Three-Mode Abstracts, Part S

INDEX

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• Saile, H. (1979).
  Zur Struktur der Einschätzung von Lebensereignissen. Eine Untersuching über Beurteilungsunterschiede mittels dreimodaler Faktorenanalyse. Unpublished master thesis: University of Trier, Trier, FRG.
  Partially reported in Gräser et al., 1981.

  

• Saldanha, T. C. B., De Araujo, M. C. U., & Neto, B. D. (1999).
  Simultaneous multicomponent analysis by UV-VIS spectrophotometry. Quimica Nova, 22, 847-853.
  This review presents the evolution of simultaneous multicomponent analysis by absorption spectrophotometry in the ultraviolet and visual regions in terms of some qualitative and quantitative analysis techniques, otimization methods, as well as applications and modern trends.

• Sanchez, E., & Kowalski, B.R. (1990).
  Tensorial resolution: A direct trilinear decomposition. Journal of Chemometrics, 4, 29-45.
  
  Trilinear arrays of data are known to have unique factor analysis decompositions which correspond to the true physical factors that form the data, such that a unique solution can be found in many cases for each order X, Y and Z. This is in contrast to the well-known second-order bilinear data factor analysis, where the abstract solutions obtained are not unique and at best cannot be easily compared with the underlying physical factors owing to a rotational ambiguity. This paper introduces a method for reducing the problem to a rectangular generalized eigenvalue-eigenvector equation where the eigenvectors are the contravariant form (pseudo-inverse) of the actual factors. It is shown that the method works well when the factors are linearly independent in at least two orders (e.g. X_ir and Y_jr are full rank matrices). Finally, it is shown how trilinear decompositions relate to multicomponent calibration, curve resolution and chemical analysis.

• Sands, R. & Young, F.W. (1980).
  Component models for three-way data: ALSCOMP3, an alternating least squares algorithm with optimal scaling features. Psychometrika, 45, 39-67.
  An alternating least squares (ALS) method is proposed for the weighted Euclidean (a three-mode three-way generalization of the two-mode three-way INDSCAL model) and for the replicated PCA model, where 'subjects' in the third mode are treated as replications. The data may be defined at various measurement levels with various measurement characteristics. It is the only method which allows for other than metric data. Compared with the other ALS methods (Lohmöller & Wold, 1980; Kroonenberg & De Leeuw, 1980) the treated models are somewhat less general. Illustrated with a Monte Carlo study, and data on perception of political figures and roles.

  

• Sanguineti, V., Laboissiere, R., & Payan, Y. (1997).
  A control model of human tongue movements in speech. Biological Cybernetics, 77, 11-22.**
  Tongue movements during speech production have been investigated by means of a simple yet realistic biomechanical model, based on a finite elements modeling of soft tissues, in the framework of the equilibrium point hypothesis (x-model) of motor control. In particular, the model has been applied to the estimation of the "central" control commands issued to the muscles, for a data set of mid-sagittal digitized tracings of vocal tract shape, recorded by means of low-intensity x-ray cineradiographies during speech. In spite of the highly non-linear mapping between the shape of the oral cavity and its acoustic consequences, the organization of control commands preserves the peculiar spatial organization of vowel phonemes in acoustic space. A factor analysis of control commands, which have been decomposed into independent or "orthogonal" muscle groups, has shown that, in spite of the great mobility of the tongue and the highly complex arrangement of tongue muscles, its movements can be explained in terms of the activation of a small number of independent muscle groups, each corresponding to an elementary or "primitive" movement. These results are consistent with the hypothesis that the tongue is controlled by a small number of independent "articulators", for which a precise biomechanical substrate is provided. The influence of the effect of jaw and hyoid movements on tongue equilibrium has also been evaluated, suggesting that the bony structures cannot be considered as a moving frame of reference, but, indeed, there may be a substantial interaction between them and the tongue, that may only be accounted for by a "global" model. The reported results also define a simple control model for the tongue and, in analogy with similar modelling studies, they suggest that, because of the peculiar geometrical arrangement of tongue muscles, the central nervous system (CNS) may not need a detailed representation of tongue mechanics but rather may make use of a relatively small number of muscle synergies, that are invariant over the whole space of tongue configurations.

• Sato, M. & Sato, Y. (1994).
  On a multicriteria fuzzy clustering method for 3-way data. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 2, 127-142.
  A fuzzy clustering procedure for three-mode data is presented in which a clustering need not be the same for attributes, so that it is a multicriteria optimisation problem. Practical solutions in this case are Pareto efficient, but non-fuzzy are difficult to find due to the combinatorial character in contrast with fuzzy clustering. Illustrated with artificial data and growth curves of physical characteristics of Japanese boys.

• Sato, M. & Sato, Y. (1997).
  Generalized fuzzy clustering model for 3-way data. In Proceedings of the International Conference on Fuzzy Logic (pp. 132-137). Zichron Yakov, Israel: Ministry of Science.
  A method of classification for longitudinal asymmetric 3-way data is proposed. A fuzzy clustering method is proposed for asymmetric similarity data by using asymmetric aggregation operators. The clustering need not be the same for attributes, so that it is a multicriteria optimisation problem. Practical solutions in this case are Pareto efficient, but non-fuzzy are difficult to find due to the combinatorial character in contrast with fuzzy clustering. Weights are introduced for each occasion to show the salience of each cluster.

• Sato-Ilic, M. & Sato, Y. (1998).
  A dynamic additive fuzzy clustering model. In A. Rizzi, M. Vichi, & H.-H. Bock (Eds.), Advances in data science and classification (pp. 117-124). Berlin: Springer.
  A dynamic clustering model is presented in which clusters are constructed in order to find the features of dynamic change. This is done by introducing the concepts of dynamic MDS and dynamic PCA into an additive clustering model.

• Saurina, J., Hernández-Cassou, S., & Tauler, R. (1995a).
  Continuous-flow titration system for the generation of multivariate spectrophotometric data in the study of acids-base equilibria. Analytica Chimica Acta, 312, 189-198.
  In the present work a continuous flow system to carry out spectrophotometric titrations is developed. The titrant solution is generated on-line from mixing two different stock buffer solutions. The composition of the titrant agent is sequentially varied along the titration by changing the ratio of flow rates of both buffer channels, and therefore the pH can be modified. One spectrum is recorded at each pH value when the absorbance achieves the steady state. The spectral data have been treated by means of a recently developed self-modelling multivariate curve resolution method (SPFAC procedure). This method has been applied to the study of the acid-base equilibria of 1,2-naphthoquinone-4-sulfonate (NQS). Four titrations with concentrations of NQS ranging from 1.6 X 10(-4) to 7.3 X 10(-4) M have been performed, and, in every case, 24 spectra at different pH have been registered. Three species are detected in the range of pH studied (6.9-12.3). Their distribution plot with pH and their unit spectrum have been obtained.

• Saurina, J., Hernández-Cassou, S., & Tauler, R. (1995b).
  Multivariate curve resolution applied to continuous-flow spectrophotometric titrations: reaction between amino-acids and 1,2-naphthoquinone-4-sulfonic acid. Analytical Chemistry, 67, 3722-3726.**
  A continuous-flow acid-base titration system has been developed for the study and analytical application of chemical reactions between amino acids and 1,2-naphthoquinone-4-sulfonate. For each titration, a set of spectra are obtained at pH values from 6.5 to 12.5. Multivariate curve resolution is applied to provide an optimal estimation of concentration and spectra profiles of the species formed during the chemical reaction. Resolution of these chemical species is greatly improved when several runs of different spectrophotometric titrations of the same chemical reaction system (multiple correlated data matrices) are analyzed simultaneously, allowing the quantitative determination of the concentration of amino acid that has reacted in each case.

• Saurina, J., Hernández, S. & Tauler, R. (1997).
  Multivariate curve resolution and trilinear decomposition methods in the analysis of stopped-flow kinetic data for binary amino acid mixtures. Analytical Chemistry, 69, 2329-2336.
  The kinetic development of the reaction between amino acids and 1,2-naphtoquinone-4-sulfonate (NQS) is carried out by a stopped-flow methodology. Each kinetic run was monitored spectrophotometrically by using a diode array detector, which produced a set of spectra registered at different times during the process. The resolution of the derivative species formed during the kinetic reaction by multivariate curve resolution and the quantitative determination of amino acids in unknown samples in the presence of interferences were studied by both constrained singular value decomposition (called ALS) and direct trilinear decomposition (TLD) in order to compare the ability of both methods in the resolution and quantification of such kinetic data. Because the trilinearity required for TLD was not completely fulfilled the ALS-based method outperformed TLD.

• Saurina, J., Hernández-Cassou, S., Tauler, R., & Izquierdo-Ridorsa, A. (1998).
  Multivariate resolution of rank-deficient spectrophotometric data from first-order kinetic decomposition reactions. Journal of Chemometrics, 12, 183-203.
  The effect of a rank deficiency upon curve resolution in simple kinetic reaction-based systems is studied. Firstly, simulated rank-deficient spectrophotometric data of a mixture of two reagents, each one yielding its own reaction product by a first-order kinetic reaction, are analysed. Four different situations are considered according to the differences in the spectral responses of the reaction constituents and to the differences in the rate constants between the two kinetic processes. A variation of the rate constant between runs for a certain kinetic process is also taken into account. Secondly, the resolution of a real rank-deficient data system, corresponding to the study of the pH-dependent decomposition of 1,2-naphthoquinone-4-sulphonate, is investigated. All these studies were carried out using a multivariate curve resolution method based on the alternating least squares optimization of the kinetic and spectral profiles of the species present in the system.

• Saurina, J., Hernández-Cassou, S., Tauler, R., & Izquierdo-Ridorsa, A. (1999a).
  Procedure for the quantitative determination of mixtures of nucleic acid components based on multivariate spectrophotometric acid-base titrations. Analytical Chemistry, 71, 126-134.
  A new procedure for the quantitative determination of mixtures of nucleic acid components, based on continuous spectrophotometric acid-base titrations and multivariate curve resolution, is proposed, The procedure simultaneously takes into account the spectroscopic and acid-base properties of the compounds, which leads to a higher selectivity. Furthermore, quantitative determination of an analyte in a complex mixture is performed using a synthetic solution as standard containing only the analyte of interest. An intrinsic difficulty in the analysis of spectrometric titration data is the presence of rank deficiency due to closure for the mixtures of two or more compounds. An additional problem can be encountered in some mixtures if species spectra or species concentration profiles are practically identical (rank overlap). However, even in the presence of these rank difficulties, accurate quantitation with prediction errors lower than 5% was obtained, The presence of unknown and uncalibrated interferences in the samples does not affect the quantitative determination of the analyte of interest. The proposed procedure was successfully applied to the analysis of real samples (pharmaceuticals) using synthetic external standards.

