A Algorithm of the Singular Value Decomposition for Three-Way Array
ZHU Er-yi, WANG Xiao-hua, HANG Wei
College of Chemistry and Chemical Engineering Xiamen University and the Ministryof Education Key Lab of Spectrochemical Analysis & Instrumentation，Xiamen 361005, China
Abstract：A algorithm of the singular value decomposition for three-way array is proposedin this paper. The algorithm is suitable to deal with the actual problems of pattern recognition and classification model with three-way array data. Similarto the algorithm of the singular value decomposition for matrix, the algorithmis obtained by saving the problem of extremum subject to constraint conditions.Comparing with the existent algorithms of trilinear decomposition the algorithm is simple and fast in calculation, suitable to deal with the actual bigger data problems. The algorithm is easy to expand into the situation for multi-way array spectral data.
Key words：Trilinear decomposition;Singular value decomposition;PCA
朱尔一，王小华，杭 纬 . 一种三维矩阵的奇异值分解算法 [J]. 光谱学与光谱分析, 2015, 35(03): 587-590.
ZHU Er-yi, WANG Xiao-hua, HANG Wei . A Algorithm of the Singular Value Decomposition for Three-Way Array . SPECTROSCOPY AND SPECTRAL ANALYSIS, 2015, 35(03): 587-590.
[1] Kroonenberg P M., Applied Multiway Data Analysis, John Wiley & Sons, Inc., Hoboken, New Jersey, 2008. [2] Smilde A, Bro R, Geladi P. Multi-Way Analysis: Applications in the Chemical Sciences, John Wiley & Sons, Ltd, England, 2004. 111. [3] Wu Hailong, Li Yong，Yu Ruqin. Journal of Chemometrics , 2014, 28: 476. [4] Olivieri A C. Analytical Methods 2012, 4: 1876. [5] Wu Hailong, Nie Jinfang, Yu Ruqin et al. Analytica Chimica Acta, 2009, 650: 131. [6] Wu H L, Shibukawa M, Oguma K. Journal of Chemometrics. 1998, 12: 1. [7] Chen Z P, Wu H L, Yu R Q, et al. Chemometrics and Intelligent Laboratory Systems, 2000, 52: 75. [8] Xia A L, Wu H L, Yu R Q, et al. Journal of Chemometrics, 2005, 19: 65. [9] ZHU Er-yi, YANG Peng-yuan (朱尔一，杨芃原). Chemometric Technology and Its Application(化学计量学技术及应用). Beijing: Science Press(北京：科学出版社), 2001. 100.
