Three-Mode Abstracts, Part G

INDEX

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• Gabrielsson, A. (1979).
  Dimension analyses of perceived sound quality of sound-reproducing systems. Scandinavian Journal of Psychology, 20, 159-169.
  Perceived sound quality of loudspeakers, headphones, and hearing aids was investigated by different multivariate techniques to find out dimensions in perceived sound quality and explore their relations to physical characteristics of the systems. In connection with the description of two of these experiments various methodological questions concerning judgment methods, data treatment, interpretation of results, and implications for continued research are discussed. The combined results of eight experiments suggest the following dimensions: "Clearness/Distinctness", "Sharpness/Hardness - Softness", "Brightness - Darkness", "Fullness-Thinness", "Feeling of space", "Nearness", "Disturbing sounds", and "Loudness".

• Gabrielsson, A. & Sjögren, H. (1974, 1975).
  Adjective ratings and dimension analyses of perceived sound quality of hearing aids. I & II. (Report TA No. 75 & 77). Stockholm: Karolinska Institutet, Technical Audiology.
  In the first report 6 program sections reproduced via 5 sound reproducing systems (hearing aids) were scored on 62 ten-point adjective scales with respect to their sound quality (second report: 6x8x40). In both studies T3 was applied with various scalings and rotations, and the resulting factor spaces were in many respects very similar to those in other factor analyses, but not always so. The interpretation of the core matrices was found to be too difficult. T3 was abandoned in favour of INDSCAL.

  

• Gabrielsson, A., & Sjögren, H. (1979a).
  Perceived sound quality of hearing aids. Scandinavian Audiology, 8, 159-169.
  Four experiments dealing with perceived sound quality of hearing aids are described. The purposes were (a) to find a limited number of perceptual dimensions suitable for describing variations in perceived sound quality, (b) to find the positions of the selected hearing aids in these dimensions, (c) to explore the relations between the perceptual dimensions and the physical characteristics of the hearing aids. Using various multivariate techniques for dimension analysis, the resulting dimensions were interpreted as 'Sharpness/Hardness - Softness', 'Clearness/Distinctness', 'Brightness - Darkness', 'Fullness', 'Feeling of space', 'Nearness', 'Loudness', and 'Disturbing sounds'. Their relations to characteristics of the heaing aids were explored as well as their relations to overall evaluations. The implications for continued research and audiological applications are discussed.

• Gabrielsson, A., & Sjögren, H. (1979b).
  Perceived sound quality of sound-reproducing systems. Journal of the Acoustical Society of America, 65, 1019-1033.
  Perceived sound quality of loudspeakers, headphones, and hearing aids was invesitgated by multivariate techniques from experimental psychology with the purpose (a) to find out and interpret the meaning of relevant dimensions in perceived sound quality, (b) find out the positions of the investigated systems in these dimension, (c) explore the relations between the perceptual dimensions and the physical characteristics of the systems, and (d) explore the relations between the perceptual dimensions and overall evaluations of the systems. The resulting dimensions were interpreted as "clearness/distinctness," "sharpness/hardness-softness," "brightness-darkness," "fullness-thinness," "feeling of space," "nearness," "disturbing sounds," and "loudness." Their relations to physical variables were explored by studying the positions of the investigated systems in the respective dimensions. Their relations to overall evaluations were studied, and the implications of the investigations for continued research are discussed.

• Gailhard, I., Gros, P., Durbec, J. P., Beliaeff, B., Belin, C., Nezan, E., & Lassus, P. (2002).
  Variability patterns of microphytoplankton communities along the French coasts. Marine Ecology-Progress Series, 242, 39-50.
  Microalgal populations along French coasts (English Channel, Bay of Biscay and Mediterranean Sea) have been sampled twice a month since 1987 within the context of the French Phytoplankton and Phycotoxin Monitoring Network (REPHY). This study used these data to characterize the large-scale geographical structures of microphytoplankton communities and to determine whether 'homogeneous' geographical areas exist in which microalgal populations display similar temporal variability schemes. Once the temporal variability component shared by all sampled coastal sites was identified, the 'residual' site-specific component was analyzed. Multivariate ordination methods were used to determine seasonal and inter-annual variability. The expected-temporal pattern common to all sites was identified and the seasonal cycle of the most frequently observed phytoplankton communities along French coasts was described. The between-site analysis, using multitable comparison methods (RV-coefficient and multidimensional scaling), allowed the identification of 3 large areas (western English Channel, Bay of Biscay and Mediterranean Sea) according to the temporal variability patterns of microphytoplankton populations. The results, despite the coastal locations of REPHY sampling sites, indicate that the hydrodynamic characteristics of the different areas play a major role in the geographical structure of microalgal populations in French coastal waters.

• Galera, M. M., Vidal, J. L. M., Frenich, A. G., & Gracia, M. D. G. (1997).
  Evaluation of multiwavelength chromatograms for the quantification of mixtures of pesticides by high-performance liquid chromatography diode array detection with multivariate calibration. Journal of Chromatography, 778, 139-149.
  Three multivariate calibration methods, partial least squares (PLS-1 and PLS-2) and principal component regression, were applied to the simultaneous determination of the five pesticides iprodione, procymidone, chlorothalonil, folpet and triazophos by high-performance liquid chromatography with diode array detection. Such detection gives multiwavelength chromatograms from a single analysis of one sample. In this paper,calibration models at two different wavelengths were developed to resolve mixtures of five pesticides with overlapping chromatographic peaks. The first model, carried out at 220 nm as detector compromise wavelength, yielded satisfactory sensitivity for accurate estimation of the concentration of iprodione, procymidone, chlorothalonil acid folpet and the second model, at 200 nm, was used for accurate estimation of triazophos. Both calibration models were evaluated using the chromatograms and first-derivative (D-1) chromatograms by predicting the concentrations of independent test set samples. Finally, the proposed D-1 calibration models were successfully applied to the determination of these pesticides in groundwater and soil samples. In all cases, the PLS-1 calibration method showed superior quantitative prediction ability than the PLS-2 or principal component regression methods.

• Gallagher, N. B., Shaver, J. M., Martin, E. B., Morris, J., Wise, B. M., & Windig, W. (2004).
  Curve resolution for multivariate images with applications to TOF-SIMS and Raman Chemometrics and Intelligent Laboratory Systems, 73, 105-117.
  Multivariate curve resolution (MCR) is a powerful technique for extracting chemical information from multivariate images (MI). Two problems with MI are (1) initializing the MCR decomposition and (2) lack of selectivity in the image. Methods derived for initializing MCR with evolving data that are naturally ordered in time are not generally applicable for MI. Purity-based methods show promise and a simple, robust purity-based algorithm has been developed to initialize the MCR decomposition. This method used distance measures to find samples (or variables) on the exterior of a data set. Lack of selectivity, common in MI, generally results in a rotational ambiguity in factors extracted with MCR. Functional constraints were tested as a means to reduce this ambiguity, and the method tested showed that functional constraints could be used to account for offsets and backgrounds in Raman images. Robust initialization and introduction of functional constraints tested here are necessary steps towards the final objective of providing a simple methodology for constraining factors in a general fashion so that knowledge of the physics and chemistry can be easily incorporated in to any MCR decomposition. Additionally, the use of a sequential decomposition method (sequential MCR) is employed to help reduce mixing of recovered components in rotationally ambiguous systems.