• Saurina, J., Hernández-Cassou, S., Tauler, R., & Izquierdo-Ridorsa, A. (1999b).
  Continuous-flow and flow injection pH gradients for spectrophotometric determinations of mixtures of nucleic acid components. Analytical Chemistry, 71, 2215-2220.
  A procedure for the rapid determination of mixtures of nucleic acid components from the analysis of spectrophotometric multivariate data obtained with continuous-flow and flow injection pH-gradient systems is proposed. Three flow systems have been developed and assayed in which an on-line pH gradient is generated from the mixing and controlled dispersion of acidic and basic titrant solutions. Quantitative determinations of any particular analyte in the unknown samples in the presence of interferences is performed with a single pure standard for this analyte. They are carried out using an alternating least squares multivariate curve resolution procedure. The methods proposed have been validated using synthetic and real sample mixtures. The results obtained are concordant with the labeled values, and the relative prediction errors are around 5%.

• Saurina, J. (2000a).
  Analytical application of pH-gradients in flow injection analysis and related techniques. Reviews in Analytical Chemistry, 19, 157-178.
  pH gradients in flow systems have proved useful for performing multiple analytical tasks. Although the reproducibility, sampling frequency and degree of automation makes these techniques highly attractive from an analytical point of view, data generated often suffer from poor selectivity. From a historical perspective, following their initial application at the end of the seventies, these methods fell into disuse as a consequence of interference problems. Today, the potentiality of pH-gradients has greatly increased, mainly in combination with mathematical procedures for data analysis addressed at improving the selectivity. This paper describes the existing systems for the generation of pH gradients and provides an overview of applications dealing with the study of pH-dependent processes, quantitative determinations and the calculation of stability constants. The characteristics, advantages and shortcomings of the different techniques are outlined. Furthermore, a number of examples developed in our working group are described in more detail.

• Saurina, J., Hernández-Cassou, S., Izquierdo-Ridorsa, A., & Tauler, R. (2000b).
  pH-Gradient spectrophotometric data files from flow-injection and continuous flow systems for two- and three-way data analysis. Chemometrics and Intelligent Laboratory Systems, 50, 263- 271.
  This paper describes a contribution to Chemometrics and Intelligent Laboratory Systems Elsevier's data base of files. Mixtures of nucleosides and a pharmaceutical preparation composed of cytosine and inosine-5'-monophosphate are analyzed using three different pH-gradient spectrophotometric flow-injection and continuous flow systems. Results for one of the flow-injection systems and for the continuous-flow system are reported for the first time in this paper. Resolution and quantitation of the constituents in the mixtures are given using a multivariate curve resolution method based on a constrained alternating least squares optimization.

• Saurina, J., Leal, C., Compano, R., Granados, M., Tauler, R. & Prat, M. D. (2000c).
  Determination of triphenyltin in sea-water by excitation-emission matrix fluorescence and multivariate curve resolution. Analytica Chimica Acta, 406, 237-245.
  A new method for the determination of triphenyltin (TPhT) in sea-water is proposed. The method is based on solid-phase extraction (SPE), reaction with flavonol in a Triton X-100 micellar medium to yield a fluorimetrically active derivative and excitation-emission fluorescence measurements. TPhT was quantified by an alternating least squares (ALS)-multivariate curve resolution (MCR) procedure and a single synthetic standard. In order to select the optimum conditions for the analysis, the procedure was assessed using synthetic samples. With the proposed method, TPhT was quantified in sea-water samples at low ng l(-1) level with an overall prediction error of around 12%.

  
     

• Schenone, A., Firenze, F., Acquarone, F., Gambaro, M., Masulli, F., & Andreucci, L. (1996).
  Segmentation of multivariate medical images via unsupervised clustering with ´adaptive resolution´. Computerized Medical Imaging and Graphics, 20, 119-129.
  The need for quantitative information is becoming increasingly important in the clinical field. In this paper we present an interactive X11 based system, devoted to segmentation of multivariate medical images, including an unsupervised neural network approach to clustering. The following steps are considered in the analysis sequence: feature extraction, reduction of dimensionality, unsupervised data clustering, voxel classification, interactive postprocessing refinement. The environment turns out to be extremely interactive, thus making the user able to display and modify data during processing, to set parameters, to choose different methods and different tools for each step, and to define online the whole analysis sequence.

• Schiffman, S.S., Reynolds, M.L., & Young, F.W. (1981).
  Introduction to multidimensional scaling. New York: Academic Press. (Review by P.M. Kroonenberg and W.A. van der Kloot, 1984).
  This book contains three parts:
  1. Foundations of MDS and data suitable for MDS.
  2. Methods and applications.
  3. Theory.
  The following models and algorithms for individual differences multidimensional scaling are presented: INDSCAL, ALSCAL, and MULTISCALE. Both program descriptions and illustrative applications are provided. Young, Carroll and Ramsay discuss the theory behind their own programs.

• Schmitt, N., Coyle, B.W. & Saari, B.B. (1977).
  A review and critique of analyses of multitrait-multimethod matrices. Multivariate Behavioral Research, 12, 447-478.
  T3 (Method III) is discussed as one of the techniques appropriate for multi-trait multi-method matrices. A small example constructed from the data of 310 persons being rated on 7 traits by 4 raters is used as illustration. The unrotated core matrix is nicely diagonal.

  

• Schneider, J. F., & Krolak-Schwerdt, S. (1994).
  Dreimodale Faktorenanalyse von Wertkonzepten: Ein Methodenvorschlag für interkulturelle Vergleiche. [Three-mode factor analysis of value concepts: Proposal of a method for intercultural comparison]. Gruppendynamik, 25, 117-131.
  The present paper shows the usefulness of various methods of three-mode factor analysis for the cross-cultural comparisons of value concepts. Data were obtained from 300 German and 300 American students, using the Individual and Organizational Values SYMLOG rating form. The comparative structural analyses of the samples made it apparent that the SYMLOG rating forms used did not yield the expected correspondence to the theoretical three-dimensional value space. The masons and consequences of these findings for further studies in this field are discussed. The methodological approach outlined in this paper can supplement the criteria formulated Bales et al. (1997) for adaptation of SYMLOG rating items to particular populations and cultural contexts and it provides more adequate procedures for data analysis.

• Schönemann, P. H. (1972).
  An algebraic solution for a class of subjective metrics models. Psychometrika, 37, 441-451.
  It is shown that an obvious generalization of the subjective metrics model by Bloxom, Horan, Carroll and Chang has a very simple algebraic solution which was previously considered by Meredith in a different context. This solution is readily adapted to the special case treated by Bloxom, Horan, Carroll and Chang. In addition to being very simple, this algebraic solution also permits testing the constraints of these models explicitly. A numerical example is given.

• Schott, J. R. (1998).
  Estimating correlation matrices that have common eigenvectors. Computational Statistics & Data Analysis, 27, 445-459.
  In this paper we develop a method for obtaining estimators of the correlation matrices from k groups when these correlation matrices have the same set of eigenvectors. These estimators are obtained by utilizing the spectral decomposition of a symmetric matrix; that is, we obtain an estimate, say P', of the matrix P containing the common normalized eigenvectors along with estimates of the eigenvalues for each of the k correlation matrices. It is shown that the rank of the Hadamard product, P' O P', is a crucial factor in the estimation of these correlation matrices. Consequently, our procedure begins with an initial estimate of P which is then used to obtain an estimate P' such that P' O P' has its rank less than or equal to some specified value. Initial estimators of the eigenvalues of Q, the correlation matrix for the ith group, are then used to obtain refined estimators which, when put in the diagonal matrix D', as its diagonal elements, are such that P'D'P' has correlation-matrix structure.

• Schulz, U. (1972).
  Ein euklidisches Modell der Multidimensionalen Skalierung unter Berücksichtigung individueller Differenzen [A Euclidean model for individual differences multidimensional scaling]. In Bericht über den 28. Kongreß der Deutschen Gesellschaft für Psychologie, Band 2: Psychologische methodik und mathematische psychologie (pp. 75- 89).
  A Euclidean MDS model is proposed in which the stimuli by subjects are represented both in an individual space which is derived from a common group space via a linear transformation. An algorithm is proposed and its properties are investigated both theoretically and via a simulated example.

• Schulz, U. (1975).
  Zu einem Dekompositionsmodell der multidimensionalen Skalierung mit individueller Gewichtung der Dimensionen. Psychologische Beitrage, 17, 167-187.
  A model for multidimensional scaling is formulated in which the individual differences of the subjects are regarded by means of respective weighting of the dimensions of the group. In case of faultlessness of data it is tried to find out under what conditions a realization is existing. A method of construction is mentioned for a special realization. Finally the author investigates under what conditions there is only one realization and what transformations can be permitted if there should be more than one realization.

• Schulz, U., & Pittner, P.M. (1978).
  Zur multidimensionale Skalierung individueller Differenzen: Zwei Modelle mit Rechenalgorithmen. Psychologische Beitrage, 20, 294-315.
  The authors suggest two calculative algorithms for the determination of solutions for two models of multi-dimensional caling with regard to individual differences. The special numerical problems are dealt with in great detail. On the basis of an example taken from pertinent literature the properties of algorithms are pointed out and brought in relation to existing methods.

  
     

• Seasholtz, M. B. (1999).
  Making money with chemometrics. Chemometrics and Intelligent Laboratory Systems, 45, 55-63.
  Chemometricians have been formally employed at Dow Chemical since 1988. In that time, chemometric methods have been applied in a number of analytical chemistry applications. These have resulted in making money for the company in a variety of ways, and several recent case studies are presented. These applications have been positive for the company in terms of (1) better process control, (2) faster verification of raw material identification and quality, and (3) faster analysis of wastewater. The analytical methods used are NIR and NMR spectroscopy. The chemometric methods include pattern recognition and multivariate calibration.

• See, K., & Smith, E.P. (1996).
  A graphical tool for three-factor experiments with one observation per cell. Communications in Statistics. Part B, Simulation and Computation, 25, 709-732.
  The joint-plot graphical display is proposed as a data analytic tool for diagnosing the type of model to fit to three-factor data. It is a three-way generalization of the biplot display which is useful in graphically diagnosing models for two-way data joint-plots of the three-way array have been used to help understand the underlying structure of the data when all of the three ways or factors are of equal consideration from the view point of exploratory data analysis. In this paper, it is shown that joint-plots can help in understanding the interactions between factors in three factor experiments and in assessing the type of the model to fit. Illustrations from physical and biological science show how to use diagnostic rules in search for models to describe the given data.

