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中文摘要：
极限学习机理论（extreme learning machine,ELM）作为一种新的化学计量学方法,在近红外光谱定量分析中的应用研究,已引起学术界的高度重视。然而,由于光谱数据维数较高,建立 ELM模型时需要大量的隐节点,导致隐含层输出矩阵维数高且存在高度共线性,用现有的 Moore-Penrose广义逆算法求取隐含层输出矩阵与待测性质间的回归模型往往会存在病态问题。基于ELM建立光谱波长变量与性质之间的回归模型,提出以 ELM模型隐含层输出矩阵作为新的变量,采用作者最新提出的基于变量投影重要性的改进叠加PLS算法（stacked partial least squares regression algorithm based on variable importance in the proj ection, VIP-SPLS）,建立新变量与待测性质间的回归模型。VIP-SPLS算法充分利用了每个隐节点的输出信息,能有效解决高维共线性问题,同时具有模型集成的优点,从而改进了 ELM模型的性能。将提出的改进 ELM算法（improved ELM,iELM）应用于标准近红外光谱数据集,结果表明 iELM模型的精度相对于现有的 PLS模型和 ELM模型分别显著提升了29.06%和27.47%。
英文摘要：
Extreme learning machine （ELM）has been applied in near infrared spectral analysis as a novel chemometric method which attracted the attentions of various researchers.However,the dimension of spectral data is usually very high while more hidden nodes should be incorporated in original ELM model for spectral data.Thus the problems of high dimension and high co-linearity in the output matrix of hidden layer of ELM model are inevitable.The solutions obtained with the existing Moore-Pen-rose generalized inverse can be ill-conditional due to the high dimension and high colinearity in the hidden layer output matrix. This study aims to propose an improved ELM to build spectral regression model.The proposed method firstly uses extreme learning machine （ELM）to relate spectral variables to response variable;then the output of each hidden node are treated as new variables;VIP-SPLS （improved stacked PLS based on variable importance in the proj ection）proposed by our group recently is used to build the regression model between those new variables and the response variable.In this paper,this method is called as improved ELM （iELM）.VIP-SPLS model can fully utilize the output information of each hidden node and can effectively solve the problems of high dimension and high colineariy.At the same time,VIP-SPLS also has the advantage of model ensemble. Therefore,the performance of ELM model used for spectral data can be improved if the VIP-SPLS is incorporated to relate the hidden layer output matrix and response variable.The proposed method is applied to a commonly used benchmark NIR spectral data for evaluation.The results demonstrate that the precision improvement of iELM model is 29.06% to PLS model and 27.47% to original ELM model,respectively.
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