Review of robust multivariate statistical methods in high dimension

General ideas of robust statistics, and specifically robust statistical methods for calibration and dimension reduction are discussed. The emphasis is on analyzing high-dimensional data. The discussed methods are applied using the packages chemometrics and rrcov of the statistical software environment R. It is demonstrated how the functions can be applied to real high-dimensional data from chemometrics, and how the results can be interpreted.     

化学计量学中的稳健估计方法

稳健统计学是八十年未才基本定型的统计学分支，它是针对实际情况中假设模型常常只是对实际数据的一种近似而导致传统统计学推断失误而发展起来的。稳健统计学构造一些新的具有稳健性的方法，使得在假设模型满足时，稳健方法具有接近最优的性能；在实际数据与假设模型有差别时，其性能仍为次优的；而在实际数据与假设模型差别大时，统计方法的性能也不会变得过差。本文介绍了稳健估计的一般概念。综述了化学计量学中的稳健估计方法，     

蓝色圆珠笔字迹的高效液相色谱分析与模式识别研究

该文收集市售蓝色圆珠笔样品16份,结合模式识别技术对其高效液相色谱数据进行研究。利用相关系数法计算色谱图相对峰面积的相似度,定量地评价样品间的差异性。选取16个样品3个批次间的最小相似度(λ=0.92)作为判定是否源于同种样品的阈值,相似度小于0.92的数据为89份,占全部比对样品的74.2%;根据液相色谱图的保留时间、峰数及峰形差异将所有样品分为3类,进一步利用系统聚类法依据相似度的大小将第一类样品分为3小类。该文提出的采用相对峰面积相似度评价样品差异的方法,能够显著提高分辨能力,促进圆珠笔字迹的自动化识别。高效液相色谱法获取数据,模式识别技术分析数据的方法为圆珠笔字迹的分类与鉴别提供了新思路。     

Unsupervised random forest: a tutorial with case studies

Unsupervised methods, such as principal component analysis, have gained popularity and wide‐spread acceptance in the chemometrics and applied statistics communities. Unsupervised random forest is an additional method capable of discovering underlying patterns in the data. However, the number of applications of unsupervised random forest in chemometrics has been limited. One possible cause for this is the belief that random forest can only be used in a supervised analysis setting. This tutorial introduces the basic concepts of unsupervised random forest and illustrates several applications in chemometrics through worked examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Increasing the scope and power of flow-injection analysis through chemometric approaches

The objective of this paper is to illustrate how chemometrics can enhance the scope and power of flow injection analysis (FIA) by considering a few simple but representative cases where the ability of chemometrics to improve performance is not readily apparent. In principle, there are two phases when chemometrics can be usefully combined with FIA: first when developing an FIA method and, second, when treating raw data acquired from an FIA detection system. The most obvious application of chemometrics for the FIA practitioner is to use experimental design to replace the obsolete, but too often used one-variable-at-a-time approach when optimising an FIA method. Therefore, methods for screening variables and system optimisation are discussed. Raw data acquired from most FIA systems are first-order data, containing information about the dispersed sample plug. However, the information that is extracted when using FIA for routine purposes is of zero-order: predominantly peak height values. It is shown by a simple example that a chemometric approach in such cases can again provide additional useful information about the sample. First-order spectral data and second-order data more or less require a chemometrics approach for successful analysis, and examples of such applications are briefly discussed.     

MATLAB在化学计量学中的应用

化学计量学是数学和统计学，化学及计算机科学相互交叉形成的一门新的化学分支学科，是解决化学问题的强有力工具，目前运用于化学计量学的商品软件有MATLAB、Maple,MathCAD,EXCEL,SPSS等。MATLAB是一种高性能的数值计算的科学计算语言，具有程序开发环境简洁直观，数值稳定性好，函数资源丰富的特点，本文以几种常用的化学计量学方法为例，讨论了MATLAB在化学中的应用。     

Sparse models by iteratively reweighted feature scaling: a framework for wavelength and sample selection