• See, K., & Smith, E. P. (1998).
  Testing interaction in three-way ANOVA tables with a single observation per cell. Communications in Statistics. Part A, Theory and Methods, 27, 839-866.
  A common approach in analyzing nonreplicated data is to omit the highest order interaction and regard it as error. This paper discusses the use of a multiplicative model, called a quadrilinear model in order to separate variability due to the three-factor interaction from random error, and also examines its significance in nonreplicated three-factor experiments. The quadrilinear model is a nonreplicated three-way multiplicative model with quadrilinear terms. These estimated quadrilinear terms can be obtained by performing a three-mode principal component analysis of the residuals. in particular, we derive a criterion to select an appropriate number of multiplicative terms to describe significant three-factor interaction. A table of degrees of freedom associated,with the three-factor interaction term is constructed by applying Monte Carlo simulations. An ANOVA table with estimated experimental error variance and error degrees of freedom is provided. These methods are appropriate when it is reasonable to assume that a dominant principal component of the residuals exists. The proposed methods are illustrated using a biological science example.

• Selli, E., Zaccaria, C., Sena, F;.,Tomasi, G., & Bidoglio, G. (2004).
  Application of multi-way models to the time-resolved fluorescence of polycyclic aromatic hydrocarbons mixtures in water. Water Research, 38, 2269-2276.
  The time-resolved laser-induced fluorescence of a series of polycyclic aromatic compounds (PAHs) and mixtures of these latter in aqueous solution was measured by means of an apparatus equipped with optical fibers, which allows their real time in situ monitoring. The potential of such spectroscopic technique, yielding 4-way fluorescence data arrays, together with the application of multi-way models to the matricized data, was tested for the resolution of complex aqueous mixtures containing low concentrations of PAHs, as typical fluorescent pollutants in aquatic systems. PARAllel FACtors analysis was employed for the qualitative resolution of PAHs mixtures and for calculating the fluorescence lifetimes of single PAHs; n-way partial least squares analysis was applied for evaluating the concentration of the single PAHs in the aqueous mixtures.

• Sena, M.M., Fernandes, J.C.B., Rover, L., Poppi, R.J. & Kubota,L.T. (2000).
  Application of two- and three-way chemometric methods in the study of acetylsalicylic acid and ascorbic acid mixtures using ultraviolet spectrophotometry. Analytica Chimica Acta, 409, 159-170.
  In this work, mixtures of acetylsalicylic acid (ASA) and ascorbic acid (AA) were studied by ultraviolet spectrophotometry using parallel factor analysis (PARAFAC) and partial least square (PLS). Parafac was used for spectra deconvolution. The estimated first pK_a was equal to 3.41 and 4.10 for ASA and AA, respectively. Multivariate calibration models using PLS at different pH and N-way PLS were elaborated for simultaneous determination of ASA and AA in pharmaceutical samples. The best models for the system were obtained with N-way PLS2 and PLS2 at pH 1.1.

• Sena, M. M., Fernandes, J. C. B., Rover, L., Poppi, R. J. & Kubota, L. T. (2000b).
  Evaluation of the use of chemometric methods in soil analysis. Quimica Nova, 23, 547-556.
  One of the major interests in soil analysis is the evaluation of its chemical, physical and biological parameters, which are indicators of soil quality (the most important is the organic matter). Besides there is a great interest in the study of humic substances and on the assessment of pollutants, such as pesticides and heavy metals, in soils. Chemometrics is a powerful tool to deal with these problems and can help soil researchers to extract much more information from their data. In spite of this, the presence of these kinds of strategies in the literature has obtained projection only recently. The utilization of chemometric methods in soil analysis is evaluated in this article. The applications will be divided in four parts (with emphasis in the first two): (i) descriptive and exploratory methods based on Principal Component Analysis (PCA); (ii) multivariate calibration methods (MLR, PCR and PLS); (iii) methods such as Evolving Factor Analysis and SIMPLISMA; and (iv) artificial intelligence methods, such as Artificial Neural Networks.

• Sena, M. M., & Poppi, R. J. (2004).
  N-way PLS applied to simultaneous spectrophotometric determination of acetylsalicylic acid, paracetamol and caffeine. Journal of Pharmaceutical and Biomedical Analysis, 34, 27-34.
  In this work, a simple and rapid analytical procedure was proposed for simultaneous determination of acetylsalicylic acid (ASA), paracetamol (PRC, also known as acetaminophen) and caffeine (CAF) in pharmaceutical formulations based on multivariate calibration and UV spectrophotometric measurements (210-300 nm). The calibration set was constructed with nine solutions in the concentration ranges from 10.0 to 15.0 mug ml(-1) for ASA and PRC and from 2.0 to 6.0 mug ml(-1) for CAF, according to an experimental design. The procedure was repeated at four different pH values: 2.0, 3.0, 4.0 and 5.0. Partial least squares (PLS) models were built at each pH and used to determinate a set of synthetic mixtures. The best model was obtained at pH 5.0. An N-way PLS model was applied to a three-way array constructed using all the pH data sets and enabled better results. This calibration model provided root mean squares errors of prediction (RMSEP) from 11.5 to 35% lower than those obtained with PLS at pH 5.0, depending on the analyte. The results achieved for the determination of these drugs in commercial tablets were in agreement to the values specified by the manufactures and the recovery was between 94.7 and 104.5%.

• Sena, M. M., Trevisan, M. G., & Poppi, R. J. (2005).
  PARAFAC: A chemometric tool for multi-dimensional data treatment. Applications in direct determination of drugs in human plasma by spectrofluorimetry. Quimica Nova, 28, 910-920.
  Since the last decade, the combined use of chemometrics and molecular spectroscopic techniques has become a new alternative for direct drug determination, without the need of physical separation. Among the new methodologies developed, the application of PARAFAC in the decomposition of spectrofluorimetric data should be highlighted. The first objective of this article is to describe the theoretical basis of PARAFAC. For this purpose, a discussion about the order of chemometric methods used in multivariate calibration and the development of multi-dimensional methods is presented first. The other objective of this article is to divulge for the Brazilian chemical community the potential of the combination PARAFAC/spectrofluorimetry for the determination of drugs in complex biological matrices. For this purpose, two applications aiming at determining, respectively, doxorrubicine and salicylate in human plasma are presented.

• Serneels, S., Moens, M., Van Espen, P. J., & Blockhuys, F. (2004).
  Identification of micro-organisms by dint of the electronic and trilinear partial least squares regression. Analytica Chimica Acta, 516, 1-5.
  Ventilator-associated pneumonia is one of the most lethal infections occurring in intensive care units of hospitals. In order to obtain a faster method of diagnosis, we proposed to apply the electronic nose to cultures of the relevant micro-organisms. This allowed to halve the time of the analysis. In the current paper, we focus on the application of some chemometrical tools which enhance the performance of the method. Trilinear partial least squares (tri-PLS) regression is used to perform calibration and is shown to produce satisfactory predictions. Sample specific prediction intervals are produced for each predicted value, which allows us to eliminate erroneous predictions. The method is applied to an external validation set and it is shown that only a single observation out of 22 is being wrongly classified, so that the method is acceptable for inclusion in the clinical routine.

       

• Shaffer, R. E., Rose-Pehrsson, S. L., & McGill R. A. (1998).
  Multiway anaysis of preconcentrator-sampled surface acoustic wave chemical sensor array data. Field Analytical Chemistry and Technology, 2, 179-192.
  New data processing methods for preconcentrator-sampled surface acoustic wave (SAW) sensor arrays are described. The preconcentrator-sampling procedure is used to collect and concentrate analyte vapors on a porous solid sorbent, Subsequent thermal desorption provides a crude chromatographic separation of the collected vapors prior to exposure to the SAW array. This article describes experiments to test the effects of incorporating retention information into the pattern-recognition procedures and to explore the feasibility of multiway classification methods. Linear discriminant analysis (LDA) and nearest-neighbor (NN) pattern-recognition models are built to discriminate between SAW sensor array data for four toxic organophosphorus chemical agent vapors and one agent simulant collected under a wide variety of conditions. Classification results are obtained for three types of patterns: (a)first-order patterns; (b) first-order patterns augmented with the time of the largest peak; and (c) second-order patterns with the use of the SAW frequency for each sensor over a broad time window. Classification models for the second-order patterns are also developed with the use of unfolded and multiway partial least-squares discriminants (uPLSD and mPLSD) and NN and LDA of the scores from unfolded and multiway principal-component analysis (uPCA and mPCA), It is determined that classification performance improves when information about the desorption time is included, Treating the preconcentrator-sampled SAW sensor array as a second-order analytical instrument and using a classification model based upon either uPLSD, uPCA-LDA, or NN results in the correct identification of 100% of the patterns in the prediction set. With the second-order patterns, the other pattern-recognition algorithms only do slightly worse.

• Shapiro, A., & Ten Berge, J. M. F. (2002).
  Statistical inference of Minimum Rank Factor Analysis. Psychometrika, 67, 79-94.
  For any given number of factors, Minimum Rank Factor Analysis yields optimal communalities for an observed covariance matrix in the sense that the unexplained common variance with that number of factors is minimized, subject to the constraint that both the diagonal matrix of unique variances and the observed covariance matrix minus that diagonal matrix are positive semidefinite. As a result, it becomes possible to distinguish the explained common variance from the total common variance. The percentage of explained common variance is similar in meaning to the percentage of explained observed variance in Principal Component Analysis, but typically the former is much closer to 100 than the latter. So far, no statistical theory of MRFA has been developed. The present paper is a first start. It yields closed-form expressions for the asymptotic bias of the explained common variance, or, more precisely, of the unexplained common variance, under the assumption of multivariate normality. Also, the asymptotic variance of this bias is derived, and also the asymptotic covariance matrix of the unique variances that define a MRFA solution. The presented asymptotic statistical inference is based on a recently developed perturbation theory of semidefinite programming. A numerical example is also offered to demonstrate the accuracy of the expressions.