• Gandour, J.T. (1978).
  Perceived dimensions of 13 tones: A multidimensional scaling investigation. Phonetica, 35, 169-179.
  24 native speakers of American English made direct ratings of dissimilarity between 13 pitch patterns superimposed on a synthetic speech-like syllable. A multidimensional scaling analysis of the data revealed four perceptual dimensions, which weer interpreted as average pitch, endpoint, extreme endpoint and length. The relative importance of these dimensions varied across individual subjects.

• Gandour, J.T., & Harshman, R.A. (1978).
  Crosslanguage differences in tone perception: A multidimensional scaling investigation. Language and Speech, 21, 1-33.
  Using an individual differences multidimensional scaling model of perception, this crosslanguage investigation seeks to determine what dimensions underlie the perception of linguistic tone, and to what extent an individual's language background (Thai, Yoruba or American English) influences his perception. Dissimilarities data were obtained from subjects' paired-comparison judgments of 13 different pitch patterns superimposed on a synthetic speech-like syllable. A multidimensional scaling analysis of the data for the total group revealed that five dimensions - interpretively labeled, AVERAGE PITCH, DIRECTION, LENGTH, EXTREME ENDPOINT and SLOPE - best summarize the perceptual structure underlying the dissimilatities data. Language subgroup variation in relative importance of these dimensions appears to be primarily related to subgroup differences in the way pitch is used to convey linguistic information. Discriminant analysis showed that most individual speakers of a tone language (Thai or Yoruba) can be easily distinguished from speakers of a nontone language (English) on the basis of their distinctive patterns of perceptual saliency for these five dimensions. Regression analysis indicated that the DIRECTION and SLOPE dimensions closely correspond to certain earlier proposed binary distinctive features of tone.

• Gao, L., & Rhen, S. (1999).
  Simultaneous spectrophotometric determination of four metals by the kernel partial least squares method. Chemometrics and Intelligent Laboratory Systems, 45, 87-93.
  Simultaneous determination of Mn, Zn, Co and Cd was studied by two methods, classical partial least squares (PLS) and kernel partial least squares (KPLS), with 2-(5-bromo-2-pyridylazo)-5-diethylaminephenol (5-Br-PADAP) and cetyl pyridinium bromide (CPB). Two programs, SPGRPLS and SPGRKPLS, were designed to perform the calculations. Eight error functions were calculated for deducing the number of factors. Data reductions were performed using principal component analysis. The KPLS method was applied for the rapid determination from a data matrix with many wavelengths and fewer samples. Experimental results showed both methods to be successful even where there was severe overlap of spectra.

• García, I., Sarabia, L., Ortiz, M. C., & Aldama, L. M. (2004a).
  Building robust calibration models for the analysis of estrogens by gas chromatography with mass spectrometry detection. Analytica Chimica Acta, 526, 139-146.
  Five hormonal growth promotants (diethylstilbestrol, hexestrol, dienestrol, 17-beta-estradiol and 17-alpha-ethynylestradiol) have been analysed by gas chromatography with mass spectrometry detection (GC/MS, SIM mode) for four non-consecutive days. The aim is to build models with stable predictions. The strategies applied are internal standardization and global models carried out by gathering signals recorded on several days. Two models were examined: univariate models (with standardized peak area) and PARAFAC2 (the analyte scores were standardized by the scores of the internal standard). Internal standardization has been proved to be efficient for both models of dienestrol and ethynylestradiol. The mean relative error in absolute value when samples recorded on a different day to the calibration set are quantified by PARAFAC2 is 7.00% and 7.11% for dienestrol and ethynylestradiol, respectively. For diethylstilbestrol and estradiol, internal standardization was combined with global calibration models built with signals recorded under several sources of variability (different days). Thus predictions become steadier over time and in the estradiol example, errors decrease from 33.10% to 9.76%. The mean relative error in absolute value with PARAFAC2 updated models oscillates between 6.34% for ethynylestradiol and 10.74% for diethylstilbestrol. For univariate updated models errors range from 6.42% to 14.19% for ethynylestradiol and estradiol respectively. The combination of both strategies has been proved to be efficient independently of the analyte and of the signal order.

• García, I., Sarabia, L. A., & Ortiz, M. C.(2004b).
  Detection capability of tetracyclines analysed by a fluorescence technique: comparison between bilinear and trilinear partial least squares models. Analytica Chimica Acta, 501, 193-203.
  According to the committee decision of 12 August 2002 (2002/657/EC) the capability of detection, CCbeta, must be set in all analytical methods not only at concentration levels close to zero but also at the maximum permitted limit (PL). In this work we describe a methodology which evaluates the capability of detection of a fluorescence technique with soft calibration models (bilinear and trilinear PLS) to determine tetracyclines (group B1 substances from annex 1 of Directive 96/23/EC). Its estimation is based on the generalisation of the procedure described in International Union of Pure and Applied Chemistry and in the ISO standard 11843 for univariate signals which evaluates the probabilities of false positive (alpha) and false negative (beta). The capability of detection, CCbeta, estimated from the second-order signal and the trilinear PLS model is 9.93 mug l(-1) of tetracycline, 17.75 mug l(-1) of oxytetracycline and 26.31 mug l(-1) of chlortetracycline, setting alpha and beta at 0.05. The capability of detection, CCbeta, determined around the PL (100 mug kg(-1) in milk and muscle) with the second-order signal is 109.4 mug l(-1) of tetracycline, 117.0 mug l(-1) of oxytetracycline and 124.9 mug l(-1) of chlortetracycline, setting alpha and beta at 0.05. The results were compared with those obtained with zero and first-order signals. The effect of the interferences on the capability of detection was also analysed as well as the number of standards used to build the models and their calibration range. When a tetracycline is quantified in presence of uncalibrated ones by means of the trilinear PLS model the errors oscillate between 14.70% for TC and 9.57% for OTC.

• García, I., Sarabia, L., Ortiz, M. C., & Aldama, L. M. (2004c).
  Three-way models and detection capability of a gas chromatography-mass spectrometry method for the determination of clenbuterol in several biological matrices: the 2002/657/EC European Decision. Analytica Chimica Acta, 515, 55-63.
  Clenbuterol has been extracted by mixed solid-phase extraction from two biological matrices (bovine hair and urine) and detected by GC/MS (selected ion monitoring (SIM) and full-SCAN modes). The analytical signal has been modelled with univariate and three-way models, namely DTLD, PARAFAC, PARAFAC2, Tucker3 and trilinear PLS. Since clenbuterol is a banned substance a comparative study of the capability of detection (CCbeta, X-0 = 0) has been performed as a function of the sample (hair, 74 mug kg(-1) and urine, 0.36 mug l(-1)), the mode in which the signals are monitored (SCAN, 283 mug kg(-1) and SIM, 74 mug kg(-1)) and the statistical model (univariate, 283 mug kg(-1) and trilinear PLS, 20.91 mug kg(-1)). The capability of detection has been calculated as stated in ISO 11843 and Decision 2002/657/EC setting in all cases the probabilities of false positive and of false negative at 0.05. The identification of the mass spectra must be done to confirm the presence of clenbuterol and has been carried out through PARAFAC. The correlation coefficient between the spectra estimated by PARAFAC and the library spectra is 0.96 (hair, SCAN mode) and 1.00 (hair and urine, SIM mode). The Decision 2002/657/EC advocates the use of independent mass fragments to identify banned compounds. These recommendations together with the effect of the number of ions registered on the capability of detection have lead us to select five uncorrelated fragments (86, 243, 262, 264 and 277) from the data set of 210 ions by hierarchical clustering of variables.

