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Direct decomposition of three-way arrays using a non-negative approximation

Sun, Jiangming LU orcid ; Li, Tonghua ; Cong, Peisheng ; Xiong, Wenwei ; Tang, Shengnan and Zhu, Li LU (2010) In Talanta 83(2). p.541-548
Abstract

Non-negative matrix approximation (NNMA) has been used in diverse scientific fields, but it still has some major limitations. In the present study a novel trilinear decomposition method, termed three-way NNMA (TWNNMA), was developed. The method decomposes three-way arrays directly without unfolding and overcomes the restriction of locking zero elements in the deduced multiplicative update rules by adding a positive symmetric matrix. Direct trilinear decomposition was used as the TWNNMA initialization method and experimental results confirm that this greatly accelerated the convergence. An obvious advantage of TWNNMA is the uniqueness of the non-negative solution, which facilitates a better understanding of the underlying physical... (More)

Non-negative matrix approximation (NNMA) has been used in diverse scientific fields, but it still has some major limitations. In the present study a novel trilinear decomposition method, termed three-way NNMA (TWNNMA), was developed. The method decomposes three-way arrays directly without unfolding and overcomes the restriction of locking zero elements in the deduced multiplicative update rules by adding a positive symmetric matrix. Direct trilinear decomposition was used as the TWNNMA initialization method and experimental results confirm that this greatly accelerated the convergence. An obvious advantage of TWNNMA is the uniqueness of the non-negative solution, which facilitates a better understanding of the underlying physical realities of complex data. TWNNMA was applied in complex systems such as chemical kinetics, second-order calibration and analysis of GC-MS data. The results demonstrate that TWNNMA, differing from previous trilinear decomposition methods, is comparable to existing second-order calibration methods and represents a promising resolution method for complex systems.

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author
; ; ; ; and
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Kinetics, Non-negative matrix approximation, PARAFAC, Second-order calibration
in
Talanta
volume
83
issue
2
pages
541 - 548
publisher
Elsevier
external identifiers
  • scopus:78649989712
ISSN
0039-9140
DOI
10.1016/j.talanta.2010.09.035
language
English
LU publication?
no
id
53aec1f9-6c32-44c2-ad89-e314e1a6e95e
date added to LUP
2023-04-24 16:41:43
date last changed
2023-04-27 07:29:22
@article{53aec1f9-6c32-44c2-ad89-e314e1a6e95e,
  abstract     = {{<p>Non-negative matrix approximation (NNMA) has been used in diverse scientific fields, but it still has some major limitations. In the present study a novel trilinear decomposition method, termed three-way NNMA (TWNNMA), was developed. The method decomposes three-way arrays directly without unfolding and overcomes the restriction of locking zero elements in the deduced multiplicative update rules by adding a positive symmetric matrix. Direct trilinear decomposition was used as the TWNNMA initialization method and experimental results confirm that this greatly accelerated the convergence. An obvious advantage of TWNNMA is the uniqueness of the non-negative solution, which facilitates a better understanding of the underlying physical realities of complex data. TWNNMA was applied in complex systems such as chemical kinetics, second-order calibration and analysis of GC-MS data. The results demonstrate that TWNNMA, differing from previous trilinear decomposition methods, is comparable to existing second-order calibration methods and represents a promising resolution method for complex systems.</p>}},
  author       = {{Sun, Jiangming and Li, Tonghua and Cong, Peisheng and Xiong, Wenwei and Tang, Shengnan and Zhu, Li}},
  issn         = {{0039-9140}},
  keywords     = {{Kinetics; Non-negative matrix approximation; PARAFAC; Second-order calibration}},
  language     = {{eng}},
  month        = {{12}},
  number       = {{2}},
  pages        = {{541--548}},
  publisher    = {{Elsevier}},
  series       = {{Talanta}},
  title        = {{Direct decomposition of three-way arrays using a non-negative approximation}},
  url          = {{http://dx.doi.org/10.1016/j.talanta.2010.09.035}},
  doi          = {{10.1016/j.talanta.2010.09.035}},
  volume       = {{83}},
  year         = {{2010}},
}