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 language | English |
---|---|
Title of host publication | 32nd International Conference on Machine Learning, ICML 2015 |
Editors | Francis Bach, David Blei |
Publisher | International Machine Learning Society (IMLS) |
Pages | 2012-2020 |
Number of pages | 9 |
ISBN (Electronic) | 9781510810587 |
State | Published - 2015 |
Event | 32nd International Conference on Machine Learning, ICML 2015 - Lile, France Duration: 6 Jul 2015 → 11 Jul 2015 |
Publication series
Name | 32nd International Conference on Machine Learning, ICML 2015 |
---|---|
Volume | 3 |
Conference
Conference | 32nd International Conference on Machine Learning, ICML 2015 |
---|---|
Country/Territory | France |
City | Lile |
Period | 6/07/15 → 11/07/15 |
Bibliographical note
Publisher Copyright:© Copyright 2015 by International Machine Learning Society (IMLS). All rights reserved.