• García, J.M., Jimenez, A.I., Arias, J.J., Khalaf, K.D., Moralesrubio, A., & Delaguardia, M. (1995).
  Application of the partial least-squares calibration method to the simultaneous kinetic determination of propoxur, carbaryl, ethiofencarb and formetanate. Analyst, 7, 7.
  A method based on the application of partial least-squares analysis to bilinear data was used for the simultaneous determination of propoxur, carbaryl, ethiofencarb and formetanate by a kinetic-spectrophotometric method. The procedure is based on the different rate constants of the reactions between p-aminophenol, in the presence of potassium metaperiodate, and the phenolic and naphtholic compounds obtained from the alkaline hydrolysis of the pesticides using a stopped-flow injection procedure. Mixtures containing 2-10 mu g ml(-1) of propoxur, 2-8 mu g ml(-1) of carbaryl, 2-10 mu g ml(-1) of ethiofencarb and 2-10 mu g ml(-1) of formetanate were successfully resolved with errors of less than 5%.

• García, J. A. J.., Plaza, J. G., & Pavon, J. M. C.(1994).
  Resolution of overlapped peaks in liquid-chromatography by use of derivative spectrophotometry and multivariate-analysis and its application in the determination of active components in insecticide formulations. Fresenius Journal of Analytical Chemistry, 349, 542-545.
  Two procedures for the determination of active components in insecticide formulations have been devised. The first is based in the use of derivative spectra of the components obtained by a diode-array spectrophotomer around the maxima signal of the chromatographic peak. In the second method, mixtures are resolved by the partial least-squares (PLS) regression method from standard spectra of the pure components; spectra of the components were also registered around the maxima signal of the peak. Both procedures have been applied to the analysis of diverse mixtures of active components (piperonyl butoxide, neopynamine and fenitrothion) in insecticide formulations with satisfactory results.

• Gardner, W. P., Shaffer, R. E., Girard, J. E., & Callahan, J. H. (2001).
  Application of quantitative chemometric analysis techniques to direct sampling mass spectrometry. Analytical Chemistry, 73, 596-605.
  This paper explores the use of direct sampling mass spectrometry coupled with multivariate chemometric analysis techniques for the analysis of sample mixtures containing analytes with similar mass spectra, Water samples containing varying mixtures of toluene, ethyl benzene, and cumene were analyzed by purge-and-trap/direct sampling mass spectrometry. Multivariate calibration models were built using partial least-squares regression (PLS), trilinear partial least-squares regression (tri-PLS), and parallel factor analysis (PARAFAC), with the latter two methods taking advantage of the differences in the temporal profiles of the analytes. The prediction errors for each model were compared to those obtained with simple univariate regression. Multivariate quantitative methods were found to be superior to univariate regression when a unique ion for quantitation could not be found. For prediction samples that contained unmodeled, interfering compounds, PARAFAC outperformed the other analysis methods. The uniqueness of the PARAFAC model allows for estimation of the mass spectra of the interfering compounds, which can be subsequently identified via visual inspection or a library search.

• Gargallo, R., Tauler, R., Sanchez, F., & Massart, D. L. (1996).
  Validation of alternating least-squares multivariate curve resolution for chromatographic resolution and quantitation. Trac-Trends in Analytical Chemistry, 15, 279-286.
  The application of multivariate curve resolution using the alternating least-squares (ALS) method for the resolution and quantitation of mixtures of two co-eluted compounds is validated for hydrocortisone (main compound) and prednisone(impurity) in liquid chromatography with diode array detection. The recovery of the spectra of the co-eluted compounds and their quantitation are discussed in relation to the initial estimates provided by evolving factor analysis and SIMPLISMA methods. Quantitation errors below 1.5% have been obtained for the main compound for resolution values of 0.4 or above, and impurity concentrations in the range 0.5-20%.

  
         

• Geladi, P. (1989).
  Analysis of multi-way (multi-mode) data. Chemometrics and Intelligent Laboratory Systems 7, 11-30.
  The concepts data matrix and multivariate data analysis are rapidly becoming popular and well-known words in chemistry. Many methods used in the laboratory can produce data arrays of a greater complexity than the data matrix. The broad picture easily gets lost here, not least because of the need for systematization and generalization.

• Geladi, P. (1992a).
  Some special topics in multivariate image-analysis. Chemometrics and Intelligent Laboratory Systems, 14, 375-390.
  Methods for multivariate image analysis are based on the definition of the multivariate image as a stack of congruent images collected for different variables (wavelengths). The article describes theories and three different types of examples for analysis when the images available are not congruent. This requires transformation to a common base used to construct a multivariate image. After that, a multivariate analysis can be carried out and the loading plots can be used for exploratory analysis and classification. Two new strategies are introduced: one for comparing within a set of noncongruent univariate images and one for comparing within a set of multivariate images.

• Geladi, P. (1995).
  Sampling and Local Models for Multivriate Image Analysis. Mikrochimica Acta120, 211-230.
  Local models are a very important concept for microscopic and macroscopic imaging. Different methods of sub-sampling a multivariate image are described both in general and for three examples. The need for sub-sampling and its influence on multivariate image analysis and visualization are studied. Examples from MRI (256×256), satellite imaging (7 × 512 × 512) and biofuel studies (6 × 512 × 512)are used to illustrate som of the principles involved.

  

• Geladi, P., & Aberg, P. (2001).
  Three-way modelling of a batch organic synthesis process monitored by near infrared spectroscopy. Journal of Near Infrared Spectroscopy, 9, 1-9.
  Multivariate monitoring by near infrared (NIR) spectroscopy of an organic synthesis as a batch process gives three-way data of the type batch number x NIR wavelength x time, The data can be analysed by three-way decomposition methods such as parallel factor analysis (PARAFAC). The batch process is the synthesis of an ester carried out by students in the laboratory. The synthesis is monitored by fibre-optic probe NIR measurement every ten minutes. The NIR spectra obtained have no distinct peaks and simply doing curve resolution on them is very difficult, but it is shown that pretreatment of the NIR spectra can lead to a good PARAFAC model and a chemical interpretation of the unique loadings obtained. The interpretation of the spectral loadings is carried out by comparison with pure chemical spectra. The data set is available from the authors.

• Geladi, P., Bergner, H. & Ringqvist, L. (2000).
  From experimental design to images to particle size histograms to multiway analysis. An example of peat dewatering. Journal of Chemometrics, 14, 197-211.
  The efficiency of peat dewatering by filtering slurries is dependent on the sizes of fine and colloidal particles that clog the filter. A designed experiment was carried out to check the use of different treatments on particle coagulation. The resulting particle sizes were studied under the microscope by automated digital image analysis, leading to area histograms for 21 size classes. Seven treatments on five peat types give a two-way ANOVA in all-qualitative variables, but the 21 response variables are a bit too much for an ANOVA or MANOVA analysis. The data can also be arranged in a 5 (peat types) x 7 (treatments) x 21 (size classes) three-way array. This array is analyzed by parafac and gives an effective three-way rank of 4. The three-way data have no obvious underlying trilinear structure, and curve resolution results are not expected. The three-way analysis gives a very parsimonious model that is easily interpreted as a function of the problem definition. The emphasis is on visualization of the results.

