Review pubs.acs.org/ac
Chemometrics Barry K. Lavine† and Jerome Workman, Jr.‡,§,⊥ †
Department of Chemistry, Oklahoma State University, Stillwater, Oklahoma 74078, United States Unity Scientific, Brookfield, Connecticut 06804, United States § National University, La Jolla, California 92037, United States ⊥ Liberty University, Lynchburg, Virginia 24502, United States ‡
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CONTENTS
Pattern Recognition Multivariate Curve Resolution Multivariate Calibration Author Information Notes Biographies References
(and seconds) away. A regression technique requiring hard coding of algorithms and days to compute in the mid-1980s has become a trivial matter for the uninitiated today. Since multivariate analysis methods are now standard in basic and applied research, the number of publications during the past few years containing data analysis is burgeoning. However, rapid and simple computations do not necessarily improve one’s ability to interpret the results. This still requires significant understanding of the algorithms as well as working with them in various experiments. The clear demarcation of chemometric terminology is essential for the mathematical techniques of chemometrics to be applied successfully beyond research investigation for practical analytical methods. The standardization of terminology and processing methods provides a necessary framework for moving to broader, more accepted techniques, in medical and regulatory applications, as well as serious process and heavily regulated analytical environments. An established set of terminology is essential for chemometrics maturing into an improved basis for cooperative international commerce, improved understanding, and expansion of research. As mentioned in the previous review, there is an ongoing effort by IUPAC in defining chemometric terms. This group has continued with a project to create glossary terms and concepts used in chemometrics.2 This will be accomplished by consultation with the community through a wiki site, a Web site that can be modified by users. Over time, new terms can be added, and consensus definitions developed. These definitions will be published as IUPAC recommendations. The use of multivariate methods for quantitative analysis, qualitative analysis, and data mining continues to increase due to the availability of many software tools as well as training courses, both commercial and academic. Nonspecialists have discovered the advantages offered by chemometrics in basic or applied research, as its applications include improved experimental design and increased extraction of information from many types of chemical related data. Several texts on chemometrics as it pertains to multivariate analysis have been published during the review period of late 2009 through 2012. With modern self-publishing options, virtual plagiarism from free Wikipedia content, and other publishers directly publishing dissertations disguised as well constructed and edited books, we limit this discussion to actual books published using traditional standards and well-established publishers. For the review period, the most notable book publications in chemometrics
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his Review, the nineteenth of this series, and the seventeenth with the title of “Chemometrics,” covers the most significant developments in the field from December 2009 through October 2012. As in the previous review covering the period from January 2008 through December 2009, new developments in chemometrics across major fields including novel applications are selected, and recent trends within the field are addressed.1 This Review is limited to 200 or less citations, so only the most noteworthy papers are cited, taking into account the purpose of covering the topics as well as possible. Space limitation restrict the potential for more comprehensive coverage of this subject, so authors should not feel slighted if they have not been cited. This is a challenging task for the reviewers as the number of citations and diversity of publications within the field of chemometrics has continued to increase rapidly during the past two decades. If one were to search for publications using the keywords multivariate data analysis or image analysis or astrophysical spectroscopic data analysis to broaden the perspective of applications of chemometrics, then the number of papers published during this review period listing each of these keywords would be in the tens of thousands. The fields of biophysics, basic engineering, and biomedical science include thousands of citations about chemometric-like data processing methods during this review period. There has been an increased use of multivariate methods across broad ranges of scientific disciplines, and multivariate analysis tools have become routine for most graduate, and even undergraduate, level scientific disciplines. In fact, undergraduate nursing students are now required to understand multivariate regression technique in such courses as Biomedical Statistics. Today, the use of YouTube tutorials and automated data analysis software packages combined with extremely powerful laptop computers have allowed access to complex mathematical functions. By importing data from Excel or simple text format files and simply clicking on a series of tabs and feature selection windows, advanced computations can be performed. Standard forms of algorithms are available as well as customization of pre- and postprocessing algorithms, making previously difficult and time-consuming matrix computations only a few clicks © 2012 American Chemical Society
Special Issue: Fundamental and Applied Reviews in Analytical Chemistry 2013 Published: November 9, 2012 705
