NDLI: Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix

Content Provider	Springer Nature Link
Author	Chen, Pei
Copyright Year	2008
Abstract	Low-rank matrix approximation has applications in many fields, such as 3D reconstruction from an image sequence and 2D filter design. In this paper, one issue with low-rank matrix approximation is re-investigated: the missing data problem. Much effort was devoted to this problem, and the Wiberg algorithm or the damped Newton algorithm were recommended in previous studies. However, the Wiberg or damped Newton algorithms do not suit for large (especially “long”) matrices, because one needs to solve a large linear system in every iteration. In this paper, we revitalize the usage of the Levenberg-Marquardt algorithm for solving the missing data problem, by utilizing the property that low-rank approximation is a minimization problem on subspaces. In two proposed implementations of the Levenberg-Marquardt algorithm, one only needs to solve a much smaller linear system in every iteration, especially for “long” matrices. Simulations and experiments on real data show the superiority of the proposed algorithms. Though the proposed algorithms achieve a high success rate in estimating the optimal solution by random initialization, as illustrated by real examples; it still remains an open issue how to properly do the initialization in a severe situation (that is, a large amount of data is missing and with high-level noise).
Starting Page	125
Ending Page	142
Page Count	18
File Format	PDF
ISSN	09205691
Journal	International Journal of Computer Vision
Volume Number	80
Issue Number	1
e-ISSN	15731405
Language	English
Publisher	Springer US
Publisher Date	2008-04-17
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Low-rank matrix approximation Missing data problem Subspace Singular value decomposition Levenberg-Marquardt algorithm Pattern Recognition Image Processing and Computer Vision Artificial Intelligence (incl. Robotics) Computer Imaging, Vision, Pattern Recognition and Graphics
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Vision and Pattern Recognition Software

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