A Partial Least Squares‐Based Consensus Regression Method for the Analysis of Near‐Infrared Complex Spectral Data of Plant Samples

Abstract

A consensus regression approach based on partial least square (PLS) regression, named as cPLS, for calibrating the NIR data was investigated. In this approach, multiple independent PLS models were developed and integrated into a single consensus model. The utility and merits of the cPLS method were demonstrated by comparing its results with those from a regular PLS method in predicting moisture, oil, protein, and starch contents of corn samples using the NIR spectral data. It was found that cPLS was superior to regular PLS with respect to prediction accuracy and robustness.     

A Miniaturized Voltammetric Electronic Tongue

Abstract

A miniaturized electronic tongue based on pulsed voltammetry has been developed. It was made by inserting three types of wires acting as working electrodes (gold, platinum, and rhodium; diameter 0.25 mm) into a platinum tube acting as a counter electrode (diameter 2 mm; length 4 mm). The arrangement was connected to a potentiostat controlled by a computer. Due to the small size of the miniaturized electronic tongue, and since no reference electrode is used, the setup is very simple and convenient. In order to characterize the analytical possibilities of the miniaturized electronic tongue, some initial experiments were performed. These include the determination of trace amounts of cadmium and lead (in the µM range) in 5 µL samples. Furthermore, the setup was placed under the real tongue of a volunteer to follow saliva composition during exercise.     

The superiorities of bayes linear unbiased estimator in multivariate linear models

In this article,the Bayes linear unbiased estimator (BALUE) of parameters is derived for the multivariate linear models.The superiorities of the BALUE over the least square estimator (LSE) is studied in terms of the mean square error matrix (MSEM) criterion and Bayesian Pitman closeness (PC) criterion.     

Real-life applications of the MULVADO software package for processing DOSY NMR data

MULVADO is a newly developed software package for DOSY NMR data processing, based on multivariate curve resolution (MCR), one of the principal multivariate methods for processing DOSY data. This paper will evaluate this software package by using real-life data of materials used in the printing industry: two data sets from the same ink sample but of different quality. Also a sample of an organic photoconductor and a toner sample are analysed. Compared with the routine DOSY output from monoexponential fitting, one of the single channel algorithms in the commercial Bruker software, MULVADO provides several advantages. The key advantage of MCR is that it overcomes the fluctuation problem (non-consistent diffusion coefficient of the same component). The combination of non-linear regression (NLR) and MCR can yield more accurate resolution of a complex mixture. In addition, the data pre-processing techniques in MULVADO minimise the negative effects of experimental artefacts on the results of the data. In this paper, the challenges for analysing polymer samples and other more complex samples will also be discussed.     

矩阵伸缩的多元多重向量值小波包的双正交性

1引言 小波分析是二十世纪八十年代中期发展起来的一个数学分枝,其应用涉及自然科学与工程技术的许多领域[1-3].向量值小波从属多小波理论范畴.文献[4]引入向量值小波的概念,讨论了多重向量值双正交小波的存在性及其构造.Bacchelli等[5]证明了多重向量值双正交小波的存在性.文献[6]运用多重向量值双正交小波变换研究海洋涡流现象.     

多元函数空间的对称分解

引进一种多元函数空间的对称分解方法,并讨论了由对称算符组成的正交幂等系统的简单构造.     

带有辅助信息的多元失效时间数据的估计标准部分似然方法

在许多实际研究中, 由于预算限制, 主协变量值只能对某一个有效集进行准确测量, 但同时对应此主协变量的辅助信息则对全部个体均可以观测. 利用这些辅助协变量的信息有助于提高统计研究的效率. 本文在基于共同基准危险率的边际模型框架下, 我们提出了一些统计推断方法来分析多元失效时间数据. 对于回归参数, 我们提出标准的估计部分似然方程来估计它, 同时也给出了累积基准危险率函数的Breslow 型估计. 得到的估计可以证明是相合的和渐近正态的. 利用模拟分析结果来表明了提出的方法在有限样本下的可行性.     

参数未知的多变量设置调整问题研究

针对存在起始设置偏差过程参数未知的多变量过程,考虑不同质量特性对总体的质量损失影响不同,研究了在调整费用恒定下的统计过程调整问题.基于过程的状态空间方程模型,利用贝叶斯方法对过程的未知参数和设置偏差进行估计,结合过程的费用结构给出了过程的调整策略.通过仿真与其他的调整策略进行了对比分析,仿真结果表明,提出的调整策略能够更为有效地减少过程的质量损失.     

Determination of rank by augmentation (DRAUG)

Determining the rank of a chemical matrix is the first step in many multivariate, chemometric studies. Rank is defined as the minimum number of linearly independent factors after deletion of factors that contribute to random, nonlinear, uncorrelated errors. Adding a matrix of rank 1 to a data matrix not only increases the rank by one unit but also perturbs the primary factor axes, having little effect on the secondary axes associated with the random errors in the measurements. The primary rank of a data matrix can be determined by comparing the residual variances obtained from principal component analysis (PCA) of the original data matrix to those obtained from an augmented matrix. The ratio of the residual variances between adjacent factor levels represents a Fisher ratio that can be used to distinguish the primary factors (chemical as well as instrumental factors) from the secondary factors (experimental errors). The results gleaned from model studies as well as those from experimental studies are used to illustrate the efficacy of the proposed methodology. The method is independent of the nature of the error distribution. Limitations and precautions are discussed. An algorithm, written in MATLAB format, is included. Copyright © 2011 John Wiley & Sons, Ltd.     

Construction of stable multivariate calibration models using unsupervised segmented principal component regression

In multivariate spectral calibration by principal component regression (PCR), the principal components (PCs) are calculated from the response data measured at all employed instrument channels; however some channels are redundant and their responses do not possess useful information. Thus, the extracted PCs possess mixed information from both useful and redundant channels. In this work, we propose a segmentation approach based on unsupervised pattern recognition to identify the most informative spectral region and then to construct a stable multivariate calibration model by PCR. In this method, the instrument channels are clustered into different segments via Kohonen self‐organization map. The spectral data of each segment are then subjected to PCA and the derived PCs are used as input variables for an inverse least square (ILS) regression model employing stepwise selection of the informative PCs. The proposed method was evaluated by the analysis of four simulated and six experimental data sets. It was found that our proposed method can model the above data sets with prediction errors lower than conventional partial least squares (PLS) and PCR methods. In addition, the prediction ability of our method was better than the previously reported models for these data sets. Copyright © 2011 John Wiley & Sons, Ltd.