University of Illinois Urbana-Champaign

On alternating minimization algorithms for matrix completion

Shah, Remi

This item is only available for download by members of the University of Illinois community. Students, faculty, and staff at the U of I may log in with your NetID and password to view the item. If you are trying to access an Illinois-restricted dissertation or thesis, you can request a copy through your library's Inter-Library Loan office or purchase a copy directly from ProQuest.

Permalink

https://hdl.handle.net/2142/104034

Description

Title
On alternating minimization algorithms for matrix completion
Author(s)
Shah, Remi
Contributor(s)
Katselis, Dimitrios
Issue Date
2019-05
Keyword(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.
Type of Resource
text
Language
en
Permalink
http://hdl.handle.net/2142/104034

Owning Collections

Senior Theses - Electrical and Computer Engineering PRIMARY
The best of ECE undergraduate research