In the past decade, there has been an increase in the use of sparse multivariate calibration methods in chemometrics. Sparsity describes a parsimonious state of model complexity and can be defined in terms of a subset of samples or covariates (e.g., wavelengths) that are used to define the calibration model. With respect to their classical counterparts such as principal component regression or partial least squares, sparse models are more easily interpretable and have been shown to exhibit non‐inferior prediction performance. However, sparse methods are still not as fast as the classical methods in spite of recent numerical advances. In addition, for many chemometricians, sparse methods are still “black‐box” algorithms whose internal workings are not well understood. In this paper, we describe a simple framework whereby classical multivariate calibration methods can be iteratively used to generate sparse models. Moreover, this approach allows for either wavelength or sample sparsity. We demonstrate the effectiveness of this approach on two spectroscopic data sets. Copyright © 2013 John Wiley & Sons, Ltd.     

Multivariate calibration: What is in chemometrics for the analytical chemist?

Chemometrics has been used for some 30 years but there is still need for disseminating the potential benefits to a wider audience. In this paper, we claim that proper analytical chemistry (1) must in fact incorporate a chemometric approach and (2) that there are several significant advantages of doing so. In order to explain this, an indirect route will be taken, where the most important benefits of chemometric methods are discussed using small illustrative examples. Emphasis will be on multivariate data analysis (for example calibration), whereas other parts of chemometrics such as experimental design will not be treated here. Four distinct aspects are treated in detail: noise reduction; handling of interferents; the exploratory aspect and the possible outlier control. Additionally, some new developments in chemometrics are described.     

Covariances Simultaneous Component Analysis: a new method within a framework for modeling covariances

In modern omics research, it is more rule than exception that multiple data sets are collected in a study pertaining to the same biological organism. In such cases, it is worthwhile to analyze all data tables simultaneously to arrive at global information of the biological system. This is the area of data fusion or multi‐set analysis, which is a lively research topic in chemometrics, bioinformatics, and biostatistics. Most methods of analyzing such complex data focus on group means, treatment effects, or time courses. There is also information present in the covariances among variables within a group, because this relates directly to individual differences, heterogeneity of responses, and changes of regulation in the biological system. We present a framework for analyzing covariance matrices and a new method that fits nicely in this framework. This new method is based on combining covariance prototypes using simultaneous components and is, therefore, coined Covariances Simultaneous Component Analysis (COVSCA). We present the framework and our new method in mathematical terms, thereby explaining the (dis)similarities of the methods. Systems biology models based on differential equations illustrate the type of variation generated in real‐life biological systems and how this type of variation can be modeled within the framework and with COVSCA. The method is subsequently applied to two real‐life data sets from human and plant metabolomics studies showing biologically meaningful results. Copyright © 2015 John Wiley & Sons, Ltd.     

Does chemometrics enhance the performance of electroanalysis?

This review explores the question whether chemometrics methods enhance the performance of electroanalytical methods. Electroanalysis has long benefited from the well-established techniques such as potentiometric titrations, polarography and voltammetry, and the more novel ones such as electronic tongues and noses, which have enlarged the scope of applications. The electroanalytical methods have been improved with the application of chemometrics for simultaneous quantitative prediction of analytes or qualitative resolution of complex overlapping responses. Typical methods include partial least squares (PLS), artificial neural networks (ANNs), and multiple curve resolution methods (MCR-ALS, N-PLS and PARAFAC). This review aims to provide the practising analyst with a broad guide to electroanalytical applications supported by chemometrics. In this context, after a general consideration of the use of a number of electroanalytical techniques with the aid of chemometrics methods, several overviews follow with each one focusing on an important field of application such as food, pharmaceuticals, pesticides and the environment. The growth of chemometrics in conjunction with electronic tongue and nose sensors is highlighted, and this is followed by an overview of the use of chemometrics for the resolution of complicated profiles for qualitative identification of analytes, especially with the use of the MCR-ALS methodology. Finally, the performance of electroanalytical methods is compared with that of some spectrophotometric procedures on the basis of figures-of-merit. This showed that electroanalytical methods can perform as well as the spectrophotometric ones. PLS-1 appears to be the method of practical choice if the %relative prediction error of ∼±10% is acceptable.     

