| A novel trilinear decomposition algorithm： Three-dimension non-negative matrix factorization |
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| 作者姓名： | Hong Tao Gao Dong Mei Dai Tong Hua Li |
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| 作者单位： | [1]College of Chemistry and Molecular Engineering, Qingdao University of Science ＆ Technology, Qingdao 266042, China [2]Department of Chemistry, Jining Teachers College, Jining 273100, China [3]Department of Chemistry, Tongji University, Shanghai 200092, China |
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| 基金项目： | The authors thank the 0utstanding Adult-Young Scientific Research Encouraging Foundation of Shandong Province for financial support （No. 2005BS10004）. |
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| 摘 要： | Non-negative matrix factorization(NMF)is a technique for dimensionality reduction by placing non-negativity constraints onthe matrix.Based on the PARAFAC model,NMF was extended for three-dimension data decomposition.The three-dimension non-negative matrix factorization(NMF3)algorithm,which was concise and easy to implement,was given in this paper.The NMF3algorithm implementation was based on elements but not on vectors.It could decompose a data array directly without unfolding,which was not similar to that the traditional algorithms do.It has been applied to the simulated data array decomposition andobtained reasonable results.It showed that NMF3 could be introduced for curve resolution in chemometrics.
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| 关 键 词： | 三维非负矩阵 因式分解 三线素分解算法 化学计量学 |
| 收稿时间： | 2006-11-06 |
A novel trilinear decomposition algorithm: Three-dimension non-negative matrix factorization |
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| Hong Tao Gao Dong Mei Dai Tong Hua Li.A novel trilinear decomposition algorithm: Three-dimension non-negative matrix factorization[J].Chinese Chemical Letters,2007,18(4):495-498. |
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| Authors: | Hong Tao Gao Dong Mei Dai Tong Hua Li |
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| Institution: | 1. College of Chemistry and Molecular Engineering, Qingdao University of Science & Technology, Qingdao 266042, China;2. Department of Chemistry, Jining Teachers College, Jining 273100, China;3. Department of Chemistry, Tongji University, Shanghai 200092, China |
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| Abstract: | Non-negative matrix factorization(NMF)is a technique for dimensionality reduction by placing non-negativity constraints on the matrix.Based on the PARAFAC model,NMF was extended for three-dimension data decomposition.The three-dimension non-negative matrix factorization(NMF3)algorithm,which was concise and easy to implement,was given in this paper.The NMF3 algorithm implementation was based on elements but not on vectors.It could decompose a data array directly without unfolding,which was not similar to that the traditional algorithms do.It has been applied to the simulated data array decomposition and obtained reasonable results.It showed that NMF3 could be introduced for curve resolution in chemometrics. |
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| Keywords: | Three-dimension non-negative matrix factorization NMF3 Algorithm Data decomposition Chemometrics |
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