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
Checksum (MD5)
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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Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)
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