Efficient algorithm for low-rank matrix factorization with missing components and performance comparison of latest algorithms

Takayuki Okatani, Takahiro Yoshida, Koichiro Deguchi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

60 Citations (Scopus)

Abstract

This paper examines numerical algorithms for factorization of a low-rank matrix with missing components. We first propose a new method that incorporates a damping factor into the Wiberg method to solve the problem. The new method is characterized by the way it constrains the ambiguity of the matrix factorization, which helps improve both the global convergence ability and the local convergence speed. We then present experimental comparisons with the latest methods used to solve the problem. No comprehensive comparison of the methods that have been proposed recently has yet been reported in literature. In our experiments, we prioritize the assessment of the global convergence performance of each method, that is, how often and how fast the method can reach the global optimum starting from random initial values. Our conclusion is that top performance is achieved by a group of methods based on Newton-family minimization with damping factor that reduce the problem by eliminating either of the two factored matrices. Our method, which belongs to this group, consistently shows a 100% global convergence rate for different types of affine structure from motion data with a very high population of missing components.

Original languageEnglish
Title of host publication2011 International Conference on Computer Vision, ICCV 2011
Pages842-849
Number of pages8
DOIs
Publication statusPublished - 2011 Dec 1
Event2011 IEEE International Conference on Computer Vision, ICCV 2011 - Barcelona, Spain
Duration: 2011 Nov 62011 Nov 13

Other

Other2011 IEEE International Conference on Computer Vision, ICCV 2011
CountrySpain
CityBarcelona
Period11/11/611/11/13

ASJC Scopus subject areas

  • Software
  • Computer Vision and Pattern Recognition

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    Okatani, T., Yoshida, T., & Deguchi, K. (2011). Efficient algorithm for low-rank matrix factorization with missing components and performance comparison of latest algorithms. In 2011 International Conference on Computer Vision, ICCV 2011 (pp. 842-849). [6126324] https://doi.org/10.1109/ICCV.2011.6126324