一种基于变量稳定性和可信度的紫外-可见特征波长选择方法

针对多组分金属离子混合溶液的紫外-可见吸收光谱(UV-Vis)重叠严重、难以分离的问题，提出了一种基于稳定性和可信度偏最小二乘法(SCPLS)的特征波长选择方法。在SCPLS中，引入指数衰减函数(EDF)以迭代的方式对波长变量进行选择。在每次迭代中对蒙特卡罗采样所得到的数据集建模，计算各波长变量的稳定性和可信度指标，并通过EDF选择具有较高稳定性和可信度的变量，选择的变量作为新的变量集进入下一次变量选择迭代。迭代全部完成后，计算每一次迭代所选的变量集建模的交叉验证均方根误差（RMSECV），选择RMSECV最小的变量集作为波长变量选择的结果。利用Zn(Ⅱ)， Cu(Ⅱ) 和Co(Ⅱ)混合溶液的紫外-可见光谱数据集和Zn(Ⅱ)和Co(Ⅱ)混合溶液的紫外-可见光谱数据集对所提方法性能进行了验证，并与全波段偏最小二乘、移动窗口偏最小二乘法(MWPLS)、蒙特卡罗无信息变量消除方法 (MC-UVE)、竞争性自适应加权算法 (CARS)和稳定性竞争自适应加权算法(SCARS)进行了比较分析。结果表明：该方法不仅能降低波长选择的复杂度，还能在保证波长选择过程稳定的情况下，选出对模型重要的波长变量，较之其他方法所提出的方法选取的变量建立的模型RMSECV最小，对于Zn(Ⅱ)，Cu(Ⅱ) 和Co(Ⅱ)数据集，使用SCPLS方法得到的Zn(Ⅱ)，Cu(Ⅱ)和Co(Ⅱ)的RMSECV值分别比全光谱PLS下降60.5%，40.2%和31.8%，与SCARS相比分别下降29.8%，26.1%和0.8%，Zn(Ⅱ)，Cu(Ⅱ)和Co(Ⅱ)平均相对误差分别为2.14%，1.25%和0.74%，其中Zn(Ⅱ)的最大相对误差为4.67%，Cu(Ⅱ)的最大相对误差为3.99%，Co(Ⅱ)的最大相对误差为3.12%；对于Zn(Ⅱ)和Co(Ⅱ)数据集，使用SCPLS方法得到的Zn(Ⅱ)和Co(Ⅱ)的RMSECV值分别比全光谱PLS下降39.4%和24.9%，与SCARS相比分别下降35.3%和13.3%，Zn(Ⅱ)和Co(Ⅱ)平均相对误差分别为1.23%，1.10%，其中Zn(Ⅱ)的最大相对误差为4.45%，Co(Ⅱ)的最大相对误差为4.57%，有效提高光谱建模精度。

A Wavelength Selection Method of UV-Vis Based on Variable Stability and Credibility

This paper proposes a wavelength selection method based on stability and credibility partial least squares (SCPLS), to solve the problem that the ultraviolet visible （UV-Vis） spectra of multi-metal ion mixture solution were seriously overlapped and difficult to separate. In SCPLS, an exponentially decreasing function (EDF) is applied to select the variables in an iterative manner. In each iteration, a series of models are built with the sub-datasets sampled using the Monte Carlo strategy. Then, the stability and credibility of each variable are calculated, and the variables with high stability and credibility are selected by the EDF. Subsequently, the selected variables are used to construct a new variable subset for the next iteration. After the selection iterations are terminated, the root mean square error of cross validation (RMSECV) of each subset is calculated. The variable subset with the minimum RMSECV value is considered to be the optimal variable subset. The performance of SCPLS is evaluated with UV-Vis Spectral data set of Zn(Ⅱ), Cu(Ⅱ) and Co(Ⅱ) mixture solution and UV-Vis Spectral data set of Zn(Ⅱ) and Co(Ⅱ) mixture solution, and compared with that of full spectrum partial least squares (PLS) modeling and the moving window PLS (MWPLS), Monte Carlo uninformative variable elimination (MC-UVE), competitive adaptive reweighted sampling (CARS) and stability competitive adaptive reweighted sampling (SCARS) methods. The results show that SCPLS can not only reduce the complexity of the wavelength selection, but also ensure the stability of the wavelength selection process. And it can select the subset with the minimum RMSECV value. Thus, the RMSECV of Zn(Ⅱ), Cu(Ⅱ) and Co(Ⅱ) models obtained by SCPLS are 60.5%，40.2% and 31.8% respectively lower than that of full spectrum PLS, and 29.8%，26.1% and 0.8% respectively lower than that of SCARS. The average relative error of Zn(Ⅱ), Cu(Ⅱ) and Co(Ⅱ) is 2.14%, 1.25% and 0.74% respectively, of which the maximum relative error of Zn(Ⅱ) is 4.67%, the maximum relative error of Cu(Ⅱ) is 3.99%, and the maximum relative error of Co(Ⅱ) is 3.12%. And the RMSECV of Zn(Ⅱ) and Co(Ⅱ) models obtained by SCPLS are 39.4% and 24.9% respectively lower than that of full spectrum PLS, and 35.3% and 13.3% respectively lower than that of SCARS. The average relative error of Zn(Ⅱ) and Co(Ⅱ) are 1.23% and 1.10% respectively, of which the maximum relative error of Zn(Ⅱ) is 4.45% and the maximum relative error of Co(Ⅱ) is 4.57%. The proposed method can efficiently improve modeling accuracy.