仪器噪声在近红外光谱偏最小二乘模型内的传播效应

Propagation Effect of Instrument Noise in Partial Least Squares Models of Near-infrared Spectroscopy

在实际多元校正应用中有很多因素会影响偏最小二乘(PLS)模型的预测效果,作为光谱数据本源的仪器噪声是其中的重要影响因素。以往的研究工作多使用各种滤波器或平滑方法来降低仪器噪声的影响,然而对于仪器噪声如何影响偏最小二乘的建模过程和模型预测能力鲜有报道。该文阐述并论证了仪器噪声怎样通过第一个隐变量的计算被引入模型中,经过对偏最小二乘计算过程的理论推导,论述了噪声的引入对偏最小二乘权重向量、载荷向量计算具有累积效应,并随着后续隐变量的计算不断在模型中传递,从而对偏最小二乘模型产生影响。同时对偏最小二乘模型的预测误差进行理论分解,将其划分为无噪理想模型本身的误差和由噪声传播导致的误差。结果表明,仪器噪声不仅会降低偏最小二乘模型的预测性能,还会影响偏最小二乘模型的最优复杂度选择。

In the practical application of multivariate calibration,instrument noise is one of the key factors influencing the prediction ability of partial least squares(PLS)modeling.Plenty of research works have been reported to mitigate the negative influences of instrument noise by various de-noised methods.However,effects of instrument noise in PLS modeling have not received adequate attention.The main point of this work is to illustrate how instrument noise could be involved in PLS model and demonstrate its propagation effect on calculations of weight vectors and loading vectors through theoretical analysis.Moreover,the prediction error of PLS model was divided into two parts,i.e.the prediction error of noise-free model and the error caused by noise propagation and accumulation.Results showed that instrument noise could not only decrease the prediction ability of PLS models,but also influence the model selection.