• Shaywitz, B.A., Shaywitz, S.E., Pugh, K.R., Constable, R.T., Skudlarski, P., Fulbright, R.K., Bronen, R.A., Fletcher, J.M., Shankweiler, D.P., Katz, L., & Gore, J.C. (1995).
  Sex-differences in the functional-organization of the brain for language. Nature, 373, 607-609.**
  A much debated question is whether sex differences exist in the functional organization of the brain for language(1-4). A long-held hypothesis posits that language functions are more likely to be highly lateralized in males and to be represented in both cerebral hemispheres in females(5,6), but attempts to demonstrate this have been inconclusive(7-17). Here we use echo-planar functional magnetic resonance imaging(18-21) to study 38 right-handed subjects (19 males and 19 females) during orthographic (letter recognition), phonological (rhyme) and semantic (semantic category) tasks. During phonological tasks, brain activation in males is lateralized to the left inferior frontal gyrus regions; in females the pattern of activation is very different, engaging more diffuse neural systems that involve both the left and right inferior frontal gyrus. Our data provide clear evidence for a sex difference in the functional organization of the brain for language and indicate that these variations exist at the level of phonological processing.

• Shikiar, R. (1974a).
  An empirical comparison of two individual differences multidimensional scaling models. Educational and Psychogical Measurement, 34, 823-828.
  For each of five similarity judgment tasks (8-20 stimuli; 115 (student) judges), the INDSCAL and three-mode scaling object space solutions were compared, and found to be very similar. The comparisons of the subject spaces were less similar due to largely unexplained reasons.

• Shikiar, R. (1974b).
  The perception of politicians and political issues: a multidimensional scaling approach. Multivariate Behavioral Research, 9, 461-477.
  Similarity judgments among all possible pairs of the 8 candidates for the 1972 presidency election (USA), among the 12 attributes, and among all candidate-attribute combinations were analysed using Tucker (1972). The components were validated by regression analyses using additional variables.

  
   

• Siciliano, R. (1992).
  Reduced-rank models for dependence analysis of contingency tables. Statistica Applicata, 4, 481-501.
  In the framwork of contingency table analysis, the present paper overviews some of the contributions by the French, Anglo-Saxon, Italian and Dutch schools. Special attention in Italy is given to dependence analysis for the case that a set of response variables can be distinguished from a set of exploratory variables. Dependence models which provide a reduced-rank decomposition of a (transformed) matrix of conditional probabilities are discussed.

• Siciliano, R., & Mooijaart, A. (1997).
  Three-factor association models for three-way contingency tables. Computational Statistics & Data Analysis, 24, 337 - 356.
  A general formulation of association models is introduced for the analysis of contingency tables. The two-factor and three-factor interaction matrices are decomposed into matrices of lower rank. In particular, the three-factor interaction is decomposed by the PARAFAC model. Various conditional models can be used to validate special assumptions for the data such as departures from conditional independence in the context of sets of contingency tables. The problem of identification is discussed. Two sets of data are analysed to illustrate the versatility in the interpretaiton and the advantages of the models developed here.

  

• Sidiropoulos, N.D., & Bro, R. (1999).
  Mathematical programming algorithms for regression-based nonlinear filtering in N-dimensional real space. IEEE Transactions on signal processing, 47, 771-782.
  This paper is concerned with regression under a "sum" of partial order constraints. Examples include locally monotonic, piecewise monotonic, runlength constrained, and unimodal and oligomodal regression. These are of interest not only in nonlinear filtering but also in density estimation and chromatographic analysis. It is shown that under a least absolute error criterion, these problems can be transformed into appropriate finite problems, which can then be efficiently solved via dynamic programming techniques. Although the result does not carry over to least squares regression, hybrid programming algorithms can be developed to solve least squares counterparts of certain problems in the class.

• Sidiropoulos, N.D., & Bro, R. (2000).
  On the uniqueness of multilinear decomposition of N-way arrays. Journal of Chemometrics, 14, 229-239.
  We generalize Kruskal's fundamental result on the uniqueness of trilinear decomposition of three-way arrays to the case of multilinear decomposition of four- and higher-way arrays. The result is surprisingly general and simple and has several interesting ramifications.

• Sidiropoulos, N.D., Bro, R., & Giannakis, G.B. (2000).
  Parallel factor analysis in sensor array processing. IEEE Transactions on Signal Processing, 48, 2377-2388.
  This paper links multiple invariance sensor array processing (MI-SAP) to parallel factor (PARAFAC) analysis, which is a tool rooted in Psychometrics and Chemometrics. PARAFAC is a common name for low-rank decomposition of three- and higher way arrays. This link facilitates the derivation of powerful identifiability results for MI-SAP, shows that the uniqueness of single- and multiple-invariance ESPRIT stems from uniqueness-of low-rank decomposition of three-way arrays, and allows tapping on the available expertise for fitting the PARAFAC model. The results are applicable to both data-domain and subspace MI- SAP formulations. The paper also includes a constructive uniqueness proof for a special PARAFAC model.

• Sidiropoulos, N.D., Giannakis, G.B., & Bro, R. (2000).
  Blind PARAFAC receivers for DS-CDMA systems. IEEE Transactions on Signal Processing, 48, 810-823.
  This paper links the direct-sequence code-division multiple access ( DS-CDMA) multiuser separation-equalization-detection problem to the parallel factor (PARAFAC) model, which is an analysis tool rooted in psychometrics and chemometrics. Exploiting this link, it derives a deterministic blind PARAFAC DS-CDMA receiver with performance close to nonblind minimum mean-squared error (MMSE). The proposed PARAFAC receiver capitalizes on code, spatial, and temporal diversity-combining, thereby supporting small sample sizes, more users than sensors, and/or less spreading than users. Interestingly, PARAFAC does not require knowledge of spreading codes, the specifics of multipath (interchip interference), DOA-calibration information, finite alphabet/constant modulus, or statistical independence/whiteness to recover the information-bearing signals. Instead, PARAFAC relies on a fundamental result regarding the uniqueness of low-rank three-way array decomposition due to Kruskal (and generalized herein to the complex-valued case) that guarantees identifiability of all relevant signals and propagation parameters. These and other issues are also demonstrated in pertinent simulation experiments.

• Sidiropoulos, N. D., & Liu, X. (2001).
  Identifiability results for blind beamforming in incoherent multipath with small delay spread. IEEE Transactions on Signal Processing, 49, 228-236.
  Several explicit identifiability results are derived for deterministic blind beamforming in incoherent multipath with small delay spread. For example, it is shown that if the sum of spatial and fractional sampling diversities exceeds two times the total number of paths, then identifiability can be guaranteed even for one symbol snapshot. The tools come from the theory of low-rank three-way array decomposition (commonly referred to as parallel factor analysis (PARAFAC) and data smoothing in one and two dimensions, New results regarding the Kruskal-rank of certain structured matrices are also included, and they are of interest in their own right.

• Simons, S. J. R., Ni, X., Tabe, H. T., West, R. M., & Williams, R. A. (1999).
  Reduction of tomographic data for use in control of multiphase processes. Chemical Engineering Communications, 175, 99-115.
  Tomograhic sensors are ideally suited to the on-line control of multiphase processes. Little work to date however has been undertaken to determine what type and style of information is required from an image to provide effective process control. In this paper, a possible strategy is presented; namely, a combination of Principal Component Analysis (PCA) and Neural Networks (NN) is used to convert multivariate data from tomographic images into useful information suitable for the control and optimization of chemical processes.

• Sinha, A. E., Fraga, C. G., Prazen, B. J. & Synovec, R. E. (2004a).
  Trilinear chemometric analysis of two-dimensional comprehensive gas chromatography-time-of-flight mass spectrometry data. Journal of Chromatography A, 1027, 269-277.
  Two-dimensional comprehensive gas chromatography (GC x GC) is a powerful instrumental tool in its own right that can be used to analyze-complex mixtures. generating selective data that is applicable to multivariate quantitative analysis and pattern recognition. It has been recently demonstrated that by coupling GC x GC to time-of-flight mass spectrometry (TOFMS), a highly selective technique is produced. One separation on a GC x GC[TOFMS provides retention times on two chromatographic columns and a complete mass spectrum for each component within the mixture. In this manuscript, we demonstrate how the selectivity of GC x GC/TOFMS combined with trilinear chemometric techniques such as trilinear decomposition (TLD) and parallel factor analysis (PARAFAC) results in a powerful analytical methodology. Using TLD and PARAFAC. partially resolved components in complex mixtures can be deconvoluted and identified using only one data set without requiring either signal shape assumptions or fully selective mass signals. Specifically, a region of overlapped peaks in a complex environmental sample was mathematically resolved with TLD and PARAFAC to demonstrate the utility of these techniques as applied to GC x GC/TOFMS data of a complex mixture. For this data, it was determined that PARAFAC initiated by TLD performed a better deconvolution than TLD alone. After deconvolution. mass spectral profiles were then matched to library spectra for identification. A standard addition analysis was performed on one of the deconvoluted analytes to demonstrate the utility of TLD-initiated PARAFAC for quantification without the need for accurate retention time alignment between sample and standard data sets. (C) 2003 Elsevier B.V. All rights reserved.

• Sinha, A. E., Hope, J. L., Prazen, B. J., Fraga, C. G., Nilsson, E. J., & Synovec, R. E. (2004b).
  Multivariate selectivity as a metric for evaluating comprehensive two-dimensional gas chromatography-time-of-flight mass spectrometry subjected to chemometric peak deconvolution. Journal of Chromatography A, 1056, 145-154.
  Two-dimensional gas chromatography (GC x GC) coupled to time-of-flight mass spectrometry (TOFMS) [GC x GC-TOFMS)] is a highly selective technique well suited to analyzing complex mixtures. The data generated is information-rich, making it applicable to multivariate quantitative analysis and pattern recognition. One separation on a GC x GC-TOFMS provides retention times on two chromatographic columns and a complete mass spectrum for each component within the mixture. In this report, we demonstrate how GC x GC-TOFMS combined with trilinear chemometric techniques, specifically parallel factor analysis (PARAFAC) initiated by trilinear decomposition (TLD), results in a powerful analytical methodology for multivariate deconvolution. Using PARAFAC, partially resolved components in complex mixtures can be deconvoluted and identified without. Requiring a standard data set, signal shape assumptions or any fully selective mass signals. A set of four isomers (iso-butyl, sec-butyl, tert-butyl, and n-butyl benzenes) is used to investigate the practical limitations of FARAFAC for the deconvolution of isomers at varying degrees of chromatographic resolution and mass spectral selectivity. In this report, multivariate selectivity was tested as a metric for evaluating GC x GC-TOFMS data that is subjected to PARAFAC peak deconvolution. It was found that deconvolution results were best with multivariate selectivities over 0.18. Furthermore, the application of GC x GC-TOFMS followed by TLD/PARAFAC is demonstrated for a plant metabolite sample. A region of GC x GC-TOFMS data from a complex natural sample of a derivatized metabolic plant extract from Huilmo (Sisyrinchium striatum) was analyzed using TLD/PARAFAC, demonstrating the utility of this analytical technique on a natural sample containing overlapped analytes without selective ions or peak shape assumptions.