• Geladi, P., & Forsstrom, J. (2002).
  Monitoring, of a batch organic synthesis by near-infrared spectroscopy: modeling and interpretation of three-way data Journal of Chemometrics, 329-338.
  Three-way data of the type batch x time x NIR wavelength were obtained by NIR spectroscopic multivariate monitoring of an organic synthesis as a batch process. The model synthesis, an ester synthesis, was carried out as an experimental design. Unexpected technical problems caused a blocking effect that forced a modification of the design. After preprocessing of a reduced three-way array, the spectral data in the three-way array were subjected to parallel factor analysis (PARAFAC). The loadings from this analysis could be interpreted and explained as a function of the synthesis studied. For the spectral interpretation, spectra of pure chemicals were needed. The paper is an illustration of what can be done with three-way modeling in order to increase the understanding of a reaction, and it attempts to show how the results can be interpreted and presented. The data sets are available from the authors.

• Geladi, P., Bengtsson, E., Esbensen, K., & Grahn, H. (1992b).
  Image-analysis in chemistry. I. Properties of images, graylevel operations, the multivariate image. Trac-Trends in Analytical Chemistry, 11, 41-53.
  The use of imaging and images in chemical and technological applications is treated in two parts. Part I focuses on the generation and properties of images. The result of image registration is an analog or digital image, a representation of intensities as a function of position coordinates x, y (and sometimes also z) in a non-homogeneous material. Certain univariate operations for reducing noise and errors, improving contrast, measuring and counting particles etc. can be carried out on digitized images. A simple example from bioenergy research is given. In this first part a multivariate image is defined and an explanation is given of how it can be obtained. Operations on multivariate images and interpretations of multivariate results are presented in part II.

• Geladi, P., Grahn, H., Esbensen, K., & Bengtsson, E. (1992c).
  Image-analysis in chemistry. II. Multivariate image-analysis. Trac-Trends in Analytical Chemistry, 11, 121-130.
  Part I [Trends Anal. Chem., 11 (1992) 41] focused on the generation of univariate digital images in the chemical laboratory and in industrial situations and on the possible use of operations on univariate images. The concept of a multivariate image was introduced and an example given. This part focuses on the use of multivariate methods to extract problem-dependent, useful information from multivariate images. The example of the powder mixtures given in Part I is further analyzed by principal component analysis. Concepts of exploratory analysis, classification and regression are explained. The use of visual interpretation and statistical diagnostics is emphasized. Ideas about future developments of multivariate image analysis are introduced.

• Geladi, P., Manley, M.& Lestander, T. (2003)
  Scatter plotting in multivariate data analysis Journal of Chemometrics, 17 503-511.
  In data analysis, many situations arise where plotting and visualization are helpful or an absolute requirement for understanding. There are many techniques of plotting data/parameters/residuals. These have to be understood and visualization has to be made clearly and interpreted correctly. In this paper the classical favourites in chemometrics, scatter plots, are looked into more deeply and some criticism based on recent literature references is formulated for situations of principal component analysis, PARAFAC three-way analysis and regression by partial least squares. Biplots are also afforded some attention. Examples from near-infrared spectroscopy are given as illustrations. Copyright (C) 2003 John Wiley Sons, Ltd.

• Geladi, P.,Swerts, J. & Lindgren, F. (1994).
  Multiwavelength microscopic image analysis of a piece of painted chinaware: classification and regression. Chemometrics and Intelligent Laboratory Systems, 24, 145-167.
  A multivariate microscopic study of a piece of painted china poreclain is undertaken by image analysis. The object has archeological and artistic value and therefore a detailed study may be worthwhile. The use of multivariate image analysis intends the exploration of the artefact (artistic object) in more spectral and spatial detail than by just visual inspection. The study is used as a means of introducing and further exploring the different aspects of multivariate image analysis. The goal of the paper is twofold: (1) showing how the multivariate image is constructed and analyzed and (2) using some of the obtained results to introduce and further expand some of the techniques of multivariate image analysis. The example image has a size of 6 x 512 x 512. Classifications by feature space segmentation and by regression are shown to be useful and objective methods of acquiring insight in measurement errors and in the artistic detail of the painting. Some new concepts for multivariate analysis are introduced. One of them is related to the comparison of regression models.

• Geladi, P., Sethson, B., Nystrom, J., Lillhonga, T., Lestander, T. & Burger, J. (2004).
  Chemometrics in spectroscopy - Part 2: Examples. Spectrochemica Acta Part B- Atomic Spectroscopy, 59 1347-1357.
  Some of the principles and main methods of chemometrics are illustrated by examples. The examples ate from electrochemistry, process analytical chemistry and multivariate imaging. Principal component analysis, partial least squares regression and multivariate image analysis are used to illustrate the power of chemometrical thinking. The emphasis is on plotting and visualization for showing the salient features of a model or data set.

• Geladi, P., Xie, Y. L., & Hopke, P. (1998).
  Regression on parameters from three-way decomposition. Journal of Chemometrics, 12 337-354.
  This paper presents work on the combination of (a) environmental chemistry, (b) three-way analysis by Parafac constrained to non-negative results and (c) multivariate calibration. For two different environmental examples it is shown how the loading parameters from an independent three-way analysis can be used in a regression against external data. This combination leads to an easier interpretation of the results. The data are from Arctic aerosol studies. The subjectively obtained Parafac loadings are regressed against temperature anomalies.

• Gemperline, P.J., Rulifson, R.A., & Paramore, L. (2002).
  Multi-way analysis of trace elements in fish otoliths to track migratory patterns. Chemometrics and Intelligent Laboratory Systems, 60, 135-146.
  Spawning striped bass in the Shubenacadie watershed of Nova Scotia, Canada exhibit three dorsal coloration patterns: green, indicative of fish from the ocean; black, indicative of fish that overwinter in a fresh headwater lake, and mottled fish of unknown origin. Microchemical analysis of growth rings in fish otoliths (calcareous particles found in the inner car of certain lower vertebrates), measured by laser ablation-inductively coupled plasma/mass spectrometry (LA-ICP/MS), from fish captured during the 1999 Shubenacadie spawning period were analyzed by Tucker-3 multi-way principal component models. Using this technique, multidimensional patterns were discovered in the trace element measurements indicating that migratory patterns of individual striped bass can be tracked from the time-dependent trace element record deposited in the otoliths. Of the nine fish analyzed by LA-ICP/MS, trace element composition at year 0 suggested that all nine fish originated from the same locale. Differentiation in the trace element record was observed in subsequent years. Clustering of the trace element data for six fish unambiguously coincided with dorsal coloration. The three remaining fish exhibited trace element patterns that suggested migration between freshwater and marine conditions at one or more periods during life.

