Multi-way Spectral Analysis Methods Based on Support Tensor Machines

DU Shu-xin; LI Lin-jun

doi:10.3788/fgxb20133404.0523

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Multi-way Spectral Analysis Methods Based on Support Tensor Machines

更新时间：2020-08-12

- Multi-way Spectral Analysis Methods Based on Support Tensor Machines
- Chinese Journal of Luminescence Vol. 34, Issue 4, Pages: 523-528(2013)
- 作者机构：
  
  浙江大学宁波理工学院信息科学与工程分院,浙江宁波,315100
- 作者简介：
- 基金信息：
  
  863"
- DOI：10.3788/fgxb20133404.0523
  CLC： O657.3
- Received：12 December 2012，
  
  Revised：31 January 2013，
  
  Published：2013
- 稿件说明：
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杜树新, 李林军. 基于支持张量机的多维光谱定量分析方法[J]. 发光学报, 2013,34(4): 523-528

DU Shu-xin, LI Lin-jun. Multi-way Spectral Analysis Methods Based on Support Tensor Machines[J]. Chinese Journal of Luminescence, 2013,34(4): 523-528
杜树新, 李林军. 基于支持张量机的多维光谱定量分析方法[J]. 发光学报, 2013,34(4): 523-528 DOI： 10.3788/fgxb20133404.0523.

DU Shu-xin, LI Lin-jun. Multi-way Spectral Analysis Methods Based on Support Tensor Machines[J]. Chinese Journal of Luminescence, 2013,34(4): 523-528 DOI： 10.3788/fgxb20133404.0523.

摘要

现代光谱仪器强大的多维光谱数据产生能力使得多维光谱数据定量分析方法成为迫切需要研究的课题。针对多维光谱定量分析中的多维光谱数据以张量模式表达的特点

研究了基于支持张量机的多维光谱定量分析方法。该方法保留了多维光谱数据所固有的结构信息及数据的内在相关性

减少了模型中的待定模型参数

也克服了平行因子法、多维偏最小二乘等方法中需要预估组分数的缺点。对水体中化学耗氧量和总有机碳的检测进行了实验检验。实验结果表明:与现有的多维光谱定量分析方法比较

本方法提高了校正模型性能

并且模型对需预先确定的参数

和

的变化不敏感。

Abstract

The powerful ability of generating multi-way spectral data in modern spectrum instruments makes multi-way spectral quantitative analysis method become one of the important topics. Since the multi-way spectrometry is represented as a tensor

a new multi-way spectral quantitative analysis method based on support tensor machines (STM) is presented. The presented methods preserve the intrinsic structure of the multi-way spectrometry. Due to the reduction of model parameter number

the methods represented by tensor reduce the over-fit problem in the case of small samples. Unlike the conventional methods such as parallel factor analysis (PARAFAC) and multi-way partial least squares (N-PLS)

the presented methods do not need to estimate the component number. The experiments for detecting chemical oxygen demand (COD) and total organic carbon (TOC) in water are carried out. The experimental results show that the presented methods are improved with comparison to the existing multi-way spectral quantitative analysis methods

and the models are not sensitive to the pre-determined parameters

and

关键词

Keywords

references

Nie J F. Studies on Novel Second-order Tensorial Calibration Algorithms and Their Applications to Three-dimensional Fluorescence Analysis [D]. Changsha: Hunan University, 2010 (in Chinese).[2] Bro R. PARAFAC: Tutorial and applications [J]. Chemometrics and Intelligent Laboratory Systems, 1997, 38(1):149-171.[3] Bro R. Multiway calibration multilinear PLS [J]. J. Chemometrics, 1996, 10(1):47-61.[4] Du S X, Shen J C, Yuan Z B. Multi-way partial least squares modeling for three-dimensional fluorescence spectrometry [J]. Laser Journal (激光杂志), 2012, 33(1):36-37 (in Chinese).[5] Tao D, Li X, Hu W, et al. Supervised tensor learning [C]//Proceedings of the Fifth International Conference on Data Mining, Houston: EDM, 2005:450-457.[6] Tao D, Li X, Hu W, et al. Supervised tensor learning [J]. Knowledge and Information Systems, 2007, 13(1):1-42.[7] Cai D, He X, Han J. Learning with tensor representation[R]. Department of Computer Science Technical Report No.2716, University of Illinois at Urbana-Champaign (UIUCDCS-R-2006-2716), 2006.[8] Liu Y, Liu Y. Chan K C C. Tensor-based locally maximum margin classifier for image and video classification [J]. Computer Vision and Image Understanding, 2011, 115(3):300-309.[9] Zhang Z, Chow T W S. Maximum margin multisurface support tensor machines with application to image classification and segmentation [J]. Expert Systems with Applications, 2012, 39(1):849-860[10] Kotsia I, Guo W, Patras I. Higher rank support tensor machines for visual recognition [J]. Pattern Recognition, 2012, 45(12):4192-4203.[11] Guo W, Kotsia I, Patras I. Tensor learning for regression [J]. IEEE Transactions on Image Processing, 2012, 21(2):816-827.[12] Du S X, Wu X L, Wu T J. Support vector machine for ultraviolet spectroscopy water quality analyzers [J].Chin. J. Anal. Chem.(分析化学), 2004, 32(9):1227-1230 (in Chinese).[13] Du S X, Du Y F, Yuan Z B. Characteristic region selection methods for three-dimensional fluorescence spectrometry [J]. Chin. J. Lumin.(发光学报), 2012, 33(3):341-345 (in Chinese).

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