/157145"},"canonical_url":"https://search.dev.ndltd.org/etd/mit/oai:dspace.mit.edu:1721.1/157145","repository":{"repo_id":"mit","name":"MIT","base_url":"https://dspace.mit.edu/oai/request"},"display":{"title":"Distributed Singular Value Decomposition Through Least Squares","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_html":"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_has_math":false,"creators":["Zhao, Freddie"],"institution":"Massachusetts Institute of Technology","degree_name":"Master","degree_level":null,"degree_discipline":null,"degree_department":"Massachusetts Institute of Technology. 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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."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["M.Eng."]},{"key":"dc:title","label":"Title","values":["Distributed Singular Value Decomposition Through Least Squares"]}]}],"canonical_facts":{"dc:contributor.advisor":["Shah, Devavrat"],"dc:contributor.department":["Massachusetts Institute of Technology. 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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."],"dc:description.degree":["M.Eng."],"dc:identifier.uri":["https://hdl.handle.net/1721.1/157145"],"dc:publisher":["Massachusetts Institute of Technology"],"dc:rights":["Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)","Copyright retained by author(s)"],"dc:rights.uri":["https://creativecommons.org/licenses/by-nc-nd/4.0/"],"dc:title":["Distributed Singular Value Decomposition Through Least Squares"],"dc:type":["Thesis"],"thesis:degree_name":["Master","Master of Engineering in Electrical Engineering and Computer Science"]},"updated_at":"2026-07-22T22:22:20Z"}