TY - GEN
T1 - Multiplicative update for a class of constrained optimization problems related to NMF and its global convergence
AU - Takahashi, Norikazu
AU - Seki, Masato
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/11/28
Y1 - 2016/11/28
N2 - Multiplicative updates are widely used for nonnegative matrix factorization (NMF) as an efficient computational method. In this paper, we consider a class of constrained optimization problems in which a polynomial function of the product of two matrices is minimized subject to the nonnegativity constraints. These problems are closely related to NMF because the polynomial function covers many error function used for NMF. We first derive a multiplicative update rule for those problems by using the unified method developed by Yang and Oja. We next prove that a modified version of the update rule has the global convergence property in the sense of Zangwill under certain conditions. This result can be applied to many existing multiplicative update rules for NMF to guarantee their global convergence.
AB - Multiplicative updates are widely used for nonnegative matrix factorization (NMF) as an efficient computational method. In this paper, we consider a class of constrained optimization problems in which a polynomial function of the product of two matrices is minimized subject to the nonnegativity constraints. These problems are closely related to NMF because the polynomial function covers many error function used for NMF. We first derive a multiplicative update rule for those problems by using the unified method developed by Yang and Oja. We next prove that a modified version of the update rule has the global convergence property in the sense of Zangwill under certain conditions. This result can be applied to many existing multiplicative update rules for NMF to guarantee their global convergence.
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U2 - 10.1109/EUSIPCO.2016.7760286
DO - 10.1109/EUSIPCO.2016.7760286
M3 - Conference contribution
AN - SCOPUS:85005939708
T3 - European Signal Processing Conference
SP - 438
EP - 442
BT - 2016 24th European Signal Processing Conference, EUSIPCO 2016
PB - European Signal Processing Conference, EUSIPCO
T2 - 24th European Signal Processing Conference, EUSIPCO 2016
Y2 - 28 August 2016 through 2 September 2016
ER -