• Geng, C., & Mooshammer, C. (2000).
  Modeling the German stress distinction. In Proceedings of the Fifth Seminar on Speech Production: Models and Data (pp. 161-164). Kloster Seeon Germany, 1-4 May.
  Low dimensional and speaker-independent linear vocal tract parametrications can be obtained using the 3-mode PARAFAC factor analysis procedure first introduced by Harshman et al. (1977). The following study used PARAFAC to investigate the stress distinction in German vowel production. Tongue movements of six German speakers were recorded by means of EMMA. The data was entered into the classical PARAFAC1 model treating the stress distinction for each subject as two different speakers. This gave a reasonable 2-factor solution, but was not without drawbacks. The model turned out to be capable of recovering gross anatomical properties of our subjects, but failed to return intraindividual differences in tongue shapes with respect to word stress. This indicated that the strict linearity assumptions required in the classical PARAFAC model were too strong to capture stress specific variation in full detail. We supposed that a model closely related to PARAFAC, PARAFAC2, should allow to account for systematic variation produced by word stress by imposing weaker structure on the data. As will be shown, PARAFAC2 modeled the physical properties of the vocal tract shape in a more realistic and plausible way.

• Gensch, D. H., & Javalgi, R. G. (1988).
  Issues and advances in product positioning models in marketing-research. Mathematical and Computer Modelling, 10, 929-949.
  Mathematical models used for product positioning are proliferating at a rapid rate. To provide a structure to this research, we have categorized the models/algorithms into three basic approaches: utility functions, maps and trees. In this article we identify and discuss the recent advances related to these approaches, discuss data requirements and indicate issues that influence that choice of the particular product positioning approach best-suited for various situations.

• Gervini, D., & Rousson, V. (2004).
  Criteria for evaluating dimension-reducing components for multivariate data. American Statistician, 58, 72-76.
  Principal components are the benchmark for linear dimension reduction, but they are not always easy to interpret. For this reason, some alternatives have been proposed in recent years. These methods produce components that, unlike principal components, are correlated and/or have nonorthogonal loadings. This article shows that the criteria commonly used to evaluate principal components are not adequate for evaluating such alternatives, and proposes two new criteria that are more suitable for this purpose.

  
         

• Gimeno, R. A., Beltran, J. L., Marce, R. M., & Borrul, F. (2000).
  Determination of naphthalenesulfonates in water by on-line ion-pair solid-phase extraction and ion-pair liquid chromatography with fast-scanning fluorescence detection. Journal of Chromatography A, 890, 289-294.
  A fast analytical method for quantifying a mixture of 12 naphthalenesulfonates and naphthalenedisulfonates has been developed. This method consists of on-line ion-pair solid-phase extraction with PLRP-s sorbent and ion-pair liquid-chromatography using fast-scanning fluorescence spectrometer as a detection system and multivariate calibration. As complete separation is unnecessary, the compounds were analysed in isocratic conditions and the chromatographic analysis took only 25 min. Three-way partial least-squares (PLS) was used to carry out multivariate calibration for spiked tap water. in these conditions, quantification limits were between 0.01 and 3 mu g l(-1). Repeatability was also evaluated and relative standard deviations (n = 3) were between 0.5 and 4, depending on the compound. Finally, spiked tap and Ebro river waters were analysed to evaluate prediction capability of the method.

• Giordani, P., & Kiers, H. A. L. (2004).
  Three-way component analysis of interval-valued data. Journal of Chemometrics, 18, 253-264.
  Vertices Principal Component Analysis (V-PCA) and Centers Principal Component Analysis (C-PCA) are variants of Principal Component Analysis (PCA) to deal with two-way interval-valued data. In this case the observation units are represented as hyperrectangles instead of points. Tucker3 and CANDECOMP/PARAFAC are component analysis techniques to analyze the underlying structure of three-way data sets. In the present paper, after recalling the above mentioned methods, we extend the C-PCA and V-PCA methods to deal with three-way interval-valued data by means of Tucker3 and CANDECOMP/PARAFAC and we describe how to represent the observation units in the obtained low-dimensional space. Furthermore, an application of the extended methods—called Three-way Vertices Principal Component Analysis (3V-PCA) and Three-way Centers Principal Component Analysis (3C-PCA)—to three-way interval-valued air pollution data is described.

• Gitin, S.R. (1970).
  A dimensional analysis of manual expression. Journal of Personality and Social Psychology, 15, 271- 277.
  T3 was performed to investigate 78 subjects' ratings of 36 photographs of manual expressions on 40 semantic-differential- type scales. The expression on scale configurations were varimax rotated, but the core matrix (= 1 core plane) is given for the unrotated components. It shows a nice 'simple' (diagonal) structure.

• Gilbert, D.A., Sutherland, M., & Kroonenberg, P.M. (2000).
  Exploring subject-related interactions in repeated measures data using three- mode principal components analysis. Nursing Research, 49, 57- 61.
  In this paper a case is made for analyzing subject-related interactions in repeated measures data in some detail rather than stopping at significance tests. In particular, such interactions can be usefully modeled with multiplicative models, and three-way interactions with three-mode principal component models. The proposal is illustrated with data on the judgments of relational communication by nurses.

  
       

• Glasbey, C. A., & Glidewell, S. M. (2001).
  The application of multivariate statistical methods to NMR imaging. Computers and Electronicx in Agriculture, 32, 85-100.
  Statistical methods are used to integrate the information content in multivariate NMR images which had been obtained using different instrumental settings. Empirical and mechanistic models of multivariate pixel values are compared, making use of a novel reparametrisation of the mechanistic parameters to improve numerical stability. A new approach is presented to integrating the information using colour image displays. Projection pursuit is used to identify optimal instrumental settings in synthetic images, Methods are illustrated using seven cross-sectional NMR microscopy images of a blackberry, which was chosen as typical of Fruit specimens with hard tissue distributed in a soft matrix.

       

• Goodchild, M. F., Klinkenberg, B., & Janelle D. G. (1993).
  A factorial model of aggregate spetiotemporal behavior - application to the diurnal cycle. Geographical Analysis, 25, 277-294.
  The cross-sectional nature of much social data, coupled with the static view provided by maps and current spatial data handling software, have produced a tradition of research on urban spatial structure that is largely two-dimensional and derived from residential locations. The paper presents an analysis of a space-time diary data set collected in Halifax, Nova Scotia. A series of transformations are used to convert the individual diary records to a three-mode matrix of intensities, which is then analyzed using the PARAFAC three- mode factor model Home / work is found to be the strongest organizing dimension of the urban space-time, followed by entertainment, shopping, and education / work. We show how these dimensions appear to varying degrees in different locations, time periods, and human activities. The paper argues for a dynamic view of urban spatial structure in which only the physical facilities remain static.

• Gower, J.C. (1975).
  Generalised Procrustes analysis. Psychometrika, 40, 33-51.
  Suppose P_j⁽ⁱ⁾ (i = 1, 2, ... , m, j = 1, 2, ... , n) give the locations of mn points in p-dimensional space. Collectively these may be regarded as m configurations, or scalings, each of n points in p-dimensions. The problem is investigated of translating, rotating, reflecting and scaling the m configurations to minimize the goodness-of-fit criterion Sigma_i=1^m Sigma_j=1ⁿ Delta² (P_j⁽ⁱ⁾ G_j), where G_j is the centroid of the m points P_j⁽ⁱ⁾ (i = 1, 2, ..., m). The rotated positions of each configuration may be regarded as individual analyses with the centroid configuration representing a consensus, and this relationship with individual scaling analysis is discussed. A computational technique is given, the results of which can be summarized in analysis of variance form. The special case m = 2 corresponds to Classical Procrustes analysis but the choice of criterion that fits each configuration to the common centroid configuration avoids difficulties that arise when one set is fitted to the other, regarded as fixed.