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previous reviews, is located at http://www.namics.nysaes. cornell.edu/. This site continues to host links to Australian, Belgian, British, Czech, Danish, Dutch, German, Finnish, French, Italian, North American, Norwegian, Russian, South African, Spanish, and the Swedish chemometric societies. Umea University is the original home of chemometrics society activity worldwide, and the group continues to be very active in research. Their Analytical Chemistry Springboard includes a comprehensive chemometrics links site at http://www.anachem. umu.se/cgi-bin/jumpstation.exe?Chemometrics. Other chemometric URLs often mentioned in previous reviews include: http://cheminformatics.org/ and Cheminformatics Links contains 637 Links in 90 main categories, including data sets. The Homepage of Chemometrics URL is located at http://www.chemometrics.se/editorial/index.html. The Wiley Chemometrics and Informatics site contains some updated news events, conferences, and recent publications pertaining to chemometrics on its Web site: http://www.spectroscopynow. com/, once there select the Chemometrics and Informatics tab. Wikipedia topics that involve chemometrics include the following links. Chemometrics as a separate topic is listed as http://en. wikipedia.org/wiki/Chemometrics. Other topics include multivariate statistics (http://en.wikipedia.org/wiki/Multivariate_ statistics), simple linear regression (http://en.wikipedia.org/wiki/ Simple_linear_regression), and correlation (http://en.wikipedia. org/wiki/Correlation). During 2010 through 2012, several review articles on chemometrics algorithms and analytical methods applying chemometrics have appeared in the literature. Genetic algorithms in chemometrics have been reviewed by Leardi.12 The use of sparse methods in regression and classification to suppress noisy or irrelevant variables has been the subject of a review by Filzmoser.13 Alternatively, variable selection methods have been used to identify informative variables or remove uninformative variables. Xiaobo14 has performed an extensive literature review of variable selection methods in near-infrared spectroscopy for multivariate calibration. Recent advances in calibration of multiway day have been the subject of a critical review by Olivieri.15 The particular focus of this review is directed toward the data processing algorithms used and the estimation of the figures of merit to assess model performance. The use of orthogonal based projection methods capable of separating the correlated variation of the dependent variable from the uncorrelated variation in a single model is discussed in the context of partial least squares (PLS) in multivariate classification and calibration.16 Suykens17 has reviewed support vector machines for classification problems. Approaches to achieve a probabilistic interpretation and the extension of this binary classification technique into a multiclass method are discussed. The application of chemometrics to environmental analysis of organic pollutants has been the subject of a review by de Juan, Olivieri, and Tauler.18 Pattern recognition techniques which are used to extract chemical information from cross reactive sensor arrays have been the subject of a review by Anzenbacher.19 The different techniques used in multivariate image analysis, which has garnered the interest of chemists because of its ability to perform fast, low-cost, and noninvasive analysis of products or processes has been reviewed by de Juan.20 Chemometric techniques in metabolomics which have been used to obtain results in such fields as disease diagnosis, toxicology, and pharmaceutical and environmental research has been reviewed by Trygg.21 In this review, the use of experimental design techniques to ensure the production of high quality data coupled to the use of multivariate
include texts on general chemometrics and process analytical technology where chemometrics is used to monitor fault detection and assess product quality.3−6 Several books covering details of multivariate techniques and other specialized applications of chemometrics have also been published during this period.7−11 A number of chemometric conferences were held during 2010 through 2012 covering the complete set of chemometrics topics and international venues. Notable conferences are given here with their corresponding URLs. Notable conferences with chemometrics as a main theme are listed in chronological order in the following paragraphs. For 2013, upcoming conferences include: SSC-2013 (13th Scandinavian Symposium on Chemometrics), June 7−20, Stockholm, Djurönäset, Sweden (http://www.ssc13.org/); and the CCM VIII (8th Colloquium Chemiometricum Mediterranean), June 30− July 4, Bevagna, Italy (http://www.gruppochemiometria.it/ ccm2013/index.htm). Conferences held during 2012 included: WSC-8 (8th Winter Symposium on Chemometrics), February 27−March 2, Moscow Oblast, Russia (http://wsc.chemometrics.ru/wsc8/); SACS 2012 (The second convention of the South African Chemometrics Society), May 7−11, Pretoria, South Africa; CMA4CH (Multivariate Analysis and Chemometrics applied to Cultural Heritage and Environment), May, 27−30, Rome, Italy (http:// w3.uniroma1.it/cma4ch/index2.html); QSAR2012 (15th International Workshop on Quantitative Structure−Activity Relationships), June 18−22, Tallinn, Estonia (http://qsar2012.ut.ee/); CAC-2012 (13th Chemometrics in Analytical Chemistry Conference), June 25−29, Budapest, Hungary (http://www.cac2012. mke.org.hu/); IASIM-12 (The International Association for Spectral Imaging Workshop and Conference), September 9−14, Sigulda and Jurmala, Latvia (http://www.iasim.net/); Af rodata 2012 (2nd African-European Conference on Chemometrics), November 19−23, Stellenbosch, South Africa (http://afrodata. wordpress.com/); and PICS 2012 (Chemometrics in timeresolved and imaging spectroscopy), December 3−4, Lille, France (http://lasir.univ-lille1.fr/?page_id=2503). During 2011, chemometrics conferences were as follows: SSC12 (12th Scandinavian Symposium on Chemometrics), June 7− 10, Billund, Denmark (http://equationz.homepage.dk/ssc12/); Conferentia Chemometrica 2011 September 18−21, Sümeg, Hungary (http://www.cc2011.mke.org.hu/); ICRM 2011 (5th International Chemometrics Research Meeting), September 25−29, Nijmegen, The Netherlands (http://www.icrm2011. org/); and NTCA-2011 (New Trends in Chemometrics and Applications), October 8−11, Side, Antalya, Turkey. During 2010, conferences were: WSC-7 (7th Winter Symposium on Chemometrics), February 15−19, St. Petersburg, Russia (http://wsc.chemometrics.ru/wsc7/); SCAC-2010 (5th International Symposium on Computer Applications and Chemometrics in Analytical Chemistry), June 21−25, Budapest, Hungary (http://www.vein.hu/www/egyeb/analconf/SCAC2010.html); Af roData (First African-European Conference on Chemometrics), September 20−26, Rabat, Morocco (http://afrodata. wordpress.com/); CMA4CH (Multivariate Analysis and Chemometrics applied to Cultural Heritage and Environment), September 26−29, Taormina, Italy (http://w3.uniroma1.it/ cma4ch/index2.html); and CAC-2010 (12th Chemometrics in Analytical Chemistry Conference), October 18−21, Antwerp, Belgium (http://www.ua.ac.be/main.aspx?c=.CAC2010). There are many national and local chemometric societies. The activity levels vary with the identified groups. One main link to multiple chemometric Web sites, which has been listed in 706
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parameter estimation, and optimization are also covered in this literature survey and are treated in the context of the three major application areas that are the focus of this Review.
