NDLI: On the Wiberg Algorithm for Matrix Factorization in the Presence of Missing Components

Content Provider	Springer Nature Link
Author	Okatani, Takayuki Deguchi, Koichiro
Copyright Year	2006
Abstract	This paper considers the problem of factorizing a matrix with missing components into a product of two smaller matrices, also known as principal component analysis with missing data (PCAMD). The Wiberg algorithm is a numerical algorithm developed for the problem in the community of applied mathematics. We argue that the algorithm has not been correctly understood in the computer vision community. Although there are many studies in our community, almost every one of which refers to the Wiberg study, as far as we know, there is no literature in which the performance of the Wiberg algorithm is investigated or the detail of the algorithm is presented. In this paper, we present derivation of the algorithm along with a problem in its implementation that needs to be carefully considered, and then examine its performance. The experimental results demonstrate that the Wiberg algorithm shows a considerably good performance, which should contradict the conventional view in our community, namely that minimization-based algorithms tend to fail to converge to a global minimum relatively frequently. The performance of the Wiberg algorithm is such that even starting with random initial values, it converges in most cases to a correct solution, even when the matrix has many missing components and the data are contaminated with very strong noise. Our conclusion is that the Wiberg algorithm can also be used as a standard algorithm for the problems of computer vision.
Starting Page	329
Ending Page	337
Page Count	9
File Format	PDF
ISSN	09205691
Journal	International Journal of Computer Vision
Volume Number	72
Issue Number	3
e-ISSN	15731405
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-09-15
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	matrix factorization singular value decomposition principal component analysis with missing data (PCAMD) structure from motion numerical algorithm Artificial Intelligence (incl. Robotics) Computer Imaging, Vision, Pattern Recognition and Graphics Image Processing and Computer Vision Pattern Recognition
Content Type	Text
Resource Type	Article
Subject	Artificial Intelligence Computer Vision and Pattern Recognition Software

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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