PLS‐DA for compositional data with application to metabolomics

When quantifying information in metabolomics, the results are often expressed as data carrying only relative information. Vectors of these data have positive components, and the only relevant information is contained in the ratios between their parts; such observations are called compositional data. The aim of the paper is to demonstrate how partial least squares discriminant analysis (PLS‐DA)—the most widely used method in chemometrics for multivariate classification—can be applied to compositional data. Theoretical arguments are provided, and data sets from metabolomics are investigated. The data are related to the diagnosis of inherited metabolic disorders (IMDs). The first example analyzes the significance of the corresponding regression parameters (metabolites) using a small data set resulting from targeted metabolomics, where just a subset of potential markers is selected. The second example—the approach of untargeted metabolomics—was used for the analysis detecting almost 500 metabolites. The significance of the metabolites is investigated by applying PLS‐DA, accommodated according to a compositional approach. The significance of important metabolites (markers of diseases) is more clearly visible with the compositional method in both examples. Also, cross‐validation methods lead to better results in case of using the compositional approach. Copyright © 2014 John Wiley & Sons, Ltd.     

化学计量学在毒物化学归因中的应用

近十年来,化学计量学方法与分析技术相结合,对样品进行了表征和鉴别,产生了信息量大、代表性强的样品检测方法。在法医学案件鉴定处理中,使用这些新技术和数学/统计学方法,可获得统计可信度的结果,从而有助于法医学案件以及毒性化合物中毒事件的追踪溯源。该文对毒物检测中使用的化学计量学方法进行了详细讨论,对其优缺点进行了比较总结,并对毒物化学归因中化学计量学的未来发展应用进行了展望。     

化学计量学在我国的发展

评述了化学计量学在我国近年来的发展,包括多元校正与分辨、稳健方法、化学模式识别、化学定量构效关系、分子模拟与优化、化学专家系统与库主要分支,其中特别对近年来得到飞速发展的新技术如高维数据解析方法,人工神经网络、小波变换给出了较详细的介绍。     

用于近红外光谱分析的化学计量学方法研究与应用进展

分析模型的建立是近红外光谱分析的核心技术之一,本文综述了近些年在近红外光谱分析方法中出现的一些新算法和模型建立策略,如基于核函数的非线性校正方法、集成(或共识)的建模策略、多维分辨和校正方法、基于局部样本的建模策略以及二维相关光谱等,并给出了一些方法的具体算法。     

Photochemistry and chemometrics—An overview

Photochemistry has made significant contributions to our understanding of many important natural processes as well as the scientific discoveries of the man-made world. The measurements from such studies are often complex and may require advanced data interpretation with the use of multivariate or chemometrics methods. In general, such methods have been applied successfully for data display, classification, multivariate curve resolution and prediction in analytical chemistry, environmental chemistry, engineering, medical research and industry. However, in photochemistry, by comparison, applications of such multivariate approaches were found to be less frequent although a variety of methods have been used, especially with spectroscopic photochemical applications. The methods include Principal Component Analysis (PCA; data display), Partial Least Squares (PLS; prediction), Artificial Neural Networks (ANN; prediction) and several models for multivariate curve resolution related to Parallel Factor Analysis (PARAFAC; decomposition of complex responses). Applications of such methods are discussed in this overview and typical examples include photodegradation of herbicides, prediction of antibiotics in human fluids (fluorescence spectroscopy), non-destructive in- and on-line monitoring (near infrared spectroscopy) and fast-time resolution of spectroscopic signals from photochemical reactions. It is also quite clear from the literature that the scope of spectroscopic photochemistry was enhanced by the application of chemometrics.To highlight and encourage further applications of chemometrics in photochemistry, several additional chemometrics approaches are discussed using data collected by the authors. The use of a PCA biplot is illustrated with an analysis of a matrix containing data on the performance of photocatalysts developed for water splitting and hydrogen production. In addition, the applications of the Multi-Criteria Decision Making (MCDM) ranking methods and Fuzzy Clustering are demonstrated with an analysis of water quality data matrix. Other examples of topics include the application of simultaneous kinetic spectroscopic methods for prediction of pesticides, and the use of response fingerprinting approach for classification of medicinal preparations. In general, the overview endeavours to emphasise the advantages of chemometrics’ interpretation of multivariate photochemical data, and an Appendix of references and summaries of common and less usual chemometrics methods noted in this work, is provided.     