• Gower, J.C. (1977).
  The analysis of three-way grids. In P. Slater (Ed.), Dimensions of Interpersonal Space (pp. 163-173). New York: Wiley.
  To analyse three-way data a set of models are proposed within the analysis of variance context. In particular, different ways are given to decompose the residuals after the main effects have been removed. Introducing two-way interactions leads to tractable solutions of uncertain convergence speed, but the inclusion of three- way interaction terms introduced difficulties to which no solutions were found. The position of INDSCAL within this framework is discussed.

• Gower, J.C. (1984).
  Multidimensional scaling displays. In H.G. Law, C. W. Snyder Jr, J. A. Hattie & R. P. McDonald (Eds.), Research methods for multimode data analysis (pp. 592-601). New York: Praeger.
  Graphical displays for various forms of three-mode multidimensional scaling may appear quite varied, but analysis shows that they are made up from a few basic geometrical ideas. This paper attempts to uncover these basic displays - each of which is usually appropriate to two-mode forms of analysis - and shows how they may be combined to give three-mode displays. With multidimensional scaling, like other multivariate methods, the most natural graphical displays directly reflect the properties of the algebraic form of the model fitted. Thus, when a distance matrix is fitted to data by multidimensional scaling, its simplest representation is by a set of points such that the distance between them is, or is proportional to their similarity. With an inner-product model, it is natural to plot vectors and the angle between pairs of vectors together with their lengths is the geometrical property used for interpretation. Both distances and inner-products generate symmetric matrices. These basic plotting devices are discussed in more detail in the article. The plots associated with three-mode arrays usually combine elements of the basic two-dimensional displays. From the above remarks, it should be clear that the form of plotting used cannot be entirely divorced from considerations of the model fitted.

• Gower, J.C. & De Rooij, M. (2003).
  A Comparison of th Multidimensional Scaling of Triadic and Dyadic Distances. Journal of Classification, 20, 115-136.
  We examine the use of triadic distances as a basis for multidimensional scaling (MDS). The MDS of triadic distances (MDS3) and a conventional MDS of dyadic distances (MDS2) both give Euclidean representations. Our analysis suggests that MDS2and MDS3 can be expected to give very similar results, and this is strongly supported by numerical examples. We have concentrated on the perimeter and generalized Euclidean models of triadic distances, both of which are linear transformations of dyadic distances and so might be suspected of explaining our findings: however an MDS3 of the nonlinear variance definition of triadic distance also closely approximated the MDS2 representation. An appendix gives some matrix results that we have found useful and also gives matrix representations and alternative derivations of some known properties of triadic distances.

  
       

• Grahn, H. F., & Saaf, J. (1992).
  Multivariate image regression and analysis - useful techniques for the evaluation of clinical magnetic-resonance image. Chemometrics and Intelligent Laboratory Systems, 14, 391-396.
  Multivariate image analysis (MIA) and multivariate image regression (MIR) techniques are useful tools in the extraction of information from magnetic resonance images. They aid the characterization of different tissues and can be used to describe their size and distribution. The obtained new information can be used to monitor growth, progression and effects of a treatment. The methodology is illustrated by a clinical example. The ongoing development of MIA and MIR, combining parameters from different imaging modalities, is commented on.

• Gräser, H. (1977).
  Spontane Reversionsprozesse in der Figuralwahrnehmung. Eine Untersuchung reversibler Figuren mit der Dreimodalen Faktorenanalyse (doctoral thesis). Trier, FRG: author.
  The reversion rate for 46 reversible figure of 133 subjects was determined at 15 time points. T3 as described by Bartussek (1973) was used; all factor matrices were rotated by various methods. Two different standardizations of the data were used; the merits of both are discussed. Reification with external criteria. Extended core matrices were derived by premultiplying the core matrix with component matrices. Interpretation of change factors in T3 is discussed. Includes an Appendix with a program description for T3.

• Gräser, H., Esser, H. & Saile, H. (1981).
  Einschätzung von Lebensereignissen und ihren Auswirkungen. In S.-H. Filipp (Ed.) Kritische Lebensereignisse und ihre Bewältigung (pp. 104-122). München, FRG: Urban & Schwarzenberg.
  In one of two reported studies on the perception of life events 91 subjects scored 20 life events on 19 sentiments and characteristics. The 18 scales were standardized over subjects and events. Events and scales were varimaxed, and the subjects were obliquely rotated. The core matrix, multiple regression and discriminent analysis on external variables were used to aid the interpretation of the subjects.

  

• Gredelj, S., Gerson, A.R., Kumar, S., & Cavallaro, G.P. (2001).
  Characterization of aluminium surfaces with and without plasma nitriding by X-ray photoelectron spectroscopy. Appliec Surface Science, 174, 240-250.
  Substrates of aluminium alloy 2011 have been plasma nitrided using an inductively coupled plasma source and then characterised by X-ray diffraction (XRD) and X-ray photoelectron spectroscopy (XPS). The XRD analysis confirmed the presence of a crystalline aluminium nitride (AlN) layer on the substrates surfaces. Both AlN and Al2O3 were observed by XPS on the surface of the nitrided Al substrates. The binding energy (BE) of the C 1s photoelectron of adventitious hydrocarbon was found to be dependent on the thickness of the insulating AlN/Al2O3 surface layer. None of the Al 2p, N 1s or O 1s BEs showed any shifts due to surface charge build up. The BE values of the Al 2p photoelectron for AlN, Al2O3 and metallic Al were determined to be 74.5, 75.5 and 72.7 eV, respectively. The charge shifting of the BEs of all the photoelectrons occurs simultaneously only for oxidised Al substrates (not nitrided) with a sufficiently thick oxidised surface layer. For a thinner oxidised surface layer the adventitious hydrocarbon C 1s photoelectron BE still shows charge shifting but this is not reflected in the BE of the Al 2p and O 1s XPS components.

• Green, P.E., Carmone, F.J., & Wachspress, D.P. (1976).
  Consumer segmentation via latent class analysis. Journal of Consumer Research, 3, 170-174.
  A nontechnical description of latent class analysis and a discussion of the CANDECOMP procedure and its application to consumer adoption of a new telecommunications service is presented with some suggestions for other areas in consumer and market research wheer latent class analysis might be of use.

• Green, P. E., & Devita, M. T. (1974).
  A complementarity model of consumer utility for item collections. Journal of Consumer Research, 1, 56-67.
  A model is developed that portrays certain types of interactions as well as main effects in consumer evaluation tasks. The model is illustrated with menu preference data and its potential use in other types of multi-attribhute choice situations is described.

• Groenen, P. J. F., Van Os, B. J., & Meulman, J. J. (2000).
  Optimal scaling by alternating length-constrained nonnegative least squares, with application to distance-based analysis. Psychometrika, 65, 511-524.
  An important feature of distance-based principal components analysis, is that the variables can be optimally transformed. For monotone spline transformation, a nonnegative least-squares problem with a length constraint has to be solved in each iteration. As an alternative algorithm to Lawson and Hanson (1974), we propose the Alternating Length-Constrained Non-Negative Least-Squares (ALC-NNLS) algorithm, which minimizes the nonnegative least-squares loss function over the parameters under a length constraint, by alternatingly minimizing over one parameter while keeping the others fixed. Several properties of the new algorithm are discussed. A Monte Carlo study is presented which shows that for most cases in distance-based principal components analysis, ALC-NNLS performs as good as the method of Lawson and Hanson or sometimes even better in terms of the quality of the solution.