models to extract information from the high quality data is emphasized as it is crucial to ensure a successful outcome. The use of chemometrics to analyze two-dimensional data, e.g., protein patterns from gel electrophoresis22 or 2-dimensional gas or liquid chromatography23 continues to be an area of active research with a large and burgeoning literature as evidenced by these two reviews on this subject. Analysis of high resolution NMR data from complex mixtures of biological samples, e.g., urine, fecal matter, plasma, and serum and animal tissue using pattern recognition techniques and multiway methods is discussed at great lengths by Charlton in his review.24 As pointed out by the author, the alignment of data is important as experimental parameters and sample conditions cannot always be controlled. Chemometric techniques based on factorial design and response surface methodologies have many advantages over one way optimization for analytical applications including a reduced number of experiments and the opportunity to assess interactions among variables. These techniques also enable the selection of optimum experimental conditions. Aballino25 reported on the importance of the use of experimental design techniques to maximize the extraction of information from multivariate data using pattern recognition methods in single and sequential extraction assays to study element mobility and availability in solid matrixes such as soils, sediments, sludge, and airborne particulate matter. Using D-optimal designs, Ortiz26 has shown that sulfathiazole in milk can be detected using parallel factor analysis (PARAFAC) to develop an accurate calibration from molecular fluorescence data. HPLC separations have been optimized by experimental designs that have been used to model the retention times of compounds of interest.27 In this study, the design space was computed as the probability for a criterion to lie in a selected range of acceptance. For this methodology, accurate peak detection and peak matching are crucial. Factional factorial and central composite designs were shown to be useful for enhancing cyclodextrin modified capillary electrophoresis separations of hydroxyl acids in cosmetics.28 A collection of representative papers of notable stature are summarized for this Review. The development of complex analytical instrumentation and the need to analyze larger data sets have increased the demand for newer approaches in data analysis. Chemometric analysis of results from analytical laboratory methods is providing more insight for understanding complex chemical and biological systems, both natural and man-made. Chemometrics applications covered in this Review includes metabolomics, imaging, improvements in analytical modeling methods, and fingerprinting. Chemometrics is a discipline concerned with the application of statistical and mathematical methods, as well as those methods based on formal mathematical logic, to chemistry, often analytical chemical data. Publications concerned with the development of new chemometric methods are also included in this Review. There is modest growth in specific algorithm development as the number of chemometric research groups is relatively fixed and their size is limited. Conversely, the number of researchers applying chemometrics continues to grow, and the number of publications concerned with applications of chemometric methods to chemical data also continues to grow substantially. Analytical applications and an emphasis to efficiently extract more useful information from chemical data continue to drive research in chemometrics. Development of new methods in chemometrics and novel or important applications of these methods occurred in three major areas: calibration, resolution, and pattern recognition, which are summarized below. Topics such as variable selection, data preprocessing, signal processing, library searching,
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PATTERN RECOGNITION The overall goal of pattern recognition is classification. Developing a classifier from spectral, chromatographic, or compositional data may be desirable for any number of reasons including source identification, presence or absence of disease in a patient, or assessing product quality to name just a few. The classification step is often accomplished using one of several techniques that are now fairly well established including principal component analysis, hierarchical clustering, k-nearest neighbor, statistical and regularized discriminant analysis, and artificial neural networks. Few novel pattern recognition methods were reported in the literature during the past two years. Instead, the chemical literature on pattern recognition focused on novel and not so novel applications. Nevertheless, classification of data remains an important subject in chemometrics as evidenced by the large number of citations in the Chemical Abstract database on pattern recognition applications during 2010−2012. Hence, most of the references in this section are organized according to the type of application. However, there were papers published by research groups in this period that focused on improvements in the methods used for classification. Fundamental work on classification continues to be refined in a number of aspects with special focus given to new methodology and data preprocessing. Improving the methods used for pattern recognition continues to be an active area of research in chemometrics. Several groups offered new algorithms for visualization, clustering, classification, and preprocessing of multivariate chemical data. Rukenbusch29 has introduced Gaussian mixture models for the classification of vibrational spectroscopy data. The advantage of this approach is that model regularization is coupled to the classification criterion which avoids overfitting. Evolving fuzzy classifiers have been proposed: Kelly30 as an alternative to support vector machines, artificial neural networks, and k-nearest neighbor classification. These self-learning classifiers have the potential to cope with vast amounts of high-dimensional data of varying quality to yield robust predictions. Varmuza31 has proposed a new mapping and display method called random projections to project data onto a low dimensional subspace. This method has been shown to be effective in structure similarity searches involving large numbers of binary descriptors. Co-clustering, where a data matrix is simultaneously clustered in objects and variables, has been investigated by Bro32 as a potential method that can provide both accurate and succinct information from high rank data sets. When only a subset of the variables in a data set is related to a specific clustering among the samples, coclustering becomes the method of choice. Using linear interpolation to force time base consistency between chromatograms and accurate peak patterning through wavelets, a five step procedure for peak alignment of chromatographic data has been proposed by Liang.33 Because scaling and preprocessing of data is often crucial in the development of a classifier, the potential contribution made by a study of this type to the field of chemometrics should not be underestimated. In applications of pattern recognition techniques to chromatographic data, variable alignment is crucial as it is essential that features encode the same information for all samples in a data set. Hence, accurate peak matching is crucial when chromatograms are translated into data vectors for pattern recognition analysis. Applications of pattern recognition methods continue to dominate the literature. Several studies focused on the use of pattern 707
