Low-rank matrix recovery from row-and-column affine measurements

Avishai Wagner, Or Zuk

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

6 Scopus citations

Abstract

We propose and study a row-and-column affine measurement scheme for low-rank matrix recovery. Each measurement is a linear combination of elements in one row or one column of a matrix X. This setting arises naturally in applications from different domains. However, current algorithms developed for standard matrix recovery problems do not perform well in our case, hence the need for developing new algorithms and theory for our problem. We propose a simple algorithm for the problem based on Singular Value Decomposition (SVD) and least-squares (LS), which we term SVLS. We prove that (a simplified version of) our algorithm can recover X exactly with the minimum possible number of measurements in the noiseless case. In the general noisy case, we prove performance guarantees on the reconstruction accuracy under the Frobenius norm. In simulations, our row-and-column design and SVLS algorithm show improved speed, and comparable and in some cases better accuracy compared to standard measurements designs and algorithms. Our theoretical and experimental results suggest that the proposed row-and-column affine measurements scheme, together with our recovery algorithm, may provide a powerful framework for affine matrix reconstruction.

Original languageAmerican English
Title of host publication32nd International Conference on Machine Learning, ICML 2015
EditorsFrancis Bach, David Blei
PublisherInternational Machine Learning Society (IMLS)
Pages2012-2020
Number of pages9
ISBN (Electronic)9781510810587
StatePublished - 2015
Event32nd International Conference on Machine Learning, ICML 2015 - Lile, France
Duration: 6 Jul 201511 Jul 2015

Publication series

Name32nd International Conference on Machine Learning, ICML 2015
Volume3

Conference

Conference32nd International Conference on Machine Learning, ICML 2015
Country/TerritoryFrance
CityLile
Period6/07/1511/07/15

Bibliographical note

Publisher Copyright:
© Copyright 2015 by International Machine Learning Society (IMLS). All rights reserved.

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