  
   

• Sjöberg, L. (1977).
  Choice frequency and similarity. Scandinavion Journal of Psychology, 18, 103-115.
  T3 (Tucker, 1966, Method III) was used to analyse the judgments of 215 students about 7 Swedish political parties using 18 rating scales. The judgments were requested as part of a larger study. The three component spaces for the scales and the parties were each varimax rotated, the latter yielded an (unrecognized?) three-dimensional 'horse shoe'.

• Sjöberg, L. (1984).
  Interests, effort, achievement and vocational preference. British Journal of Educational Psychology, 54, 189-205.
  The components of interest in natural sciences and technology were studied in 100 students in the science and technology divisions of the Swedish secondary school. Structural analysis of the relationships between interest and achievement related variables using Kroonenberg's TUCKALS3 program suggested that effort was mainly directed towards school subjects which students rated as important in which they perceived a high degree of ability.

   

• Skolnick, A. (1981).
  Married lives: Longitudinal perspectives on marriage. In D.H. Eichorn, J.A. Clausen, N. Haan, M.P. Honzik, & P.H. Mussen. (Eds.), Present and past in middle life (pp. 269-298). New York: Academic Press.
  This paper uses the six dimensions resulting from a PARAFAC analysis performed on Q sort data of 136 persons at several time points. The PARAFAC analyses are described in Harshman & Berenbaum (1981).

     

• Smilde, A.K. (1990).
  Multivariate calibration of reversed-phase chromatographic systems. Unpublished doctoral thesis, University of Groningen.
  Part 1. Statistical introduction.
  1. The choice of markers; 2. The linear model; 3. Biased estimation; 4. Experimental design considerations.
  Part 2. Reversed-phase chromatic introduction.
  5. The mobile phase; 6. The stationary phase; 7. Calibration of reversed-phase chromatographic systems; 8. New calibration strategies aimed at prediction of retention on new chromatographic systems.
  Part 3. Calibration of various types of stationary phases.
  9. Experimental design; 10. Two-way approach: the induced-variance criterion; 11. Two-way approach: the determinant criterion; 12. Two-way approach: other marker choices; 13. Three-way approaches.
  Part 4. Calibration of octadecyl stationary phases of different batches.
  14. Experimental design; 15. Two-way approaches; 16. Three-way approaches.

• Smilde, A.K. (1992).
  Three-way analyses: Problems and prospects. Chemometrics and Intelligent Laboratory Systems, 15, 143-157.
  Three-way methods are multivariate data analysis tools that compress and visualize simultaneous variation of combinations of variables and objects. Unfolding, Tucker and PARAFAC models are examples of such methods. The interest in such tools is increasing in chemometrics. The history of three-way methods is sketched and the basic theory is presented, together with chemical applications. Problems in the three-way analyses area re summarized. Some prospects for future use of three-way methods are given.

  

• Smilde, A.K. (1997).
  Comments on multilinear PLS. Journal of Chemometrics, 11, 367-377.
  In 1996 Bro published a paper on Multilinear Partial Least Squares (PLS) in which he proposed a generalisation of PLS to multiway situations, called multilinear PLS, which is a mixture of a trilinear model (PARAFAC) and PLS. However, Bro does not give the equations for the prediction step. In this paper these prediction equations are given in both their full and closed forms. The least squares properties of the proposed multilinear PLS are established and a more comprehensive notation is given. Using this notation, it is clear that some other multiway analysis methods such as PARAFAC and Tucker1 models can be combined with PLS. Multiway methods such as Tucker2 and Tucker3 need a different approach. A framework is given for general two-block multiway models.

• Smilde, A.K. (2001a).
  Comments on three-way analyses used for batch process data. Journal of Chemometrics, 15, 19-27.
  Recently, several papers have appeared concerning the use of three-way models for batch process data. In these papers a number of points are raised. This paper discusses some of these points and illustrates some pitfalls. More specifically, some theoretical aspects of using different three-way models for batch process data and some practical consequences are discussed. The topics of cross-validation and data preprocessing are also discussed. These issues will be discussed using small simulated examples and theoretical arguments.

• Smilde, A.K., & Doornbos, D.A. (1992).
  Simple validatory tools for judging the predictive performance of Parafac and three-way PLS. Journal of Chemometrics, 6, 11-28.
  The methods Parafac and three-way PLS are compared with respect to their ability to predict reversed-phase retention values. Special attention is paid to simple validatory tools, the meaning and use of which are explained. The simple validatory tools consist of percentages of explained variation in the training set and those that can be calculated with the use of markers. These markers are special (reference) solutes, the retention values of which are used to gain information about a new object for which predictions are wanted. Different validatory tools can be calculated with the use of these marker retention values: Percentages of used variation and mean sum of squared residuals after applying the model to these marker retention values. The validatory tools are evaluated on their power to estimate their test set counterparts: The percentages of explained variation in the test set and mean sum of squared prediction errors in the test set. Two different data sets from reversed-phase chromatography are used to evaluate the validatory tools. The first data set has a high signal-to-noise ratio and is measured under the same measurement conditions. The second data set has a low signal-to-noise ratio and is measured under different measurement conditions. Some of the simple validatory tools seem to have relevance to their test set counterparts, even in the case of the second data set.

• Smilde, A. K., Hoefsloot, H. C. J., Kiers, H. A. L., Bijlsma, S., & Boelens, H. F. M. (2001b).
  Sufficient conditions for unique solutions within a certain class of curve resolution models. Journal of Chemometrics, 15, 405-411.
  Curve resolution is a class of techniques concerned with estimating profiles underlying a set of measurements of time-evolving chemical systems. In general, the estimated profiles are not unique. Both intensity and rotational ambiguities exist in the solutions of these problems. Constraints can be imposed on the solution to decrease the ambiguity. Some chemical systems show closure. It is proven that imposing a closure constraint is sufficient to solve the intensity ambiguity but not the rotational ambiguity. Some curve resolution techniques are concerned with estimating reaction rate or equilibrium constants from measurements of evolving systems. Then a kinetic model is imposed on the measured data. It is proven that imposing a certain class of kinetic models is sufficient to solve both the rotational and the intensity ambiguity.

• Smilde, A.K., & Kiers, H.A.L. (1999).
  Multiway covariates regression models. Journal of Chemometrics, 13, 31-48.
  An abundance of methods exist to regress a y variable on a set of x variables collected in a matrix X. In the chemical sciences a growing number of problems translate into arrays of measurements X and Y, where X and Y are three-way arrays or multiway arrays. In this paper a general model is described for regressing such a multiway Y on a multiway X, while taking into account three-way structure in X and Y. A global least squares optimization problem is formulated to estimate the parameters of the model. The model is described and illustrated with a real industrial example from batch process operation. An algorithm is given in an appendix.

• Smilde, A. K., Tates, A. A., Boelens, H. F. M., Oerlemans, P., & Ruitenberg, G. (2001c).
  Systematic investigation of process and product variations in a spindraw-winding process. Chemical Engineering Science, 56, 4993-5002.
  The variation in product quality of industrial poly-ethylene terephthalate (PET) produced in a spindraw-winding process was related to on-line measured process variables. An experimental design in three process variables was used to introduce meaningful variation. Using standard multivariate data analysis techniques the relation between the variation of the product quality and the process variation could be modeled. The adequacy of these models was judged by comparing the modeling error to the known measurement error of the quality variables. It Could be established that the three process variables that were used in the experimental design are responsible for almost all variation in product quality. This shows the feasibility of the multivariate approach to systematically analyze the variation in product quality of industrial processes.

• Smilde, A.K., Tauler, R., Henshaw, J.M., Burgess, L.W., & Kowalski, B.R. (1994).
  Multicomponent determination of chlorinated hydrocarbons using a reaction-based chemical sensor. 3. Medium-rank second-order calibration with restricted Tucker models. Analytical Chemistry, 66, 3345-3351.
  The calibration of a chemical sensor for chlorinated hydrocarbon analytes based on the Fujiwara reaction is described. This sensor generates a particular type of data: medium-rank second-order data. With this type of data it is possible to calibrate the sensor in such a way that quantitation for the analytes in the presence of unknown interferents is possible. The calibration method developed is a new approach based on so-called restricted Tucker models that utilize all available chemical information.

  

• Smilde, A.K., Tauler, R., Saurina, J., & Bro, R. (1999). Calibration methods for complex second-order data. Analytica Chimica Acta, 398, 237-251.
  In this paper, different three-way methods are tested for their power and shortcomings to solve complex second-order calibration problems. The generic calibration problem is quantifying for an analyte in the presence of an unknown interferent: A second-order calibration problem. Due to rank restrictions of the data, standard second-order calibration methods like generalized rank annihilation cannot be used to solve the type of complex second-order calibration problems shown in this paper. Different real examples are tested in which it is shown that the three-way methods can, to a certain extent, deal with the complex calibrations. This stresses the fact that all second-order calibration methods should be regarded as three-way methods, and when put in this framework, can be compared with respect to their performance.

• Smilde, A.K., Van der Graaf, P.H., Doornbos, D.A., Steerneman, T., & Sleurink, A. (1990).
  Multivariate calibration of reversed-phase chromatographic systems: Some designs based on three-way data analysis. Analytica Chimica Acta, 235, 41-51.
  When retention measurments are available for a set of solutes on different stationary phases, with varying mobile phase compositions, the resulting data set can be used to calibrate a new stationary phase. Two models are tested for this purpose: three-way partial least squares and parallel factor analysis.

• Smilde, A.K., Wang, Y., & Kowalski, B.R. (1994).
  Theory of medium-rank second-order calibration with restricted-Tucker models. Journal of Chemometrics, 8, 21-36.
  If an analytical instrument or instrumental method gives a response matrix when analyzing a pure analyte, the instrument or instrumental method is called a second-order method. Second-order methods that generate a response matrix for a pure analyte of rank one are called rank-one second-order methods. If the response matrix of a pure analyte is not rank one, essentially two cases exist: Medium rank (between two and five) and high rank (greater than five). Subsequently, medium- and high-rank second-order calibration tries to use medium- and high-rank second-order methods to analyze for analytes of interest in a mixture. a particular advantage of second-order methods is the ability to analyze for analytes of interest in a mixture which contains unknown interferences. Keeping this advantage is the challenge on moving away from rank-one second-order calibration methods. In this paper a medium-rank second-order calibration method is proposed based on least-squares restricted Tucker models. With this method the second-order advantage is retained.