• Grotti, M. (2004).
  Improving the analytical performances of inductively coupled plasma optical emission spectrometry by multivariate analysis techniques. Annali Di Chimica, 94, 1-15.
  The various multivariate analysis techniques which have been successfully applied to maximize the analytical performances of ICP-OES are reviewed. These include optimization procedures, spectral data processing and calibration methods as well as classification and pattern recognition techniques.

• Grotti, M., Rivaro, P., Leardi, R., & Magi, E. (1999).
  Three-way principal component analysis as a powerful tool to process marine environmental data sets. Annali Di Chimica, 89, 591-600.
  A study of the marine ecosystem usually requires management of large and complex data sets. The multivariate technique "Three-way principal component analysis" has been applied to a relatively small set of oceanographic data. Sea water samples were collected during the Italian Antarctic Expedition 1994-95 and the following parameters were considered: sea water temperature and salinity, dissolved oxygen, nutrients (silicate, phosphate, nitrate plus nitrite) and phytoplanktonic pigments (total chlorophyll, chlorophyll a, phaeopigments, carotenoids). The resulting plots confirmed in a self-explanatory way some well-known assumptions, thus showing that "Three-way Principal Component Analysis" is a powerful instrument for the interpretation of marine environmental data sets.

• Groves, C.L. (1978).
  Individual difference modelling of simple functional relations: Examples using three-mode factor analysis. Dissertation Abstracts International, 39 (5-B), 2475-2476.
  Simulated fallible data were used to examine the influence of several types of error on the ability of three-mode factor analysis to recover both the stimulus differences in simple functional relations data and the individual differences. Experimental data pertaining to the size-weight illusion were examined.
  
• Grung, B., & Kvalheim, O.M. (1995a).
  Detection and quantification of embedded minor analytes in three-way multicomponent profiles by evolving projections and internal rank annihilation. Chemometrics and Intelligent Laboratory Systems, 29, 213-221.
  Modern analytical instrumentation often leads to data arrays with more than two dimensions or directions. Such N-way data (N > 2) needs special resolution methods for optimising the amount of analytical information. In this work, a new interactive method designed to work with three-way data is presented. The method, evolving projections by optimised search (EPOS), presents a combined graphical and numerical way of resolving a three-way data array into the analytical profiles of the pure analytes. The method involves an internal rank annihilation step which can be performed in several ways. The graphic interactive procedure used in this work compares favourably with Lorber's noniterative rank annihilation method. Thus, our method is significantly better for resolution of analytes with low relative concentration, especially in the presence of heteroscedastic noise. The EPOS method is tested on several simulated data sets to assess its performance. A peak purity example is carried out to show a case where two-way methods are unable to provide a unique solution, whereas EPOS gives correct results.

• Grung, B., & Kvalheim, O.M. (1995b).
  Rank mapping of three-way multicomponent profiles. Chemometrics and Ingelligent Laboratory Systems, 29, 223-232.
  In this work, fast graphic procedures for assessment of number of analytes (chemical rank) in local regions of three-way unresolved multicomponent profiles are presented. Collapsing the three-way profile along one direction by matrix summation and evolving rank analysis on the resulting matrix represents a first step for the approach developed here. This procedure is efficient for detecting analytes with low net analytical signal compared to the noise level. The effect of collapsing is a reduction of random noise due to cancellations, while structure from analytes is enhanced because of the additive effect of many similar contributions. In the second step, slicing of the three-way data array into complete two- way arrays (matrices) is performed. Projections are then used across these matrices to generate a rank map. The strategy developed in this work provides a rapid approach to rank analysis and permits the analyst to take into account that the analytical information is normally not uniformly distributed in the three directions.

• Gruvaeus, G., Wainer, H., & Snyder, F. (1971).
  TREMOD: A 360/75 FORTRAN program for three-mode factor analysis. Behavioral Science, 16, 421-422.
  Description of Tucker's three-mode factor analysis.

  
       

• Gui, M., Rutan, S.C., & Agbodjan, A. (1995).
  Kinetic detection of overlapped amino acids in thin-layer chromatography with a direct trilinear decomposition method. Analytical Chemistry, 67, 3293-3299.
  Kinetic fluorescence detection (KFD) was employed to determine the concentrations of two overlapped components after a thin-layer chromatographic (TLC) separation. Two amino acids, glycine and glutamine, were used as model analytes. These species exhibited very similar retardation factors (R_f) under our experimental conditions. A reaction that produced a fluorescent product was performed subsequent to the separation, the reaction can be described by the following scheme: Amino acid + OPA --> fluorescent product --> nonfluorescent product. Here OPA stands for o-phthalaldehyde. The kinetic profile of the reaction was monitored with a charge-coupled device camera by taking sequential images of the separation medium after the reaction starts. a direct. Trilinear decomposition (TLD) method was used to analyze the resulting third-order data that consist of fluorescence intensities as a function of elution distance, reaction time, and sample number, this approach was used to determine the initial concentrations of the two overlapped components based on the different kinetics and retention exhibited by these species. This paper discusses the kinetic approach and the applicability and limitations of the direct trilinear decomposition (TLD) method using both synthetic and experimental data, efforts to optimize the experimental conditions are also reported. The major focus of this work is to explore the application of this novel kinetic fluorescence detection method for TLC separations (TLC-KFD) combined with the TLD data analysis method.

• Guimet, F., Ferre, J., Boque, R., & Rius, F. X. (2004).
  Application of unfold principal component analysis and parallel factor analysis to the exploratory analysis of olive oils by means of excitation-emission matrix fluorscence spectroscopy. Analytical Chemistry, 515, 78-85.
  Discrimination between virgin olive oils and pure olive oils is of primary importance for controlling adulterations. Here, we show the potential usefulness of two multiway methods, unfold principal component analysis (U-PCA) and parallel factor analysis (PARAFAC), for the exploratory analysis of the two types of oils. We applied both methods to the excitation-emission fluorescence matrices (EEM) of olive oils and then compared the results with the ones obtained by multivariate principal component analysis (PCA) based on a fluorescence spectrum recorded at only one excitation wavelength. For U-PCA and PARAFAC, the ranges studied were lambda(ex) = 300-400nm, lambda(em) = 400-695 nm and lambda(ex) = 300-400 nm, lambda(em) = 400-600 nm. The first range contained chlorophylls, whose peak was much more intense than those of the rest of species. The second range did not contain the chlorophylls peak but only the fluorescence spectra of the remaining compounds (oxidation products and Vitamin E). The three-component PARAFAC model on the second range was found to be the most interpretable. With this model, we could distinguish well between the two groups of oils and we could find the underlying fluorescent spectra of three families of compounds.

