加权SPXYE(WSPXYE)算法及其在近红外光谱模型转移中的应用

样本选择是模型转移的重要组成部分，其目的是在主光谱和从光谱中选择合适的样本，建立二者的转移模型，使得从光谱的预测样本能通过转移模型校正成类似于主光谱的样本，进而用主光谱的模型直接预测其浓度。目前，常用的样本选择算法有：Kennard-Stone 法 (KS法), SPXY法和SPXYE法。根据上述算法的特点，提出了一种新的样本选择方法：加权SPXYE法(WSPXYE法)，进而将其用于选择合适的转移集样本。WSPXYE同样先计算样本间的距离，其距离有三个部分组成：光谱(X)之间的归一化距离d_xs，浓度(y)之间的归一化距离d_ys，以及校正误差(e)之间的归一化距离d_es。其加权代数和d_wspxye=αd_xs+βd_ys+(1-α-β)d_es即为WSPXYE距离。计算了WSPXYE距离之后，可以根据其距离选择距离较大的样本作为转移集样本。WSPXYE是Kennard-Stone法(KS法), SPXY法和SPXYE法的推广，而KS法（α=1，β=0）、SPXY法（α=0.5，β=0.5）以及SPXYE法（α=0.333，β=0.333）则是WSPXYE法的特例。直接校正法（DS）、有信息成分提取-典型相关分析法(CCA-ICE)作为模型转移算法验证了WSPXYE方法的效果。结果显示，与KS法、SPXY法以及SPXYE法相比，WSPXYE法可以通过调节参数，选择合适的样本，获得较低的误差。

Weighted SPXYE(WSPXYE)and Its Application to Transfer Set Selection in Near Infrared Spectra

Selecting samples in the transfer set is also important in calibration transfer.The purpose of selecting samples in the transfer set is selecting standard samples of both primary and secondary spectra with the same concentrations.After that,the transfer model between primary and secondary spectra can be generated.Finally,the prediction set of secondary spectra can be corrected by transfer model and estimated by the model generated by primary spectra.The commonly used sample selection methods include Kennard-Stone(KS),SPXY and SPXYE methods.Based on the features of those methods,a new sample selection method called weighted SPXYE(WSPXYE)was proposed and applied in transfer set selection.The WSPXYE defines the distance between each paired samples in advance,which is composed of the normalized distances between spectra(d_xs),concentration(d_ys)and errors(d_es).The weighted sum of the former three distances can set as the WSPXYE distance:dwspxye=αd_xs+βd_ys+(1-α-β)d_es.After obtaining dwspxye,the samples with large values of dwspxye,can be selected as transfer set.WSPXYE is the generalization on KS,SPXY and SPXYE methods,while KS,SPXY and SPXYE methods are special cases of WSPXYE with the weights ofαandβset as 1 and 0;0.5 and 0.5 and 0.333 and 0.333,respectively.Two calibration transfer methods,including direct standardization(DS)and canonical correlation analysis combined with informative component extraction(CCA-ICE)has been applied to testing the transfer set selected by WSPXYE.Results showed that WSPXYE could choose proper weights to select good transfer samples to achieve low errors in both validation and prediction sets.