• Smilde, A.K., Westerhuis, J.A., & Boqué, R. (2000). Multiway multiblock component and coveriates regression models. Journal of Chemometrics, 14, 301-331.
  In this paper the general theory of multiway multiblock component and covariates regression models is explained. Unlike in existing methods such as multiblock PLS and multiblock PCA, in the new proposed method a different number of components can be selected for each block. Furthermore, the method can be generalized to incorporate multiway blocks to which any multiway model can be applied. The method is a direct extension of principal covariates regression and therefore works in a simultaneous fashion in which a clearly defined objective criterion is minimized. It can be tuned to fulfil the requirements of the user. Algorithms to calculate the components will be presented. The method will be illustrated with two three-block examples and compared to existing approaches. The first example is with two-way data and the second example is with a three- way array. It will be shown that predictions are as good as with the existing methods, but because for most blocks fewer components are required, diagnostic properties of the method are improved.

• Smilde, A. K., Westerhuis, J. A., & de Jong, S. (2003).
  A framework for sequential multiblock component methods. Journal of Chemometrics, 17, 323-337.
  Multiblock or multiset methods are starting to be used in chemistry and biology to study complex data sets. In chemometrics, sequential multiblock methods are popular; that is, methods that calculate one component at a time and use deflation for finding the next component. In this paper a framework is provided for sequential multiblock methods, including hierarchical PCA (HPCA; two versions), consensus PCA (CPCA; two versions) and generalized PCA (GPCA). Properties of the methods are derived and characteristics of the methods are discussed. All this is illustrated with a real five-block example from chromatography. The only methods with clear optimization criteria are GPCA and one version of CPCA. Of these, GPCA is shown to give inferior results compared with CPCA.

• Smolinski, A., & Walczak, B.(2002a).
  Exploratory analysis of chromatographic data-sets with missing elements. Initialization of the expectation-maximization algorithm. Acta Chromatographica, 12, 30-48.
  The main goal of the work presented in this paper was comparison of different methods of initialization of missing elements in chromatographic data-sets to speed up convergence of the expectation-maximization (EM) algorithm. The EM algorithm can be built into different computational procedures used for exploratory analysis, for example principal component analysis (PCA) and its generalization for N-way data, i.e. the Tucker3 model.

• Smolinski, A., Walczak, B. & Einax, J. W. (2002b).
  Exploratory analysis of data sets with missing elements and outliers. Chemosphere, 49, 233-245.
  The main goal of the presented paper was to develop a general strategy allowing exploration of contaminated data sets with missing elements, based on application of robust PLS for initial estimation of missing elements. Using robust distance, the outlying elements were identified. After their identification and replacing by missing elements, the expectation-maximization algorithm (which can be built in into different computational procedures, such as principal component analysis and its generalisation to the N-way data-the TUCKER3 model) was used for construction of the final model. (C) 2002 Elsevier Science Ltd. All rights reserved.

  
   

• Snyder Jr, C.W. (1970).
  Intrinsic individual differences in disjunctive conceptual behavior: three-mode factor analysis. Unpublished doctoral thesis, University of Pennsylvania. ( Dissertation Abstracts International, 1970, 32 (1-B), 544.)

  

• Snyder Jr, C.W. (1976).
  Multivariate analysis of intrinsic individual differences in disjunctive conceptual behavior. Multivariate Behavioral Research, 11, 195-216.
  T3 with multitrait-multimethod matrix (Tucker (1966), Method III) with learning data (40 subjects, 10 trial blocks, and 4 response measures). Relatively clear core matrix.

• Snyder Jr, C.W. (1988).
  Multimode factor analysis. In J.R. Nesselroade and R.B. Cattell (Eds.), Handbook of multivariate experimental psychology (second edition) (pp. 289-316). New York: Plenum Press.
  Multimode factor-analytic methods are designed to systematize and represent the relations in data that are classified by more than two entity sets. Unfortunately, the mathematical and conceptual extension of factor analysis to the multimode case is not straightforward. This chapter reviews the difficulties associated with multimode analysis and outlines some suggested analytic resolutions. An application in affect assessment, entailing a three-mode structural hypothesis, will be used to illustrate the different approaches.

• Snyder Jr, C.W., Bridgman, R.P., & Law, H.G. (1981).
  Three-mode factor analytic reference curves for concept identification. Personality and Individual Differences, 2, 265-272.
  T2 (common FA model on a Multi measure and multiblock matrix was used to explore the intrinsic individual differences in a figural, disjunctive conceptual behavior task. 38 students were scored on 4 response measures during 10 trial blocks. Trial blocks were varimax, the core matrix counter rotated. Rather complex core matrix, the interpretation of which was compared to individual solutions.

  

• Snyder Jr, C.W. and Law, H.G. (1979).
  Three-mode common factor analysis: Procedure and computer programs. Multivariate Behavioral Research, 14, 435-441.
  T3 (Method III) is described in step-by-step format for easy comprehension. The described procedure uses the SPSS package, subprogram FACTOR, interfaced with specialized programs written by the authors.

• Snyder Jr, C.W., & Law, H.G. (1981).
  Three-mode models for road research. In: J.M. Morris (Ed.), Proceedings of a Seminar on measuring so cial behavior in road research. Vermont South, Vic., Australia: Australian Road Research Board (pp. 39-48).*
  Factor analytic and multidimensional scaling models which can be used on three-way categorised data sets are reviewed in terms of their usefulness for road researchers. These models include Harshman's PARAFAC, Tucker's three-mode common factor analysis, Carroll & Chang's INDSCAL, and Takane, Young & De Leeuw's ALSCAL. Enough of the formalities associated with each model is presented to clarify the particular approach to data analysis. The results are characterised in terms of a hypothetical road research project on traffic noise.

  

• Snyder Jr, C.W., Law, H.G. & Pamment, P.R. (1979).
  Calculation of Tucker's three-mode common factor analysis. Behavior Research Methods & Instrumentation, 11, 609-611.
  The working of three programs is described. They were written to interface with the SPSS FACTOR routine to calculate a solution for T3 by Tucker's methode III (1966).

  

• Snyder, F.W. (1968).
  A unique variance model for three-mode factor analysis. Department of Psychology, University of Illinois, Urbana, Illinois (also doctoral thesis, 1969). (Dissertation Abstracts International, 1969, 30 (3-B), 1349).
  A 'true' T3 factor model is presented which allows for unique variances for two of the modes and for their combinations. It extends the model presented in Tucker (1966). The model is a precursor of Bentler & Lee's (1979) model. The computational procedure seems complex and cumbersome. Two illustrations: (1) 40 measures on 3 different sets of administrative tasks for 232 school administrators; (2) in each of 6 semesters 18 character and work traits of 222 students of an aviation school were rated by their teachers. Detailed numerical results.

• Snyder, F.W., & Tucker, L.R. (1970).
  Interpretation of the core matrix in three-mode factor analysis. Paper presented at the Psychometric Society Meeting.
  A special interpretation of the core array is developed. After suitable scaling and rotations and after averaging over the markers of each mode, the core array is the three-way average of the original data points. Marker variables have a score of 1 on one component and 0 on all other components. The theoretical treatment is illustrated with a hypothetical example.

• Snyder, F.W. & Wiggins, N. (1973).
  Affective meaning systems: a multivariate approach. Multivariate Behavioral Research, 5, 453-468.
  T3 was applied to the semantic differential ratings of 20 con- cepts by 100 subjects on 76 bipolar adjectival scales. The 4 scale and 5 concept factors were varimax rotated, the concept dimensions were given somewhat questionable names, and the subject dimensions were rotated by hand. An interpretation was attempted of the rather jumbled core matrix.

  
   

• Sogon, S., & Doi, K. (1990).
  Three-mode factor analysis of emblematic gesture and body manipulation viewed from the dorsal perspective. Shinrigaku-Kenkyu, 60, 356-362.
  This paper focuses on emblematic gesture and manipulation of body movements. Subjects viewed from the dorsal perspective the body movements depicting emotions displayed by two actors/actresses. Three-mode factor analyses were applied to the data. Three factors were found in the emotion-mode, three in the scene-mode, and two factors in the subjects-mode. The emotion-mode and scene-mode factors were found to correspond to a high degree. The core matrix and subjects' factor scores were correlated with a response tendency in terms of subjects' evaluations rather than their accuracy of judgment.

• Soli, S.D., Arabie, P., & Carroll, J.D. (1986).
  Discrete representation of perceptual structure underlying consonant confusions. Journal of the Acoustical Society of America, 79, 826-837.
  The perceptual representation of speech is generally assumed to be discrete rather than continuous, pointing to the need for general discrete analytic models to represent observed perceptual similarities among speech sounds. The INDCLUS (INdividual Differences CLUStering) model and algorithm [J.D. Carroll and P. Arabie] can provide this generality, representing symmetric three-way similarity data (stimuli × stimuli × conditions) as an additive combination of overlapping, and generally not hierarchical, clusters whose weights (which are numerical values gauging the importance of the clusters) vary both as a function of the cluster and condition being considered. INDCLUS was used to obtain a discrete representation of underlying perceptual structure in the Miller and Nicely consonant confusion data [G.A. Miller and P.E. Nicely (1955)]. A 14-cluster solution accounted for 82.9% of total variance across the 17 listening conditions. The cluster composition and the variations in cluster weights as a function of stimulus degredation were interpreted in terms of the common and unique perceptual attributes of the consonants within each cluster. Low-pass filtering and noise masking selectively degraded unique attributes, especially the cues for place of articulation, while high-pass filtering degraded both unique and common attributes. The clustering results revealed that perceptual similarities among consonants are accurately modeled by additive combinations of their specific and discrete acoustic attributes whose weights are determined by the nature of the stimulus degradation.

• Soltanian-Zadeh, H., & Peck, D. J. (2001).
  Feature space analysis: Effects of MRI protocols. Medical Physics, 28, 2344-2351.
  We present a method for exploring the relationship between the image segmentation results obtained by an optimal feature space method and the MRI protocols used. The steps of the work accomplished are as follows. (1) Patients with brain tumors were imaged on a 1.5 T General Electric Signa MRI System using multiple protocols (T1 and T2-weighted fast spin-echo and FLAIR). T1-weighted images were acquired before and after gadolinium injection. (2) Image volumes were co-registered. and images of a slice through the center of the tumor were selected for processing. (3) For each patient, several image sets were defined by selecting certain MR images (e.g., 4T2's + 1T1, 4T2's + FLAIR. 2T2's + 1T1). (4) Using each image set, the optimal feature space was generated and images were segmented into normal tissues and different tumor zones. (5) Segmentation results obtained using the different MRI sets were compared. Based on the analysis results from 27 image sets. we found that the locations of the clusters for the tumor zones and their corresponding regions in the image domain changed as a function of the MR images (MRI protocols) used. However. the segmentation results for the total lesion and normal tissues remained relatively unchanged.