Approaching the direct exponential curve resolution algorithm from a maximum likelihood perspective

The implementation of maximum likelihood parallel factor analysis (MLPARAFAC) in conjunction with the direct exponential curve resolution algorithm (DECRA) is described. DECRA takes advantage of the intrinsic exponential structure of some bilinear data sets to produce trilinear data by a simple shifting scheme, but this manipulation generates an error structure that is not optimally handled by traditional three-way chemometrics methods such as TLD and PARAFAC. In this work, the effects of these violations are studied using simulated and experimental data used in conjunction with the well-established TLD and PARAFAC. The results obtained by both methods are compared with the results obtained by MLPARAFAC, which is a method designed to optimally accomodate a variety of measurement error structures. The impact on the estimates of different parameters linked to the data sets and the DECRA method is investigated using simulated data. The results indicate that PARAFAC produces estimates of much poorer quality than TLD and MLPARAFAC. Also, it was found that the quality TLD estimates was comparable or only marginally poorer than the MLPARAFAC estimates. A number of commonly used algorithms were also compared to MLPARAFAC using two sets of published experimental data from kinetic studies. The MLPARAFAC estimates of rate constants were more precise than the other methods examined.     

小波分析在化学中的应用进展

小波分析是信息处理的良好工具, 本文就其在化学中改善信号质量、图谱数据压缩、结构形态、模式识别、预测预报、过程控制、奇异诊断、动力学、量子化学和分形等方面的应用作了简要评述。     

A review of the main factors influencing the FT-IR-PLS abilities exemplified with petrochemical qualimetric applications

Quality control usually involves monitoring several variables directly related with industrial necessities using univariate tests. One powerful alternative is to link multivariate analytical techniques and multivariate chemometrics. In this way, Fourier Transform Infrared spectroscopy and Partial Least Squares regression are used to discuss and review several advantages and drawbacks encountered in using such combination in industrial facilities. Typical drawbacks are selection of data pretreatment, errors in reference methods, selection of calibration and validation sets and model-aging. This review is exemplified with petrochemical applications although other fields are also considered (mainly when dealing with data pretreatment).     

A review of the main factors influencing the FT-IR-PLS abilities exemplified with petrochemical qualimetric applications

Quality control usually involves monitoring several variables directly related with industrial necessities using univariate tests. One powerful alternative is to link multivariate analytical techniques and multivariate chemometrics. In this way, Fourier Transform Infrared spectroscopy and Partial Least Squares regression are used to discuss and review several advantages and drawbacks encountered in using such combination in industrial facilities. Typical drawbacks are selection of data pretreatment, errors in reference methods, selection of calibration and validation sets and model-aging. This review is exemplified with petrochemical applications although other fields are also considered (mainly when dealing with data pretreatment).     

Chemometrics for the analysis of chromatographic data in metabolomics investigations

Metabolomics aims to better understand biological systems through the chemical analysis of an organism's metabolic profile. One common method of analysis is mass spectrometry preceded by chromatographic separations. Samples produced by metabolomics investigations can contain hundreds to thousands of compounds, which can put great strain on the instrumental analysis. In order to improve these analyses, the data analysis must not be overlooked. The ever‐evolving field of chemometrics provides many useful tools for the analysis of chromatographic data. These include methods for preprocessing data to extract a maximum amount of information from the data as well as pattern recognition in order to find the compounds that vary the most in relation to the perturbation to the biological system under study. This article aims to highlight and provide future outlooks on current chemometric methods for chromatographic‐based metabolomics investigations. Copyright © 2014 John Wiley & Sons, Ltd.