CaltechAUTHORS
  A Caltech Library Service

An Improved Initialization for Low-Rank Matrix Completion Based on Rank-L Updates

Douik, Ahmed and Hassibi, Babak (2018) An Improved Initialization for Low-Rank Matrix Completion Based on Rank-L Updates. In: 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). IEEE , Piscataway, NJ, pp. 3959-3963. ISBN 978-1-5386-4658-8. https://resolver.caltech.edu/CaltechAUTHORS:20180920-111338769

Full text is not posted in this repository. Consult Related URLs below.

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20180920-111338769

Abstract

Given a data matrix with partially observed entries, the low-rank matrix completion problem is one of finding a matrix with the lowest rank that perfectly fits the given observations. While there exist convex relaxations for the low-rank completion problem, the underlying problem is inherently nonconvex, and most algorithms (alternating projection, Riemannian optimization, etc.) heavily depend on the initialization. This paper proposes an improved initialization that relies on successive rank-l updates. Further, the paper proposes theoretical guarantees under which the proposed initialization is closer to the unknown optimal solution than the all zeros initialization in the Frobenius norm. To cope with the problem of local minima, the paper introduces and uses random norms to change the position of the local minima while preserving the global one. Using a Riemannian optimization routine, simulation results reveal that the proposed solution succeeds in completing Gaussian partially observed matrices with a random set of revealed entries close to the information-theoretical limits, thereby significantly improving on prior methods.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ICASSP.2018.8461826DOIArticle
https://ieeexplore.ieee.org/document/8461826PublisherArticle
ORCID:
AuthorORCID
Douik, Ahmed0000-0001-7791-9443
Alternate Title:An Improved Initialization for Low-Rank Matrix Completion Based on Rank-1 Updates
Additional Information:© 2018 IEEE. The authors would like to thank Dr. Philipp Walk for his helpful comments and suggestions.
Subject Keywords:Matrix completion, rank minimization, Riemannian optimization, rank-1 update, random matrices
Record Number:CaltechAUTHORS:20180920-111338769
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20180920-111338769
Official Citation:A. Douik and B. Hassibi, "An Improved Initialization for Low-Rank Matrix Completion Based on Rank-L Updates," 2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Calgary, AB, Canada, 2018, pp. 3959-3963. doi: 10.1109/ICASSP.2018.8461826
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:89785
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Sep 2018 18:25
Last Modified:03 Oct 2019 20:19

Repository Staff Only: item control page