Distributed Singular Value Decomposition Through
Least Squares
Name
zhao-fzhao1-meng-eecs-2024-thesis.pdf
Description
Thesis PDF
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574.99 KB
Format
Adobe PDF
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405c2621bc7367c8b87d9e1e45630612
Author(s)
Zhao, Freddie
Advisor(s)
Shah, Devavrat
Date Issued
September 2024
Publisher
Massachusetts Institute of Technology
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.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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