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recognition methods in spectral library searching. Ruzicka34 compared several Raman based library spectral correlation methods with SIMCA pattern recognition to discriminate between crystallizing sorbitol and noncrystallizing sorbitol from several manufacturers. Classification models developed using SIMCA performed better even when the sorbitol were adulterated with low levels of ethylene glycol and diethylene glycol. Search prefilters35,36 have also been developed for IR spectra to successfully discriminate carboxylic acids from noncarboxylic acids. A two step procedure was employed. First, the discrete wavelet transform is used to decompose each IR spectrum into wavelet coefficients that represent both the high and low frequency components of the signal. Second, a genetic algorithm for pattern recognition analysis is used to identify wavelet coefficients characteristic of functional group. Using this approach, a search prefilter for spectral library searching was developed from 435 IR absorbance spectra of 140 carboxylic acids and 295 noncarboxylic acids which included aldehydes, ketones, esters, and amides, as well as compounds containing both carbonyls and alcohols. The carboxylic acid search prefilter was successfully validated using two validation sets. The first validation set consisted of 24 carboxylic acids and 61 noncarboxylic acids, and the second validation set consisted of 264 carboxylic acids and 72 noncarboxylic acids. This same approach has been used to develop search prefilters37 to search the Paint Data Query (PDQ) database to differentiate between similar but nonidentical FT-IR spectra. Even in challenging trials where the samples evaluated were all the same manufacturer (Chrysler) with a limited production year range, the respective models and manufacturing plants could be correctly identified from a clear coat paint smear, which unlike the undercoat or color coat paint layers cannot be identified using the text based portion of the PDQ database. There were several publications that focused on the application of pattern recognition techniques to forensics. Daeid38,39 has demonstrated that degraded ignitable liquids from both light and medium petroleum distillates can be discriminated and linked to their parent unevaporated liquids through pattern recognition analysis of GC/MS analysis data using self-organizing feature maps. A potential method40 to obtain information about the type of gun and ammunition used at a crime scene was developed using principal component analysis and hierarchical clustering of cyclic voltammetric data of gunshot residue collected from the hands of shooters and analyzed using a gold microelectrode. An optical sensor array consisting of four fluorescent polymer films that responded to nitro containing explosives and its simulants were analyzed using support vector machines and the fuzzy ARTMAP network which had a perfect recognition rate.41 Furthermore, the classification of the data showed robustness to additive noise and could differentiate between simulants and explosives within 10 s at parts per billion levels. Signatures of chemical weapon precursors could be identified using two-dimensional gas chromatography42 or liquid chromatography/mass spectrometry (LC/MS) and pattern recognition methods.43 In the two-dimensional gas chromatographic study, parallel factor analysis was used to resolve overlapping GC × GC peaks ensuring clean spectra for spectral library matching. In the LC-MS study, sample matching was carried out by variance scaling and signal averaging of profiles prior to classification by k-nearest neighbor classification. Fraga44 has investigated the feasibility of the use of anionic impurities as a signature for matching cyanide salts back to their source. In this study, hierarchical clustering and principal component analysis were used to analyze ion chromatograms. Features were selected from these chromatograms using the Fisher ratio to enhance class separation
and optimize clustering. Hierarchical clustering and principal component analysis of near-infrared and Raman spectra of pharmaceutical products served as a potential method to identify counterfeit medicines.45 The results obtained using the unsupervised methods were comparable to those obtained using supervised methods such as k-nearest neighbor, partial leastsquares discriminant analysis, and neural networks. Classifiers developed in this study were able to compare the spectrum of a new counterfeit with that of a previously analyzed product to determine if the sample was a member of one of the previously discovered classes, thereby allowing a link to be established with other counterfeits in the database. Principal component analysis and hierarchical clustering were also applied to the analysis of infrared and Raman spectra of 34 red paints obtained from commercial sources.46 Six distinct clusters were detected in the 34 red paints from their spectroscopic profiles. Thus, the potential source of red paint involved in a vandalism case could be identified as to its source. Proton NMR and UV−visible spectroscopy were used to determine the potential adulteration of commercial spices with Sudan dyes.47 Two data fusion strategies (variable and decision level) combined with a multivariate classification approach, PLS discriminant analysis, have been applied to obtain the synergistic effects of combining data from these two different spectroscopic techniques. The combination of data from these two spectroscopic techniques yielded better results than the individual ones. A few papers focused on the application of pattern recognition techniques to metabolomics and the medical sciences. Mass spectral profiles of cerebrospinal fluid served as input to partial least-squares discriminant analysis models used to first classify the data.48 Using the group membership as the target, the most discriminatory projection of the data is revealed with the spectral regions contributing to this separation identified using a discriminant variable test and selectivity ratio plot developed to identify specific biomarker signatures in the data. Supervised selforganizing maps have been used to classify metabolic profiles obtained from NMR data of 96 human saliva samples with a novel discrimination index developed to determine which regions of the spectra are the most important.49 Breast cancer detection using micro FT-IR spectra and several support vector machines including bagging, boosting, and tree based models aggregated into an ensemble have been investigated as a potential method for biomedical tissue diagnostics.50 The combination of proton NMR and mass spectrometric data were used to improve the detection of metabolic profile alterations in biofluids or tissues caused by disease. Use of the first latent PLS vector from the proton NMR data and the first latent vector orthogonal signal correction (OSC) PLS vector from the mass spectral data allowed for disease classification to be expressed on a continuum scale as opposed to a binary scale allowing for more accurate disease detection.51 Applying FCV and hierarchical clustering and discriminant analysis to infrared absorbance spectral data from developing cortical bones, it was possible to correctly classify bone samples into different age groups.52 FCV clustering performed the best, and the class membership values assigned to each sample might prove beneficial in future studies where this information would be used for medical diagnostics. Finally, some novel, unusual, or interesting applications of pattern recognition reported in the recent literature. An integrated chemical and microbiological approach was used to develop a new analytical methodology to characterize the fungal load of a contaminated area in a building.53 A set of VOC profiles was developed with corresponding bioaerosol measurements as 708
