TY - GEN
T1 - Boundedness of modified multiplicative updates for nonnegative matrix factorization
AU - Katayama, Jiro
AU - Takahashi, Norikazu
AU - Takeuchi, Jun'Ichi
N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.
PY - 2013
Y1 - 2013
N2 - There have been proposed various types of multiplicative updates for nonnegative matrix factorization. However, these updates have a serious drawback in common: they are not defined for all pairs of nonnegative matrices. Furthermore, due to this drawback, their global convergence in the sense of Zangwill's theorem cannot be proved theoretically. In this paper, we consider slightly modified versions of various multiplicative update rules, that are defined for all pairs of matrices in the domain, and show that many of them have the boundedness property. This property is a necessary condition for update rules to be globally convergent in the sense of Zangwill's theorem.
AB - There have been proposed various types of multiplicative updates for nonnegative matrix factorization. However, these updates have a serious drawback in common: they are not defined for all pairs of nonnegative matrices. Furthermore, due to this drawback, their global convergence in the sense of Zangwill's theorem cannot be proved theoretically. In this paper, we consider slightly modified versions of various multiplicative update rules, that are defined for all pairs of matrices in the domain, and show that many of them have the boundedness property. This property is a necessary condition for update rules to be globally convergent in the sense of Zangwill's theorem.
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U2 - 10.1109/CAMSAP.2013.6714055
DO - 10.1109/CAMSAP.2013.6714055
M3 - Conference contribution
AN - SCOPUS:84894118092
SN - 9781467331463
T3 - 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013
SP - 252
EP - 255
BT - 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013
T2 - 2013 5th IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, CAMSAP 2013
Y2 - 15 December 2013 through 18 December 2013
ER -