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

• Published in: Chinese chemical letters Vol. 18; no. 4; pp. 495 - 498
• Main Authors: Gao, Hong Tao, Dai, Dong Mei, Li, Tong Hua
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2007; College of Chemistry and Molecular Engineering, Qingdao University of Science & Technology, Qingdao 266042, China; Department of Chemistry, Jining Teachers College, Jining 273100, China%College of Chemistry and Molecular Engineering, Qingdao University of Science & Technology, Qingdao 266042, China%Department of Chemistry, Tongji University, Shanghai 200092, China
• Subjects: Algorithm; Chemometrics; Data decomposition; NMF3; Three-dimension non-negative matrix factorization; NMF3; Data decomposition; Three-dimension non-negative matrix factorization; Algorithm; Chemometrics
• ISSN: 1001-8417; 1878-5964
• DOI: 10.1016/j.cclet.2007.02.003

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.