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curve resolution method and discovered that both methods yield the same results for data with different error structures. There were several papers published during this period that focused on improvements in the methods used for MCR. The nonuniqueness of the MCR solution can be reduced by enforcing the consistency of the computed concentration profiles with a given kinetic model.65 This is a departure from current practices where kinetic modeling is realized in a separate step. The uniqueness and rotation ambiguities in MCR methods have been the subject of a study by Tauler.66 He suggests using graphical approaches to display the bands and areas of feasible solutions in a subspace of the data. From this study, he has concluded that different MCR methods will yield different solutions depending upon the constraints and rotational ambiguities. In the absence of rotational ambiguities, all MCR methods will give the same unique solutions. A user-friendly program available in MATLAB for evaluation of rotational ambiguities in MCR has been developed by Tauler and is available for downloading.67 Rajko68,69 has also investigated feasible solution boundaries in MCR and has concluded that all MCR approaches are identical for noiseless or moderately noisy two component systems. However, he has reported that solutions obtained by MCR algorithms using alternating least-squares can lie outside the range of the data matrix. Other improvements in methodology that have been reported during this period include correlation constrained MCR70 using alternating least-squares to achieve analyte quantitation in the presence of unexpected interferences and the development of new constraints in MCR for the separation of chromatographic peaks within the same extracted component.71 A new MCR methodology based on the fitting of signals to parametric functions has been developed to resolve overlapping voltammetric bands which progressively get broader and move along the potential axis causing a loss in linearity.72 Using a similar approach, i.e., hard modeling as a constraint in multivariate curve resolution, improved concentration profiles and spectra have also been obtained in ion mobility spectroscopy.73 Estimation of sensitivity and selectivity when multivariate curve resolution is applied to second order multivariate calibration data has been proposed by Tauler and has been validated through Monte Carlo simulations.74 A large number of publications have appeared in the chemical literature on applications of MCR techniques. Only the most significant of these publications are summarized here. In almost all of these applications, the authors employed well established methods. The great diversity in the application of multivariate curve resolution methods indicates that these methods are being increasing adopted by research groups further removed from chemometrics, a consequence of the interest that chemometrics is attracting from fields removed from analytical chemistry. Only the more interesting and novel applications are cited here. Structure and dynamics of water dangling OH bonds in hydrophobic hydration shells have been studied by variable concentration Raman spectroscopy and MCR.75 MCR and alternating least-squares has been extended to multiway and multiset data analysis to investigate the temporal distribution of pollution by nitric oxide and ozone using a variety of constraints like nonnegativity, trilinearity, and interaction among components.76 Evolving factor analysis and MCR with alternating least-squares has been applied to the decomposition of a series of quantum dot fluorescence spectra to reveal the different diameters of these fractions.77 The binding interaction between Alpinetin with bovine serum albumin has been investigated under simulated physiological conditions using fluorescence spectroscopy.
input−output pairs for a discriminant to successfully predict the presence or absence of mold contamination in indoor environments. A similar approach (focusing on the chemical composition as opposed to the total particulate mass) was used to predict the toxicity of fine particulates as vehicles for the transport of toxic chemicals into the human respiratory system.54 VOC profiles of beer obtained from SPME and analyzed by gas chromatography have been used to identify the brand. In this study, linear discriminant analysis, partial least-squares discriminant analysis, and multilayer feed forward neural networks were used to discriminate the various brands of beer.55 Discriminant analysis applied to IR spectra of oil spills to assess the origin of the hydrocarbons at the coast lines was undertaken to discriminate between aliquots of six oil spillages monitored over time.56 The classification models were evaluated using a set of 45 unknowns collected on Galician beaches after a major shipwreck. Subsequent analysis of the data using the international oil fingerprinting standard protocol to establish the assignations of these samples revealed that almost perfect classification of the data was obtained using the proposed FT-IR method. NIR spectroscopy was applied to the problem of gasoline classification57 using three data sets. Several classification methods were evaluated. The results of this study demonstrate that back-propagation neural networks using principal component scores of the data as input perform poorly compared to k-nearest neighbor, support vector machines, or probabilistic neural networks. Harrington58 has shown that fuzzy rule building expert classifiers applied to high speed gas chromatography are able to classify jet fuels by type and to track possible changes in their physical properties, which is crucial to ensure aircraft fuel safety. A variety of jet fuels from both the civilian and military sector populated the training set. Attenuated total reflectance infrared absorbance spectroscopy has been used to investigate deep-fried vegetable oil from olive, sunflower, and corn oil. Accurate oil classification was achieved using a one-class partial least-squares discriminant analysis classifier and a rooted binary directed acyclic graph tree.59 Lactic acid bacteria were classified by strain from their FT-IR spectra using hierarchical clustering and statistical discriminant analysis to detect classes and create a library group.60 Partial least-squares analysis of laser induced breakdown spectroscopic data has shown that artifacts constructed from volcanic glass in California can be identified as to the original quarry site used to construct them.61 A variety of aspects of the training were investigated including the validation procedure, the number of latent variables used to construct the PLS model, and whether variable selection would improve the classification results. This study is a logical extension of a previous study published on this subject over forty years ago.
