Citation: 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. doi: 10.1016/j.cclet.2007.02.003 shu

A novel trilinear decomposition algorithm:Three-dimension non-negative matrix factorization

a College of Chemistry and Molecular Engineering, Qingdao University of Science & Technology, Qingdao 266042, China;
b Department of Chemistry, Jining Teachers College, Jining 273100, China;
c Department of Chemistry, Tongji University, Shanghai 200092, China

Received Date: 6 November 2006

Fund Project: The authors thank the Outstanding Adult-Young Scientific Research Encouraging Foundation of Shandong Province for financial support (No. 2005BS10004).

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 nonnegative 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.
- Three-dimension non-negative matrix factorization,
- NMF3,
- Algorithm,
- Data decomposition,
- Chemometrics
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