Near Infrared Spectroscopy Modeling Based on Adaptive Elastic Net Method
ZHENG Nian-nian, LUAN Xiao-li*, LIU Fei
Key Laboratory for Advanced Process Control of Light Industry of Ministry of Education, Institute of Automation, Jiangnan University, Wuxi 214122, China
Abstract：When near infrared spectral information is much larger than the sample size, it is both important and challenging to make automatic variable selection of spectral information and coefficient estimation to establish a sparse linear model between spectra and sample concentration. In this paper, adaptive Elastic Net, a variable selection method, is used to establish a quantitative calibration model between near infrared spectroscopy and o-cresol content, which is a kind of trace component and is difficult to measure in the production of polyphenylene ether. Then, the model performance is compared with the Elastic Net method. Under the circumstance that the number of variables is much larger than the sample size, although Elastic Net method can achieve variable selection, due to the fact that its coefficient estimation does not have the Oracle property, the interpretability and prediction accuracy of the model are affected. The adaptive Elastic Net method solves the above problem and improves the model performance by applying adaptive weights to L1 penalty. In order to verify model performance indicators of adaptive Elastic Net method, the number of selected independent variables (NSIV) is used to evaluate the model complexity and the complex correlation coefficient R2 is used to evaluate the interpretability of the model. Meanwhile, the prediction accuracy of the model is evaluated by using the mean relative prediction error (MRPE) and the prediction correlation coefficient (Rp). The performance indicators of Elastic Net Method are: NSIV=529, R2=0.96, MRPE=3.22％, Rp=0.97; adaptive Elastic Net method’s performance indicators are: NSIV=139, R2=0.99, MRPE=2.00%, Rp=0.99. The results show that adaptive Elastic Net’s model is better than that of Elastic Net. A simpler sparse linear model with better interpretability and higher prediction accuracy can be obtained by the adaptive Elastic Net regression.
[1] SUN Ji-cheng, MA Jin, SHEN Chao, et al. Progress in Modern Biomedicine, 2016, 16(8): 1594.
[2] ZHANG Li-pei, LU Xiong. Light Industry Science and Technology，2016，(2): 103.
[3] SHI Ting，LUAN Xiao-li，LIU Fei. Spectroscopy and Spectral Analysis, 2017, 37(4): 1058.
[4] SHI Ting，LUAN Xiao-li，LIU Fei. Vibrational Spectroscopy, 2017, 92: 302.
[5] TIAN Kuang-da, QIU Kai-xian, LI Zu-hong, et al. Spectroscopy and Spectral Analysis，2014, 32(12): 3262.
[6] YE Shu-bin, XU Liang, LI Ya-kai, et al. Spectroscopy and Spectral Analysis，2017, 37(3): 749.
[7] HUANG Xiao-han, ZHANG Ping, YANG Xiao-li, et al. Gansu Science and Technology, 2017, 33(18): 123.
[8] TANG Shou-peng，YAO Xin-feng，YAO Xia，et al. Chinese Journal of Analytical Chemistry，2009, 37(10): 1445.
[9] XU Qing-juan, YANG Bin-bin. Journal of Guangxi Teachers Education University：Natural Science Edition, 2017, 33(4): 36.
[10] Zou H，Hastie T. Journal of the Royal Statistical Society. Series B (Methodological)，2005, 67(1)：301.
[11] Zou H，Hao Helen Zhang. The Annals of Statistics，2009, 37(4)：1733.
[12] CHEN Shan-xiong, LIU Xiao-juan, CHEN Chun-rong，et al. Journal of Computer Applications，2017, 37(6): 1674.
[13] HE Xiao-qun，LIU Wen-qing. Applied Regression Analysis. Beijing：China Renmin University Press，2015.