• Soltanian-Zadeh, H., Windham, J. P., & Peck, D. J. (1996).
  Optimal linear transformation for MRI feature extraction. IEEE Transactions on Medical Imaging, 15, 749-767.
  This paper presents development and application of a feature extraction method for magnetic resonance imaging (MRI), without explicit calculation of tissue parameters. A three-dimensional (3-D) feature space representation of the data is generated in which normal tissues are clustered around prespecified target positions and abnormalities are clustered elsewhere. This is accomplished by a linear minimum mean square error transformation of categorical data to target positions. From the 3-D histogram (cluster plot) of the transformed data, clusters are identified and regions of interest (ROI's) for normal and abnormal tissues are defined. These ROI's are used to estimate signature (prototype) vectors for each tissue type which in turn are used to segment the MRI scene. The proposed feature space is compared to those generated by tissue-parameter-weighted images, principal component images, and angle images, demonstrating its superiority for feature extraction and scene segmentation. Its relationship with discriminant analysis is discussed. The method and its performance are illustrated using a computer simulation and MRI images of an egg phantom and a human brain.

• Soltanian-Zadeh, H., Windham, J. P., Peck, D. J., & Mikkelsen, T. (1998).
  Feature space analysis of MRI. Magnetic Resonance in Medicine, 40, 443-453.
  This paper presents an MRI feature-space image-analysis method and its application to brain tumor studies. The proposed method generates a transformed feature space in which the normal tissues (white matter, gray matter, and CSF) become orthonormal. As such, the method is expected to have site-to-site and patient-to-patient consistency, and is useful for identification of tissue types, segmentation of tissues, and quantitative measurements on tissues, The steps of the work accomplished are as follows: (1) Four T-2-weighted and two T-1-weighted images (before and after injection of gadolinium) were acquired for 10 tumor patients. (2) Images were analyzed by an image analyst according to the proposed algorithm, (3) Biopsy samples were extracted from each patient and were subsequently analyzed by the pathology laboratory. (4) Image-analysis results were compared with the biopsy results. Pre- and postsurgery feature spaces were also compared, The proposed method made it possible to visualize the MRI feature space and to segment the image. In all cases, the operators were able to find clusters for normal and abnormal tissues. Also, clusters for different zones of the tumor were found. The method successfully segmented the image into normal tissues (white matter, gray matter, and CSF) and different zones of the lesion (tumor, cyst, edema, radiation necrosis, necrotic core, and infiltrated tumor). The results agreed with those obtained from the biopsy samples. Comparison of pre- with postsurgery and radiation feature spaces illustrated that the original solid tumor was not present in the second study, but a new tissue component appeared in a different location of the feature space. This tissue could be radiation necrosis generated as a result of radiation.

• Soltanian-Zadeh, H., Windham, J. P., Peck, D. J., & Yagle, A. E. (1992).
  A comparative-analysis of several transformations for enhancement and segmentation of magnetic-resonance image scene sequences. IEEE Transactions on Medical Imaging, 11, 302-318.
  We compare the performance of the eigenimage filter to that of several other filters, applied to magnetic resonance image (MRI) scene sequences for images enhancement and segmentation. Comparisons are made with principal component analysis, matched, modified-matched, maximum contrast, target point, ratio, log-ratio, and angle image filters. Signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), segmentation of a desired feature (SDF), and correction for partial volume averaging effects (CPV) are used as performance measures. For comparison, analytical expressions for SNRs and CNRs of filtered images are derived, and CPV by a linear filter is studied. Properties of filters are illustrated through their applications to simulated and acquired MRI sequences of a phantom study and a clinical case; advantages and weaknesses are discussed. Our conclusion is that the eigenimage filter is the optimal linear filter that achieves SDF and CPV simultaneously.

• Sorenson, L. (1986).
  Factor analysis of open-field behavior in rats: Using the three-way PARAFAC model for longitudinal data. Paper presented at the Annual Meeting of the Canadian Psychological Association, Toronto.
  Recognition of the fact that single variable approaches to the study of animal behavior are often inadequate has led to the suggestion that "behavioral profiles" derived from multivariate measurement techniques might better describe a behavioral phenomenon. In the experiment reported here we examined one such application of multivariate techniques by subjecting a longitudinal data set obtained during open-field testing of rats to a PARAFAC analysis. The PARAFAC procedure allows one to directly analyze three-way arrays and is this very appropriate for longitudinal data. Unlike conventional two-way factor analytic models that provide many possible solutons because the factors can be arbitrarily rotated, the PARAFAC model provides a unique factor solution to a data set. A PARAFAC analysis thus provides an empirically grounded basis for selecting the best candidates for "real" factors within a given domain. Standard open-field measures were collected for twenty-six rats tested during four sessions spaced 48-hours apart. The PARAFAC analysis extracted two factors, the first reflecting emotional reactivity and the second reflecting exploration. These two factors change in temporal prominence with animals showing greater emotional reactivity on the first test session and greater levels of exploration on the third and fourth test sessions. These results are in general accord with previous findings using more conventional approaches and suggest that multivariate procedures such as these may be of great value to researchers in the behavioral neurosciences.

• SOUPAC program descriptions. Computing Services Offices, University of Illinois, Urbana, Ill., 1973.
  Describes implementations of Tucker's (1966) methods I and II for three-mode factor analysis.

  
   

• Spanjer, M.C. (1984).
  Substituent interaction effects and mathematical-statistical description of retention in liquid chromatography. Unpublished doctoral thesis, University of Utrecht.
  I. Substituent interaction effects in aromatic molecules in reversed-phase liquid chromatography.
  II. Substituent interaction effects in aromatic molecules in RP-HPLC with acetonitrile-water and tetrahudrofuran-water eluents.
  III. A comparison of some linear substituent free energy relationships.
  IV. Simultaneous description of the influence of solvent, reaction type and substituent on equilibrium constants by means of three-mode factor analysis.
  V. Three-mode factor analysis of data on the retention in normal-phase HPLC.
  

         

• Ståhle, L. (1989).
  Aspects of the analysis of three-way data. Chemometrics and Intelligent Laboratory Systems, 7, 95-100.
  An algorithm is developed for linear three-way decomposition (LTD) of three- way tables for the case of one dependent block of variables and one independent, predictor block. The algorithm is a generalization of the two-block partial least- squares (PLS) algorithm. Using simulation and real data LTD is compared with multi-way PLS with and without decomposition of the eight matrix. LTD and PLS with a one-dimensional decomposition of the weight matrix gives essentially the same results. By means of the cross-validation criterion it is shown that, in practice, optimal prediction may be obtained with a model that is neither completely trilinear nor bilinear. The multi-way PLS method with decomposition of the weight matrix to give the minimum cross-validation perdiction error is preferred.

• Ståhle, L. (1991).
  Relating multivariate time-seris by linear 3-way decomposition (LTD) and partial least-squares (PLS) analysis. Journal of Pharmaceutical and Biomedical Analysis, 9, 671-678.
  The problem of relating multivariate time-series which is common in drug development is considered. The mathematical and statistical problems involve relating two three-way tables. These tables have objects and time-points in common while the variables to be related are unique for each table. A modification is presented of the linear three-way decomposition (LTD) algorithm which directly incorporates the information that both objects and time-points are common to the two tables. A comparison is made with partial least squares (PLS) analysis both at the theoretical level and in their application to three sets of real data. Limitations of LTD are discussed, in particular the constraint imposed by the trilinearity requirement, and areas for future development are proposed.

• Stanimirova, I., Walczak, B., Massart, D. L., Simeonov, V., Saby, C. A., & Di Crescenzo, E. (2004).
  STATIS, a three-way method for data analysis. Application to environmental data. Chemometrics and Intelligent Laboratory Systems, 73, 219-233.
  The present paper deals with the data exploration of three-way environmental data with the use of "Structuration des Tableaux A Trois Indices de la Statistique" (STATIS). The performance of the method is compared with Tucker3 and PARAFAC2, two more commonly used methods in chemometric N-way data analysis. The features of STATIS are demonstrated on real data sets. Due to its robust properties, lack of special requirements for data preprocessing and ability to deal with sets of two-way tables (matrices) that do not have the same dimension for columns or rows, STATIS appears as a very attractive three-way exploratory tool.

• Stankov, L., & Chen, K. (1988).
  Can we boost fluid and crystallised intelligence? A structural modelling approach. Australian Journal of Psychology, 40, 363-376.
  The invariant factor structure model for multimode data ( McDonald, 1984)was fitted, with LISREL, to data obtained from two groups of high-school students. The experimental group was exposed to extensive training in creative problem solving over a three-year period. The control group attended normal school activities. The same battery of eight intelligence tests was administered three times: at the beginning of the experiment, at the end of training, and one year after the end of training. The results indicate that, at the last testing session, the experimental group performed better than the control group on both fluid and crystallised intelligence factors. In addition, by employing both invariant factor analysis and simultaneous factor analysis it was possible to conclude that fluid intelligence is affected slightly more by training than crystallised intelligence.

• Stedmon, C. A., Markager, S. & Bro, R. (2003).
  Tracing dissolved organic matter in aquatic environments using a new approach to fluorescence spectroscopy. Marine Chemistry, 82, 239-254.
  Dissolved organic matter (DOM) is a complex and poorly understood mixture of organic polymers that plays an influential role in aquatic ecosystems. In this study we have successfully characterised the fluorescent fraction of DOM in the catchment of a Danish estuary using fluorescence excitation-emission spectroscopy and parallel factor analysis (PARAFAC). PARAFAC aids the characterisation of fluorescent DOM by decomposing the fluorescence matrices into different independent fluorescent components. The results reveal that at least five different fluorescent DOM fractions present (in significant amounts) in the catchment and that the relative composition is dependent on the source (e.g. agricultural runoff, forest soil, aquatic production). Four different allochthonous fluorescent groups and one autochthonous fluorescent group were identified. The ability to trace the different fractions of the DOM pool using this relatively cheap and fast technique represents a significant advance within the fields of aquatic ecology and chemistry, and will prove to be useful for catchment management.