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MULTIVARIATE CURVE RESOLUTION This section is concerned with methods for the resolution and recovery of pure component spectra from the overlapped spectra of mixtures. Several reviews on multivariate curve resolution (MCR) appeared in the literature during this reporting period. Heravi62 has published a detailed review on recent trends in the application of multivariate curve resolution (MCR) for gas chromatography/mass spectrometry analysis of essential oils. A variety of topics are covered in this review including data preprocessing, uncertainty in MCR results, local rank analysis, and available software. Augusto63 has published a review describing the major advantages and pitfalls of iterative and noniterative multivariate curve resolution since 2000 for GC data, GC/MS data, and two-dimensional gas chromatography. Walczak64 compared positive matrix factorization and the weighted multivariate 709
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Multivariate curve resolution of a series of fluorescent spectra yielded a large quantity of information related to the nature of the complex formed between albumin and alpinetin.78 Time dependent conjugation of gold nanoparticles with an antiparkinsonian molecule monitored by UV−visible absorption spectroscopy was analyzed using MCR with alternating least-squares.79 Time dependent concentration profiles and pure spectra of species involved in the conjugation process were extracted from the kinetic data. Furthermore, the molecular concentration necessary for the completeness of the conjugation reaction could be estimated as well as the free energy of molecular adsorption. Size exclusion chromatography using fluorescence spectroscopy for detection and MCR was used to study the formation of Watson− Crick duplex DNA structures and intermolecular quadruplex structures from individual strands.80 MCR has been applied to the analysis of data from yeast genome wide screens using microarray technology. In this study, two algorithms were compared: conventional alternating least-squares with weighted alternated least-squares.81 The motivation for utilizing the weighted alternating least-squares was the noise and poor quality of the data. Many of the problems associated with this data were circumvented using the weighted alternating least-squares. Circular dichroism and voltammetry assisted by MCR were used to study the competitive binding of metals to phytochelatin. Using MCR with alternating least-squares, it was possible to deduce the stoichiometry of the complexes.82 MCR and alternating leastsquares was applied to time-resolved infrared difference spectra probing photoinduced ubiquinol formation in detergent isolated reaction centers of Rhodobacter sphaeroides to identify marker bands indicative of reduction events.83 A priori chemical knowledge of the system, e.g., the use of a pure spectrum of one species, was utilized to enhance the performance of MCR. Data fusion was exploited to enhance the performance of MCR with alternating least-squares for interpretation of photodegradation processes.84 Multivariate curve resolution techniques continue to be exploited in chemical analysis. The resolution of ion mobility spectroscopy can be improved using MCR. The potential for ion mobility spectroscopy and MCR to detect and quantify contraceptives in commercial tablets has been demonstrated85 with the proposed method validated for use in routine analyses. The use of MCR in liquid chromatography-infrared absorption spectroscopy has proven problematic due to intense background absorption changes during gradient elution. Using SIMPLISMA, a well-known MCR method, the background signal from gradient elution can be calculated and subtracted out to yield data with improved signal-to-noise which is amenable to analysis by MCR with alternating least-squares.86 Raman microscopy and MCR has been used to analyze counterfeit medicines to reveal the identities of the excipients and active pharmaceutical ingredients in the tablets.87 Multivariate curve resolution with alternating leastsquares coupled to high performance liquid chromatography with diode array detection was used to analyze for 11 pesticides.88 Second order data matrixes were obtained for each sample from a chromatographic system operating in the isocratic mode. Although the presence of strongly coeluting peaks caused distortions in the time dimension between runs, accurate concentration profiles of the compounds could be extracted from the data. HPLC with fluorescence detection was used to determine the presence of pteridines in urine. MCR with alternating least-squares was crucial to extract the concentration profile of each pteridine.89 A central composite design used to optimize the factors influencing the separation, e.g., buffer pH, flow rate, oven temperature, and mobile phase rate, was crucial as it ensured that MCR was able to cope
with coeluting interfering agents. Using non-negative matrix factorization, 1D spectra of the individual components of a mixture from a 2-D TOCSY spectrum could be acquired.90 The proposed method is applicable for retrieving profiles from sparsely acquired data. MCR with alternating least-squares has been applied to the problem of peak alignment in two-dimensional gas chromatography, and the performance of the proposed method91 is shown to have advantages over more established techniques such as correlation optimized warping. As noted above, there were too many applications of MCR to cite in their entirety. Multivariate curve resolution techniques continue to be exploited in spectroscopic imaging. Martin92 analyzed high contrast Raman images of uterine tissue using MCR with alternating least-squares. MCR provided the best biocontrasted images, superior to those obtained by principal component analysis or hierarchical clustering. Applications of MCR with alternating least-squares to quantitative analysis in hyperspectral image resolution have been investigated by Tauler.93 Preprocessing, the use of experimental design techniques, and the calibration validation strategy used were crucial to ensure a successful outcome. Segmentation of hyperspectral biomedical images using MCR with alternating least-squares which would allow identification of constituents when spectral libraries are available has also been investigated.94 The advantages of the use of MCR in this context include the interpretability of results and the selection of input information based on the compound in the segmentation scheme.
