基于改进非负矩阵分解的多组分气体光谱解混算法

量子电子学报 ›› 2019, Vol. 36 ›› Issue (6): 684-690.

基于改进非负矩阵分解的多组分气体光谱解混算法

杨文康，方勇华，刘家祥，吴越，张蕾蕾

1中国科学院安徽光学精密机械研究所环境光学研究中心？，安徽合肥 230031；
2 中国科学技术大学，安徽合肥 230031

收稿日期:2019-04-04 修回日期:2019-11-15 出版日期:2019-11-28 发布日期:2019-11-19
通讯作者: 方勇华（1966-），安徽黄山人，博士，研究员，博士生导师，主要从事光电信息获取与处理方面的研究。 E-mail:yhfang@aiofm.ac.cn
作者简介:杨文康（1994-），安徽六安人，研究生，主要从事光电信息处理方面的研究。E-mail：yangkk@mail.ustc.edu.cn

Multi-component gas spectral demixing algorithm based on improved non-negative matrix factorization

YANG Wenkang，FANG Yonghua，LIU Jiaxiang，WU Yue，ZHANG Leilei

1 Anhui Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Hefei 230031, China;
2 University of Science and Technology of China, Hefei 230026, China

Received:2019-04-04 Revised:2019-11-15 Published:2019-11-28 Online:2019-11-19

摘要/Abstract

摘要： 从重叠情况严重的混合气体光谱中解析出单一纯光谱数据，一直是光谱解析的难点。为了得到理想的解混精度，采用改进的非负矩阵分解算法，引入光谱的相关性约束与平滑性约束，并给出优化的梯度下降法的迭代步长，以避免算法收敛到局部不稳定点带来的影响。改进的算法既综合了矩阵的分解误差，又考虑了混合光谱特性的影响。实验数据表明，改进的非负矩阵分解得到的解混结果能够准确解析出各源光谱的特征峰形状，并且各解混结果之间几乎没有混合叠加影响部分，可以满足后续的光谱识别工作。

关键词: 光谱学；非负矩阵分解；盲源分离；梯度下降法

Abstract: It is always difficult to analyze the single pure spectral data from the mixed gas spectrum with severe overlap. In order to obtain the ideal unmixing precision, an improved non-negative matrix factorization algorithm is used to introduce the correlation constraint and smoothness constraint of the spectrum, and the iterative step size of the optimized gradient descent method is given to avoid the effects of algorithm convergence to local instability. The improved algorithm combines the decomposition error of the matrix and influence of the mixed spectral characteristics. The experimental data show that the demixing effect obtained by the improved non-negative matrix factor can accurately resolve the characteristic peak shape of each source spectrum, and there is almost no mixed superimposed influence between the demixing results, which can satisfy the subsequent spectral recognition work.

Key words: spectroscopy, non-negative matrix factorization, blind source separation, gradient descent

中图分类号:

O433

杨文康, 方勇华, 刘家祥, 吴越, 张蕾蕾. 基于改进非负矩阵分解的多组分气体光谱解混算法[J]. 量子电子学报, 2019, 36(6): 684-690.

YANG Wenkang, FANG Yonghua, LIU Jiaxiang, WU Yue, ZHANG Leilei. Multi-component gas spectral demixing algorithm based on improved non-negative matrix factorization[J]. Chinese Journal of Quantum Electronics, 2019, 36(6): 684-690.

参考文献 14

[1]	Wei Xiuli1, Zhang Lu, Gao Minguang. Quantitative analysis of aerosol inorganic ion based on nonlinear least squares algorithm[J]. Chinese Journal of Quantum Electronics（量子电子学报），2018, 35(5): 523-526（in Chinese）.
[2]	Li M, Yuan B. 2D-LDA: A statistical linear discriminant analysis for image matrix[J]. Pattern Recognition Letters, 2005, 26(5): 527-532.
[3]	Hyvarinen A. Fast and robust fixed-point algorithms for independent component analysis[J]. IEEE Transactions on Neural Networks, 2002, 10(3): 626-634.
[4]	Equitz, W. H . A new vector quantization clustering algorithm[J]. IEEE Transactions on Acoustics, Speech and Signal Processing, 1989, 37(10):0-1575？？.
[5]	Gillis N , Glineur F. Using underapproximations for sparse nonnegative matrix factorization[J]. Pattern Recognition, 2010, 43(4):1676-1687.
[6]	Vu T, Bigot B, Chng E S. Combining non-negative matrix factorization and deep neural networks for speech enhancement and automatic speech recognition[C]. IEEE International Conference on Acoustics, 2016.
[7]	Buciu I, Pitas I. Application of non-negative and local non-negative matrix factorization to facial expression recognition[C]. International Conference on Pattern Recognition. IEEE Computer Society, 2004.
[8]	Yoo J, Choi S. Weighted non-negative matrix co-tri-factorization for collaborative prediction[C]. Asian Conference on Machine Learning: Advances in Machine Learning. Springer-Verlag, 2009.
[9]	Niegowski M, Zivanovic M. ECG-EMG separation by using enhanced non-negative matrix factorization[C]. Engineering in Medicine & Biology Society, 2014.
[10]	Guillemot C, Turkan M. Neighbor embedding with non-negative matrix factorization for image prediction[C]. IEEE International Conference on Acoustics, 2012.
[11]	Lee D D, Seung H S. Algorithms for non-negtive maxtrix factorization [C]. Advance in Neural Information Processing System, 2000.
[12]	Zhang Y, Fang Y. A NMF algorithm for blind separation of uncorrelated signals[C]. International Conference on Wavelet Analysis & Pattern Recognition, IEEE, 2008.
[13]	Pauca V P, Piper J, Plemmons R J. Nonnegative matrix factorization for spectral data analysis[J]. Linear Algebra & Its Applications, 2006, 416(1):29-47.
[14]	Lin C J. On the convergence of multiplicative update algorithms for non-negative matrix factorization[M]. IEEE Press, 2007.

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