A hybrid algorithm for low-rank approximation of nonnegative matrix factorization

Nonnegative matrix factorization (NMF) is a recently developed method for data analysis. So far, most of known algorithms for NMF are based on alternating nonnegative least squares (ANLS) minimization of the squared Euclidean distance between the original data matrix and its low-rank approximation....

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Bibliographic Details
Published in:Neurocomputing (Amsterdam) Vol. 364; pp. 129 - 137
Main Authors: Wang, Peitao, He, Zhaoshui, Xie, Kan, Gao, Junbin, Antolovich, Michael, Tan, Beihai
Format: Journal Article
Language:English
Published: Elsevier B.V 28.10.2019
Subjects:
Alternately updating
Low-rank approximation
Nonnegative matrix factorization
Nonnegative Tucker decomposition
Alternately updating
Nonnegative Tucker decomposition
Low-rank approximation
Nonnegative matrix factorization
ISSN:0925-2312, 1872-8286
Online Access:Get full text
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Summary:Nonnegative matrix factorization (NMF) is a recently developed method for data analysis. So far, most of known algorithms for NMF are based on alternating nonnegative least squares (ANLS) minimization of the squared Euclidean distance between the original data matrix and its low-rank approximation. In this paper, we first develop a new NMF algorithm, in which a Procrustes rotation and a nonnegative projection are alternately performed. The new algorithm converges very rapidly. Then, we propose a hybrid NMF (HNMF) algorithm that combines the new algorithm with the low-rank approximation based NMF (lraNMF) algorithm. Furthermore, we extend the HNMF algorithm to nonnegative Tucker decomposition (NTD), which leads to a hybrid NTD (HNTD) algorithm. The simulations verify that the HNMF algorithm performs well under various noise conditions, and HNTD has a comparable performance to the low-rank approximation based sequential NTD (lraSNTD) algorithm for sparse representation of tensor objects.
ISSN:0925-2312
1872-8286
DOI:10.1016/j.neucom.2019.07.059