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MULTIVARIATE CALIBRATION Calibration involves modeling a measured response based on the amounts, concentrations, or other physical or chemical properties of a set of analytes. Multivariate calibration refers to the process of relating the analyte concentration or the measured value of the physical or chemical property to a measured response, e.g., near IR spectra of mixtures. There were a large number of citations found in the Chemical Abstract Database during this review period. PLS has come to dominate the practice of multivariate calibration because of the quality of the calibration models produced and the ease of their implementation due to availability of PLS software. Latent variables in PLS are developed simultaneously along with the calibration model. Each latent variable is a linear combination of the original measurement variables rotated to ensure maximum correlation with the information provided by the property variable. Martens95 has proposed the informative converse paradox for PLS. When a data matrix is approximated by a linear model and the fitting done by row-wise regression, only column wise interference information can be taken into account. These windows into the unknown are explained here and serve as the basis for selectivity enhancements in multivariate calibration. An ensemble strategy consisting of uninformative variable elimination and PLS for near-infrared spectroscopic calibration has been proposed.96 Different calibration sets are formed randomly from the data set, and PLS models are developed for each calibration set with uninformative variable elimination applied to each PLS model. Models that perform better for the training set are used to produce an ensemble using a simple weighted average. The advantages of this approach are demonstrated using two data sets. Resampling methods have been proposed as a means of determining the optimum number of latent factors for a PLS model.97 Esbernsen and Geladi98 have investigated the issue of model validation in PLS and have concluded that graphical inspection of t−u plots for optimal understanding of the X−Y 710
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of least-squares support vector machines has been demonstrated by Gao.116 The use of bagging for nonlinear regression models such as support vector machines to obtain more accurate and robust calibrations of spectroscopic data has been investigated by Chen.117 Applications of PLS regression dominated the literature. Use of PLS has become commonplace in analytical chemistry. A major part of the increase in the use of PLS can be attributed to improving commercial software for chemometrics, but better education of chemists in the use and application of multivariate calibration also appears to have a role. Vibrational spectroscopy has long been an area where chemometric methods are embraced, and it is no surprise that many of the applications appeared in analyses using near-IR spectroscopy. Analysis of glucose in various aqueous media has been the subject of attention from many groups. The lower levels of glucose found in physiological samples and the high background presents a special challenge in both spectroscopy and calibration. A series of papers involving different approaches of chemometrics with the use of transmission spectroscopy and FT-NIR to detect glucose in a variety of sample matrixes were published during the review period. The first involves the use of a special factorial design for the calibration set, along with a modified orthogonal signal correction calibration method, to compensate for the presence of saccharide interferences.118 The second paper119 describes the application of spectra cross-correlation for Type II outlier screening during multivariate near-infrared spectroscopic analysis of whole blood. This paper discusses improved outlier detection methods to prevent false negative results using cross-correlation methods as compared to other standard outlier techniques. Cross-correlation is shown to be an improvement for these data types. The third paper of the series120 discusses the use of a “Lucky Imaging” technique to coadd the optimum spectra to improve the signal-tonoise of a series of measured replicate spectra, as well as a method to optimize the calibration b-vector and minimize bias issues associated with multivariate calibration. The technique promises to improve overall spectral integrity during routine measurements. As noted above, there were too many applications of multivariate calibration to cite in this Review. However, representatives of these publications are summarized in the following paragraphs. These were selected on the basis of an unusual calibration or an unusual measurement system. These articles did not fit in any of the categories or divisions within this section but are noteworthy for their methodology. A calibration model developed using PLS has been able to quantitate the total protein concentration in hyperimmune serum samples.121 The influences of spectral preprocessing and the spectral window used to develop the calibration model were investigated. The best results were obtained using whole spectra preprocessed using multiplicative scatter correction and using data in a specific wavelength region. The total antioxidant activity of four Prunella L. species was predicted using chromatographic data that was modeled using orthogonal signal correction-PLS.122 The development and validation of a PLS regression model to determine biodiesel concentrations (2% to 90%) in biodiesel/diesel blends that have been characterized by near-infrared spectroscopy has been reported.123 Near infrared spectroscopy and PLS have been used to predict several gasoline properties using a Doehlert experimental design with three input variables (wavenumber range, preprocessing technique, and validation technique). The methodology124 was successfully applied to obtain PLS models to monitor gasoline quality in less than 40 modeling runs, demonstrating the efficacy and efficiency of this approach. PLS regression
relationship and for validation guidance is strongly recommended. A new expression for the variance of prediction in NIR is proposed and is predicated on the anticipated spectral error structure and the high collinearity of the spectral measurement variables.99 Data preprocessing and variable selection have become important topics in multivariate calibration. A comprehensive study on preprocessing in multivariate calibration has been undertaken by Popp100 who has demonstrated that a large amount of physically meaningful preprocessing often leads to bad results. A new methodology for alignment of chromatographic data101 is proposed based on the decomposition of a three way array using a suitably initialized and constrained PARAFAC model. Matrix alignment can be performed even when the data matrix contains unexpected chemical interferences. Spectral background removal to improve the quality and stability of a near-infrared calibration has been demonstrated by Small102 using three near-infrared absorption data sets. Wavelets have also been shown to be effective in suppressing background and noise for multivariate