• Guiteras, J., Beltran, J. L., & Ferrer, R. (1998).
  Quantitative multicomponent analysis of polycyclic aromatic hydrocarbons in water samples. Analytica Chimica Acta, 361, 233-240.
  A comparative study between three different multivariate calibration methods, classical least squares (CLS), principal component regression (PCR) and partial least squares regression (PLSR) was carried out. The calibration models for all three methods were obtained from a combination of two synchronous fluorescence spectra (recorded at 50 and 100 nm wavelength increments) for each standard of a calibration set of 70 standards, each containing ten polycyclic aromatic hydrocarbons (anthracene, benz[a]anthracene, benzo[a]pyrene, chrysene, fluoranthene, fluorene, naphthalene, perylene, phenanthrene and pyrene). The predictions of the model were compared with the relative root mean squared difference (RRMSD) obtained from the results of an external validation set, formed by 15 independent mixtures. Finally, the PLSR and PCR models were used for the determination of the above mentioned PAHs in spiked natural water samples at concentration levels between 4 and 20 ng ml(-1). Recoveries ranged from 80 to 120% in most cases, although fluorene gave significantly lower results.

• Gurden, S. P., Lage, E. M., de Faria, C. G., Joekes, I., & Ferreira, M. M. C. (2003).
  Analysis of video images from a gas-liquid transfer experiment: a comparison of PCA and PARAFAC for multivariate image analysis. Journal of Chemometrics, 17, 400-412.
  The use of chemical imaging is a developing area which has potential benefits for chemical systems where spatial distribution is important. Examples include processes in which homogeneity is critical, such as polymerizations, pharmaceutical powder blending and surface catalysis, and dynamic processes such as the study of diffusion rates or the transport of environmental pollutants. Whilst single images can be used to determine chemical distribution patterns at a given point in time, dynamic processes can be studied using a sequence of images measured at regular time intervals, i.e. a movie. Multivariate modeling of image data can help to provide insight into the important chemical factors present. However, many issues of how best to apply these models remain unclear, especially when the data arrays involved have four or five different dimensions (height, width, wavelength, time, experiment number, etc.). In this paper we describe the analysis of video images recorded during an experiment to investigate the uptake Of CO2 across a free air-water interface. The use of PCA and PARAFAC for the analysis of both single images and movies is described and some differences and similarities are highlighted. Some other image transformation techniques, such as chemical mapping and histograms, are found to be useful both for pretreatment of the raw data and for dimensionality reduction of the data arrays prior to further modeling. Copyright (C) 2003 John Wiley Sons, Ltd.

• Gurden, S.P., Westerhuis, J.A., Bijlsma S., & Smilde, A.K. (2001).
  Modelling of spectroscopic batch process data using grey models to incorporate external information. Journal of Chemometrics, 15, 101-121.
  In both analytical and process chemistry, one common aim is to build models describing measured data. In cases where additional information about the chemical system is available, this can be incorporated into the model with the aim of improving model fit and interpretability. A model which consists of a 'hard' or 'white' part describing known sources of variation and a 'soft' or 'black' part describing unknown sources of variation is called a 'grey' model. In this paper the use of a grey model is demonstrated using data from a first- order chemical batch reaction monitored by UV-vis spectroscopy. The resultant three-way data matrix is modelled using a Tucker3 structure, and external information about the spectroscopically active compounds is incorporated in the form of constraints on the model parameters with additional restrictions on the Tucker3 core matrix. The grey model is then used to analyse new batches. Different approaches to building grey models are described and some of their properties discussed.

• Gurden, S.P., Westerhuis, J.A., Bro, R., & Smilde, A.K. (2001).
  A comparison of multiway regression and scaling methods. Chemometrics and Intelligent Laboratory Systems, 59, 121-136.
  Recent years have seen an increase in the number of regression problems for which the predictor and/or response arrays have orders higher than two, i.e. multiway data. Examples are found in, e.g. industrial batch process analysis, chemical calibration using second-order instrumentation and quantitative structure-activity relationships (QSAR). As these types of problems increase in complexity in terms of both the dimensions and the underlying structures of the data sets, the number of options with respect to different types of scaling and regression models also increases. In this article, three methods for multiway regression are compared: unfold partial least squares (PLS), multilinear PLS and multiway covariates regression (MCovR). All three methods differ either in the structural model imposed on the data or the way the model components are calculated. Three methods of scaling multiway arrays are also compared, along with the option of applying no scaling. Three data sets drawn from industrial processes are used in the comparison. The general conclusion is that the type of data and scaling used is more important than the type of regression model used in terms of predictive ability. The models do differ, however, in terms of interpretability.

• Gurden, S.P., Westerhuis, J.A., & Smilde, A.K. (2002).
  Monitoring of Batch Processes Using Spectroscopy American Institute of Chemical Engineers Journal, 48, 2283-2297.
  There is an increasing need for new techniques for the understanding, monitoring and the control of batch processes. Spectroscopy is now becoming established as a means of obtaining real-time, high-quality chemical information at frequent time intervals and across a wide range of industrial applications. In this article, the role of spectroscopy for batch process monitoring is discussed in terms of both current and potential advances. The emphasis is on how to handle the measured data to extract maximum information for improved process performance and efficiency. In particular, the use of spectroscopy for statistical proces monitoring is detailed and considered as complementary to the use of engineering process data. A case study of the ultraviolet-visible monitoring of a first-order biochemical conversion reaction is described, as well as the advantages of spectroscopy for process fault detection and diagnosis. Future prospects for the use of on-line spectroscopy are also discussed.

• Guterres, M. V., Volpe, P. O. L. & Ferreira, M. M. C. (2004).
  Multiwav calibration for creatinine determination in human serum using the Jaffe reaction Applied Spectroscopy, 58, 54-60. Second-order calibration and multivariate spectroscopic-kinetic measurements in the visible region are proposed to improve the Jaffe method for creatinine assay. Analyses performed on synthetic mixtures containing bilirubin, glucose, and albumin confirm that second-order calibration is useful for creatinine determination in human serum. Quantitative determinations of creatinine with the parallel factor analysis (PARAFAC) and direct trilinear decomposition (TLD) methods were compared. It is shown that both methods can be used for creatinine determination in human serum, with an SEP (squared error of prediction) of 2.22 and coefficient of variability of 6.14% for PARAFAC, and an SEP of 2.38 and coefficient of variability of 6.57 % for TLD.

• Gutmanas, A., Jarvoll, P., Orekhov, V. Y., & Billeter, M. (2002).
  Three-way decomposition of a complete 3D N-15-NOESY-HSQC. Journal of Biomolecular NMR, 24, 191-201.
  Three-way decomposition is applied for the structural analysis of a complete three-dimensional N-15-NOESY-HSQC of the 128 residues long protein azurin. The procedure presented includes decomposition using the software MUNIN, providing an initial characterization of the complete spectrum by 355 components. This is followed by post-processing yielding a final list of 149 components, 123 of which characterize 1859 NOE peaks from backbone N-H groups. Components from three-way decomposition are defined as direct products of one-dimensional shapes along the three dimensions. Thus, a complete set of distance constraints from this spectrum is obtained by one-dimensional peak picking of the shapes along the NOE dimension. Correctness and completeness of this set of NOEs are tested for all backbone amide groups against both an independent peak picking algorithm and the three-dimensional crystal structure of azurin, and a coincidence of about 95% is observed. Automated 'demixing' of components that are 'mixed' in a complex manner due to overlap of the HN and/or N-15 frequencies is illustrated.

           

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