Please use this identifier to cite or link to this item: http://hdl.handle.net/2440/64842
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Type: Conference paper
Title: Efficient computation of robust low-rank matrix approximations in the presence of missing data using the L₁ norm
Other Titles: Efficient computation of robust low-rank matrix approximations in the presence of missing data using the L(1) norm
Author: Eriksson, A.
Van Den Hengel, A.
Citation: Proceedings of 23rd IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2010: pp.771-778
Publisher: IEEE COMPUTER SOC
Publisher Place: 10662 LOS VAQUEROS CIRCLE, PO BOX 3014, LOS ALAMITOS, CA 90720-1264 USA
Issue Date: 2010
Series/Report no.: IEEE Conference on Computer Vision and Pattern Recognition
ISBN: 9781424469840
ISSN: 1063-6919
Conference Name: IEEE Conference on Computer Vision and Pattern Recognition (23rd : 2010 : San Francisco, CA)
Statement of
Responsibility: 
Anders Eriksson and Anton van den Hengel
Abstract: The calculation of a low-rank approximation of a matrix is a fundamental operation in many computer vision applications. The workhorse of this class of problems has long been the Singular Value Decomposition. However, in the presence of missing data and outliers this method is not applicable, and unfortunately, this is often the case in practice. In this paper we present a method for calculating the low-rank factorization of a matrix which minimizes the L1 norm in the presence of missing data. Our approach represents a generalization the Wiberg algorithm of one of the more convincing methods for factorization under the L2 norm. By utilizing the differentiability of linear programs, we can extend the underlying ideas behind this approach to include this class of L1 problems as well. We show that the proposed algorithm can be efficiently implemented using existing optimization software. We also provide preliminary experiments on synthetic as well as real world data with very convincing results.
Rights: ©2010 IEEE
RMID: 0020105297
DOI: 10.1109/CVPR.2010.5540139
Appears in Collections:Computer Science publications

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