calibration in Raman spectroscopy.103 The use of feature selection to improve a principal component regression calibration has been demonstrated by Hemmateenejad104 who utilized Kohonen self-organizing maps to cluster the wavelengths into different segments. The spectral data of each segment are subjected to principal component analysis, and the derived principal components are used as independent variables in a stepwise regression procedure. A new variable selection method based on ant colony optimization to optimize a PLS model based on a fixed number of latent variables has been proposed by Oliveri and validated using simulated data.105 A modification of the successive projections algorithm for spectral variable selection in the presence of unknown interfering agents has been proposed by Arujo.106 Achievement of a satisfactory multivariate calibration model is often not the final step in many practical applications. Once it is developed, it is often necessary to transfer the calibration model to other instruments or to update the calibration model to ensure that it can be used at the point of measurement. Brown107,108 has reported on the successful application of a stacked partial leastsquares regression model for direct application of multivariate calibration models to data from a secondary spectrometer without the need of any calibration transfer. Kalivas109,110 investigated the issue of calibration maintenance and model updating in models developed using Tikhonov regularization. A new method called spectral space transformation has been reported to eliminate spectral differences induced by changes in instruments or measurement conditions.111 This method has been successfully validated using two NIR data sets. Systematic prediction error correction, which requires fewer samples and is easier to use than piece wise direct standardization to transfer a calibration between instruments, has been proposed by Chen.112 A number of papers exploring calibration methods other than PLS appeared. Support vector machines in multivariate calibration have been reviewed by Brereton.113 Support vector machines have been compared to PLS, polynomial PLS, and artificial neural networks for developing multivariate calibrations using 14 different data sets.114 Support vector machines in this study outperformed PLS and polynomial PLS and were comparable in accuracy to artificial neural networks. Pierna115 in a study comparing support vector machines to PLS and artificial neural networks reported that support vector machines outperformed artificial neural networks for nonlinear calibrations and yielded comparable results to PLS for linear calibration problems. The use of data fusion to improve the prediction ability 711
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chemometrics. This Chemometrics Review article constitutes the fifth in this series he has coauthored. In his career, Workman has focused on molecular and electronic spectroscopy, process analysis, and chemometrics and has received many key honors and awards for his work. Over the past twenty-five years, he has published widely, including numerous tutorials, oral presentations, scientific papers and book chapters, individual text volumes, software programs, and patents/inventions/trade secrets.
models developed from FT-IR spectra of motor oils for viscosity index and base number outperformed comparable models developed from principal components regression and classical leastsquares for oil parameter prediction.125 The wavelet transform has been shown to be a useful preprocessing method for nearinfrared absorption spectra. An ensemble PLS model developed by combining individual models obtained with different wavelet transform settings was used to determine wheat and gasoline properties from their corresponding near-infrared spectra.126 Fusing data from two disparate sources can improve the accuracy of a multivariate calibration. Using a four-component simplexcentroid design to prepare blended powder mixtures of pharmaceutical excipients, FT-IR and powder X-ray diffraction spectra were fused using two different methods: fusion of preprocessed data and fusion of principal component scores.127 The fusion of principal component scores generated the desired model synergism. Data fusion achieved through different wavelet scales applied to spectra and combined with the generalized regression neural network was used to quantitate nitroaniline isomers.128 The generalized regression neural network was able to outperform so-called established methods, e.g., PLS, PCR, and backpropagation neural networks. There were several papers published on higher order multivariate calibrations during this period. Oliveri129 has reviewed the current state of second order and higher order multivariate calibration methods for nonmultilinear data systems. The advantages and disadvantages of algorithms currently available to cope with these systems were discussed. Multiway calibrations of nitrofurans using different models have been compared by Ni.130 The best performing prediction model was unfolded principal component analysis residual bilinearization. Unfolded partial least-squares residual bilinearization was found to yield the best model for determining atenolol in human urine excitation emission fluorescence spectroscopy.131 Loss of trilinearity due to analyte background interactions which can vary from sample to sample and inner filter effects precluded the use of parallel factor analysis. Unfolded partial least-squares residual bilinearization has been able to achieve the second order advantage in a number of calibrations reported in studies during this period.132,133 Third and higher order multivariate calibrations have also been reported during this period. Olivieri134 reported a MATLAB graphical toolbox for third order multivariate calibration and a new algorithm for processing five-way data to achieve the second order advantage.135
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REFERENCES
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AUTHOR INFORMATION
Notes
The authors declare no competing financial interest. Biographies Barry K. Lavine is a Professor of Chemistry at Oklahoma State University in Stillwater, OK. He has published more than 100 papers in chemometrics and is on the editorial board of several journals including the Journal of Chemometrics and the Microchemical Journal. He is the Assistant Editor of Chemometrics for Analytical Letters. Lavine’s research interests encompass many aspects of the applications of computers in chemical analysis including pattern recognition, multivariate curve resolution, and multivariate calibration using genetic algorithms and other evolutionary techniques. Jerome (Jerry) Workman, Jr. is Executive Vice President of Research and Engineering (including product definition) at Unity Scientific in Brookfield, CT; Certified Core Adjunct Professor at National University, La Jolla, CA; and Adjunct Professor at Liberty University, Lynchburg, VA. He has held many technical positions involving chemical and biomedical analysis and 712
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dx.doi.org/10.1021/ac303193j | Anal. Chem. 2013, 85, 705−714