• Steeby, J. A., Hargreaves, J. A., & Tucker, C. S. (2004).
  Factors affecting sediment oxygen demand in commercial channel catfish ponds. Journal of the World Aquaculture Society, 35, 322-334.
  Sediment oxygen demand (SOD) measured in 45 commercial channel catfish ponds in northwest Mississippi using in situ respirometry (N = 167) ranged from 63 to 1,038 mg/m(2) per h. Mean SOD in this study (359 mg/m(2) per h) was greater than that reported previously for catfish ponds but was similar to SOD in semi-intensive marine shrimp ponds. Nine variables were selected and measured to assess their relative importance in accounting for variation in SOD. Six variables were included in multiple regression models that explained slightly more than half of the variation in SOD. These variables were: dissolved oxygen concentration at the beginning of respirometry incubation;, particulate organic matter concentration in water above the sediment surface; organic carbon concentration at the immediate sediment-water interface (flocculent or F-layer) combined with the upper 2 cm of sediment (Slayer); organic carbon concentration in the mature (M) underlying sediment layer; water temperature; and total depth of accumulated sediment. Sediment oxygen demand was most sensitive to changes in dissolved oxygen concentration in the overlying water, particulate organic matter concentration in the water, and the concentration of organic carbon in the combined flocculent and upper sediment (F+S) layer. Models for SOD in this research predict that the mass of sediment below the upper 2-cm surface layer on average contributes only similar to20% of total SOD. Stratification and normal daily fluctuation of dissolved oxygen concentration in eutrophic culture ponds likely limit expression of sediment oxygen demand. Maintaining aerobic conditions at the sediment-water interface will minimize accumulation of organic matter in pond sediment.

• Stefanov, Z. I. & Hoo, K. A.(2003).
  Hierarchical multivariate analysis of cockle phenomena. Journal of Chemometrics, 17, 550-568.
  The phenomena called cockle are small wrinkles on the paper surface that appear during paper production. This condition poses significant economic and operability problems in the production of magazine paper, as it deteriorates the printabilty of the paper. There are many and varied sources that can lead to cockle, and their detection is often very complicated. In this work a multivariate hierarchical approach is proposed to analyze the cause of cockle. The hierarchy has two levels, the first of which is a three-way decomposition and analysis of the data collected from sections of a paper machine. The second level is a two-way decomposition and analysis between the combined loadings from the three-way decomposition and the measured cockle data. The results show that this approach is capable of identifying the important process sections and process variables, in spite of the large dimensionality of the problem. Data analyzed from two real industrial paper machines, involving several grades of paper, are used to demonstrate the proposed hierarchical approach.

• Stellman, C. M., Booksh, K. S., Muroski, A. R., Nelson, M. P., & Myrick, M. L. (1998).
  Principal component mapping applied to Rman microspectroscopy of fiber-reinforced polymer composites. Science and Engineering of Composite Materials, 7, 51-80.
  We describe the development and implementation of a spectroscopic Raman imaging system using Principal Component data analysis. Raman microspectroscopy followed by multivariate data analysis and principal component mapping has been used to investigate the spacial variations of chemical and physical properties at interfaces in glass-reinforced composites on the micrometer scale. A protocol for monitoring chemical and physical variances via multivariate statistics has been developed and a preliminary study of a "real world" glass-reinforced composite is presented. It is demonstrated that multivariate Raman imaging is more precisely interpretable than traditional univariate methods and that by appropriately choosing distinct spectral regions (such as a cure sensitive epoxide band) for PCA, subtle compositional changes like local cure percentage may be observed.

• Stewart, T.R. (1971).
  The relation between three-mode factor analysis and multidimensional scaling of personality trait profiles. Unpublished doctoral thesis, University of Illinois, Urbana- Champaign, Ill. (Dissertation Abstracts International, 1971, 32 (2-B), 1197.)
  (see Stewart, 1974)

• Stewart, T.R. (1974).
  Generality of multidimensional representations. Multivariate Behavioral Research, 9, 507-519.
  Proposes to compare the MDS solution of combination mode similarity matrices (15 personality descriptions judged in pairs by 98 subjects), and a PCA solution of a combination- mode three-mode matrix (judgement on 4 rating scales of 81 hypothetical people by the same 98 subjects) in search for 'generality' of the multidimensional configuration. Although the usage of Tucker (1972) is claimed for the MDS, only the combination-mode aspect of it is used.

  

• Stone, M., & Jonathan, P. (1994).
  Statistical thinking and technique for QSAR and related studies. Part II: Specific methods. Journal of Chemometrics, 8, 1-20.
  Twenty-two contrasting statistical methods are reviewed for their applicability to QSAR studies and similar prediction-oriented fields. Each method is concisely specified prior to explanatory or critical comment.

• Stone, M., & Lundberg, A. (1996).
  Three-dimensional tongue surface shapes of English consonants and vowels. Journal of the Acoustical Society of America, 7, 7.**
  This paper presents three-dimensional tongue surfaces reconstructed from multiple coronal cross-sectional slices of the tongue. Surfaces were reconstructed for sustained vocalizations of the American English sounds /i, i, e, epsilon, ae, a, reverse c, o, upsilon, labda, sic, l, s, integral, theta, n, eta/. Electropalatography (EPG) data were also collected for the sounds to compare tongue surface shapes with tongue-palate contact patterns. The study was interested also in whether 3-D surface shapes of the tongue were different for consonants and vowels. Previous research and speculation had found that there were differences in production, acoustics, and linguistic usage between the two groups. The present study found that four classes of tongue shape were adequate to categorize all the sounds measured. These classes were bent raising, complete groove, back raising, and two-point displacement. The first and third classes have been documented before in the midsagittal plane [cf. R. Harshman, P. Ladefoged, and L. Goldstein, J. Acoust. Sec. Am. 62, 693-707 (1976)]. The first three classes contained both vowels and consonants, the last only consonants. Electropalatographic patterns of the sounds indicated three categories of tongue-palate contact: Bilateral, cross-sectional, and combination of the two. Vowels used only the first pattern, consonants used all three. The EPG data provided an observable distinction in contact pattern between consonants and vowels. The ultrasound tongue surface data did not. The conclusion was that the tongue actually has a limited repertoire of shapes and positions them against the palate in different ways for consonants versus vowels to create narrow channels, divert airflow, and produce sound.

• Stone, M., Shawker, T. H., Talbot, T. L., & Rich, A. H. (1988).
  Cross-sectional tongue shape during the production of vowels. Journal of the Acoustical Society of America, 83, 1586-1596.
  This study used ultrasound imaging to examine the cross-sectional shape of the tonque during the production of the ten English vowels in two consonant contexts - /p/ and /s/- and at two scan angles - anterior and posterior. Results were compared with models of sagittal tongue shape. A newly built transduder holder and head testraint maintained the ultrasound transducer in a fixed position inverior to the mandible at a chosen location and angle. The transducer was free to move only in a superior/inferior direction, and demonstrated reliable tracking of the jaw. Since the tongue is anisotrophic along its length, anterior and posterior scan angles were examined to identify differences in tongue shape. Similarly, the coarticulatory effects of the sibilant /s/ versus the bilabial /b/ were examined, to assess variability of intrinsic tongue shape for the vowels. Results showed that the subject's midsagittal tongue grooving was almost universal for the vowels. Posterior grooves were deeper than anterior grooves. In /s/ context, posterior tongue grooves for low vowels. Cross-sectional tongue shape varied with tongue position similarly to sagittal tongue shape.

• Stoop, I. (1980).
  Sekundaire analyse van de "Van jaar tot jaar data" met behulp van niet-lineaire multivariate technieken: Verschillen in de schoolloopbaan van meisjes en jongens. Research Bulletin, RB 001-80, Department of Data Theory, University of Leiden, Leiden, The Netherlands.
  As part of a reanalysis of the data from a longitudinal study of the school and vocational carreer of Dutch children, TUCKALS2 (Kroonenberg & De Leeuw, 1977, 1980, 1981c) was applied. Also the merits of the technique in relation to INDSCAL, and some problems with the preliminary version of the program were discussed. The data consisted of correlation matrices (boys and girls, resp.) based on 26 variables in the first analysis and of 7 correlation matrices (one for each occupational class of the father) based on the same 26 variables.

  

• Strordrange, L., Rajalahti, T, & Libnau, F. O. (2004).
  Multiway methods to explore and model NIR data from a batch process. Chemometrics and Intelligent Laboratory Systems, 70, 137-145.
  Multiway methods are tested for their ability to explore and model near-infrared (NIR) spectra from a pharmaceutical batch process. The study reveals that blocking of data having a nonlinear behaviour into higher-order array can improve the predictive ability. The variation in each control point is independently modelled and N-way techniques overcome the nonlinearity problem. Important issues as variable selection and how to fill in for missing values have been discussed. Variable selection was shown to be essential to be able to perform multiway modelling. For spectra not yet monitored, use of mean spectra from calibration set gave close to the best results. Decomposing the spectra by N-way techniques gave additional information about the chemical system. To support the results simulated data sets were used.

   

• Sundberg, R. (1999).
  Multivariate calibration - Direct and indirect regression methodology. Scandinavian Journal of Statistics, 26, 161-191.
  This paper tries first to introduce and motivate the methodology of multivariate calibration. Next a review is given, mostly avoiding technicalities, of the somewhat messy theory of the subject. Two approaches are distinguished: the estimation approach (controlled calibration) and the prediction approach (natural calibration). Among problems discussed are the choice of estimator, the choice of confidence region, methodology for handling situations with more variables than observations, near-collinearities (,vith countermeasures like ridge type regression, principal components regression, partial least squares regression and continuum regression), pretreatment of data, and cross-validation vs true prediction. Examples discussed in detail concern estimation of the age of a rhinoceros from its horn lengths (low-dimensional), and nitrate prediction in waste-water from high-dimensional spectroscopic measurements.

     

• Swartzman, L. C., Harshman, R. A., Burkell, J., & Lundy, M. E. (2002).
  What accounts for the appeal of complementary/alternative medicine, and what makes complementary/alternative medicine "alternative"? Medical Decision Making, 22, 431-150.
  The goal of this study was to elucidate the basis for the appeal of complementary/alternative medicine (CAM) and the basis upon which people distinguish between CAM and conventional medicine. Undergraduates (N = 173) rated 19 approaches to the treatment of chronic back pain on 16 rating scales. Data were analyzed via 3-mode factor analysis, which extracted conceptual dimensions common to both the scales and the treatments. A 5-factor solution was judged to give the best description of the raters' perceptions. One of these 5 factors clearly reflected the distinction between conventional versus CAM approaches, and a 2nd factor clearly referred to treatment appeal. The other 3 factors were invasiveness, health care professional versus patient effort, and "druglikeness." To the extent that treatment was seen as a CAM treatment (as opposed to a conventional treatment), it was seen to be more appealing, less invasive, and less druglike. Simple and partial correlations of the dimension weights indicated that both the appeal of CAM and the distinction between CAM and conventional medicine were largely driven by the view that CAM is less invasive than conventional medicine.

       

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