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Title:On alternating minimization algorithms for matrix completion
Author(s):Shah, Remi
Contributor(s):Katselis, Dimitrios
Subject(s):matrix completion
alternating minimization
least squares
matrix factorization
Abstract:Alternating minimization is a technique for solving non-convex optimization problems by alternating direction of minimization. Alternating minimization is a powerful tool for solving problems such as matrix factorization and matrix completion. This method involves solving multiple least squares problems in succession, each optimizing over a different variable, and repeating until zero error or some convergence condition is met. With the prevalence of streaming music, television, and media, recommender systems are powerful tools to increase user experience, and low-rank matrix completion can be used efficiently and accurately to predict user preferences. In low-rank matrix completion, we want to estimate a low-rank matrix with missing entries, with two matrices, i.e. 𝑋=𝑈𝑉𝑇. In this thesis, we investigate initialization, convergence and parameter tuning. In particular, we propose using non-negative matrix factorization instead of computing an SVD for initializing an algorithm. We also show results for matrix sensing, where we attempt to recover a low-rank matrix from a set of linear measurements from the matrix. As an application, we show how matrix completion can be used to reconstruct images that have significant data removed.
Issue Date:2019-05
Date Available in IDEALS:2019-06-17

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