光谱学与光谱分析 |
|
|
|
|
|
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.
|
Received: 2014-10-11
Accepted: 2014-12-30
|
|
Corresponding Authors:
ZHU Er-yi
E-mail: ryzhu@xmu.edu.cn
|
|
[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.
|
[1] |
WANG Cai-ling1,ZHANG Jing1,WANG Hong-wei2*, SONG Xiao-nan1, JI Tong3. A Hyperspectral Image Classification Model Based on Band Clustering and Multi-Scale Structure Feature Fusion[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2024, 44(01): 258-265. |
[2] |
HU Cai-ping1, HE Cheng-yu2, KONG Li-wei3, ZHU You-you3*, WU Bin4, ZHOU Hao-xiang3, SUN Jun2. Identification of Tea Based on Near-Infrared Spectra and Fuzzy Linear Discriminant QR Analysis[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(12): 3802-3805. |
[3] |
LUO Li, WANG Jing-yi, XU Zhao-jun, NA Bin*. Geographic Origin Discrimination of Wood Using NIR Spectroscopy
Combined With Machine Learning Techniques[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(11): 3372-3379. |
[4] |
FANG Zheng, WANG Han-bo. Measurement of Plastic Film Thickness Based on X-Ray Absorption
Spectrometry[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(11): 3461-3468. |
[5] |
HUANG Zhao-di1, CHEN Zai-liang2, WANG Chen3, TIAN Peng2, ZHANG Hai-liang2, XIE Chao-yong2*, LIU Xue-mei4*. Comparing Different Multivariate Calibration Methods Analyses for Measurement of Soil Properties Using Visible and Short Wave-Near
Infrared Spectroscopy Combined With Machine Learning Algorithms[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(11): 3535-3540. |
[6] |
JIA Zong-chao1, WANG Zi-jian1, LI Xue-ying1, 2*, QIU Hui-min1, HOU Guang-li1, FAN Ping-ping1*. Marine Sediment Particle Size Classification Based on the Fusion of
Principal Component Analysis and Continuous Projection Algorithm[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(10): 3075-3080. |
[7] |
CHEN Jia-wei1, 2, ZHOU De-qiang1, 2*, CUI Chen-hao3, REN Zhi-jun1, ZUO Wen-juan1. Prediction Model of Farinograph Characteristics of Wheat Flour Based on Near Infrared Spectroscopy[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(10): 3089-3097. |
[8] |
XUE Fang-jia, YU Jie*, YIN Hang, XIA Qi-yu, SHI Jie-gen, HOU Di-bo, HUANG Ping-jie, ZHANG Guang-xin. A Time Series Double Threshold Method for Pollution Events Detection in Drinking Water Using Three-Dimensional Fluorescence Spectroscopy[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(10): 3081-3088. |
[9] |
JIA Hao1, 3, 4, ZHANG Wei-fang1, 3, LEI Jing-wei1, 3*, LI Ying-ying1, 3, YANG Chun-jing2, 3*, XIE Cai-xia1, 3, GONG Hai-yan1, 3, DING Xin-yu1, YAO Tian-yi1. Study on Infrared Fingerprint of the Classical Famous
Prescription Yiguanjian[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(10): 3202-3210. |
[10] |
CAO Qian, MA Xiang-cai, BAI Chun-yan, SU Na, CUI Qing-bin. Research on Multispectral Dimension Reduction Method Based on Weight Function Composed of Spectral Color Difference[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(09): 2679-2686. |
[11] |
ZHU Yan-ping1, CUI Chuan-jin1*, CHENG Peng-fei1, 2, PAN Jin-yan1, SU Hao1, 2, ZHANG Yi1. Measurement of Oil Pollutants by Three-Dimensional Fluorescence
Spectroscopy Combined With BP Neural Network and SWATLD[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(08): 2467-2475. |
[12] |
ZHANG Zi-hao1, GUO Fei3, 4, WU Kun-ze1, YANG Xin-yu2, XU Zhen1*. Performance Evaluation of the Deep Forest 2021 (DF21) Model in
Retrieving Soil Cadmium Concentration Using Hyperspectral Data[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(08): 2638-2643. |
[13] |
CHEN Wan-jun1, XU Yuan-jie2, LU Zhi-yun3, QI Jin-hua3, WANG Yi-zhi1*. Discriminating Leaf Litters of Six Dominant Tree Species in the Mts. Ailaoshan Based on Near-Infrared Spectroscopy[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(07): 2119-2123. |
[14] |
WANG Yu-hao1, 2, LIU Jian-guo1, 2, XU Liang2*, DENG Ya-song2, SHEN Xian-chun2, SUN Yong-feng2, XU Han-yang2. Application of Principal Component Analysis in Processing of Time-Resolved Infrared Spectra of Greenhouse Gases[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(07): 2313-2318. |
[15] |
HU Hui-qiang1, WEI Yun-peng1, XU Hua-xing1, ZHANG Lei2, MAO Xiao-bo1*, ZHAO Yun-ping2*. Identification of the Age of Puerariae Thomsonii Radix Based on Hyperspectral Imaging and Principal Component Analysis[J]. SPECTROSCOPY AND SPECTRAL ANALYSIS, 2023, 43(06): 1953-1960. |
|
|
|
|