Three-Mode Abstracts, Part F

INDEX

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• Faber, N. M. (1999b).
  Note on the error analysis of the generalized rank annihilation method. Analytical Letters, 32, 2899-2906.
  The generalized rank annihilation method (gram) is a method for curve resolution and quantitation that uses two data matrices simultaneously, i.E., one for the unknown and one for the calibration sample. Requirements have been derived that ensure the unique resolution of the analyte of interest in the presence of unknown interferences if the data matrices are free from experimental error. In this paper, it is shown that the same requirements allow for correct determination of bias and variance in the quantitative results obtained by gram if the data matrices are not free from experimental error.

• Faber, N.M. (2000).
  Exact presentation of multivariate calibration model as univariate calibration graph. Chemometrics and Intelligent Laboratory Systems, 50, 107- 114.
  A proof is given that a recently introduced univariate presentation of a multivariate calibration model is exact, i.e., there are no approximations involved. The proof is based on: (1) previously proposed definitions of multivariate net analyte signal and multivariate calibration factors (sensitivity in classical model and inverse sensitivity in inverse model) and (2) the geometrical property of the true regression vector in inverse multivariate calibration that it must be proportional to the true multivariate net analyte signal vector of a particular sample. The extension of the proof to multiway calibration is briefly discussed. a practical example from near-infrared (NIR) spectroscopy is used to illustrate that the proposed univariate presentation may give more meaning to the term 'spectral overlap'.

• Faber, N.M. (2001).
  Comment on a recently proposed resampling method. Journal of Chemometrics, 15, 169-188.
  A recently introduced resampling method for determining the contribution of measurement errors to the standard error in bilinear and trilinear model estimates is critically examined. Using Monte Carlo simulations, it is shown that this method does not work as intended. A noise addition method is proposed as a generally applicable alternative. The principles involved in applied work are illustrated on real UV-vis data taken from the literature.
  
  
• Faber, N.M. (2001).
  The price paid for the second-order advantage when using the generalized rank annihilation method. Journal of Chemometrics, 15, 743-748.
  In a ground-breaking paper, Linder and Sundberg developed a statistical framework for the calibration of bilinear data (Chemometrics Intell. Lab. Syst. 1998; 42: 159-178). Within this framework they formulated three different predictor construction methods (J. Chemometrics accepted), namely a so-called naive method, a least squares (LS) method and a refined version of the latter that takes account of the calibration uncertainty. They showed that the naive method is statistically less efficient than the others under the assumption of white noise. In the current work a close relationship is established between the generalized rank annihilation method (GRAM) and the naive method by comparing expressions for prediction variance. The main conclusion is that the relatively poor efficiency of GRAM is the price one pays for obtaining the second-order advantage with a single calibration sample.

• Faber, N. M. (2002).
  Towards a rehabilitation of the generalized rank annihilation method (GRAM) Analytical and Bioanalytical Chemistry, 372, 683-687.
  The trilinear PARAFAC model occupies a central place in multiway analysis, because the components of a data array can often be uniquely resolved. This paper compares the resolution for a large variety of methods, namely the generalized rank annihilation method (GRAM), alternating least squares (ALS), alternating trilinear decomposition (ATLD), alternating coupled vectors resolution (ACOVER), alternating slice-wise diagonalization (ASD), alternating coupled matrices resolution (ACOMAR), self-weighted alternating trilinear decomposition (SWATLD), and pseudo alternating least squares (PALS). The comparison was conducted using Monte Carlo simulations. It was shown that GRAM performs well for moderately and highly overlapped data. These results argue strongly against the previously claimed superiority of the alternatives listed above.

• Faber, N.M., & Bro, R. (2002).
  Standard error of prediction for multiway PLS: 1. Background and a simulation study. Chemometrics and Intelligent Laboratory Systems, 60, 133-149.
  While a multitude of expressions has been proposed for calculating sample-specific standard errors of prediction when using partial least squares (PLS) regression for the calibration of first-order data, potential generalisations to multiway data are lacking to date. We have examined the adequacy of two approximate expressions when using unfold- or tri-PLS for the calibration of second-order data. The first expression is derived under the assumption that the errors in the predictor variables are homoscedastic, i.e., of constant variance. In contrast, the second expression is designed to also work in the heteroscedastic case. The adequacy of the approximations is tested using extensive Monte Carlo simulations while the practical utility is demonstrated in Part 2 of this series.

• Faber, N.M., Bro, R. & Hopke P.K. (2003)
  Recent developments in CANDECOMP/PARAFAC algorithms: a critical review. Chemometrics and Intelligent Laboratory Systems65 119-137.
  Several recently proposed algorithms for fitting the PARAFAC model are investigated and compared to more established alternatives. Alternating least squares (ALS), direct trilinear decomposition (DTLD), alternating trilinear decomposition (ATLD), self-weighted alternating trilinear decomposition (SWATLD), pseudo alternating least squares (PALS), alternating coupled vectors resolution (ACOVER), alternating slice-wise diagonalization (ASD) and alternating coupled matrices resolution (ACOMAR) are compared on both simulated and real data. For the recent algorithms, only unconstrained three-way models can be fitted. In contrast, for example, ALS allows modeling of higher-order data, as well as incorporating constraints on the parameters and handling of missing data. Nevertheless, for three-way data, the newer algorithms are interesting alternatives. It is found that the ALS estimated models are generally of a better quality than any of the alternatives even when overfactoring the model, but it is also found that ALS is significantly slower. Based on the results (in particular the poor performance of DTLD), it is advised that (a slightly modified) ASD may be a good alternative to ALS when a faster algorithm is desired. (C) 2002 Elsevier Science B.V. All rights reserved.

• Faber, N.M., Buydens, L.M.C., & Kateman, G. (1993).
  Standard errors in the eigenvalues of a cross-product matrix: Theory and applications. Journal of Chemometrics, 7, 495-526.
  New expressions are derived for the standard errors in the eigenvalues of a cross-product matrix by the method of error propagation. Cross-product matrices frequently arise in multivariate data analysis, especially in principal component analysis (PCA). The derived standard errors account for the variability in the data as a result of measurement noise and are therefore essentially different from the standard errors developed in multivariate statistics. Those standard errors were derived in order to account for the finite number of observations on a fixed number of variables, the so-called sampling error. They can be used for making inferences about the population eigenvalues. Making inferences about the population eigenvalues is often not the purposes of PCA in physical sciences. This is particularly true if the measurements are performed on an analytical instrument that produces two-dimensional arrays for one chemical sample: The rows and columns of such a data matrix cannot be identified with observations on variables at all. However, PCA can still be used as a general data reduction technique, but now the effect of measurement noise on the standard errors in the eigenvalues has to be considered. The consequences for significance testing of the eigenvalues as well as the usefulness for error estimates for scores and loadings of PCA, multiple linear regression (MLR) and the generalized rank annihilation method (GRAM) are discussed. The adequacy of the derived expressions is tested by Monte Carlo simulations.

• Faber, N.M., Buydens, L.M.C., & Kateman, G. (1994a).
  Generalized rank annihilation method. I: Derivation of eigenvalue problems. Journal of Chemometrics, 8, 147-154.
  Rank annihilation factor analysis (RAFA) is a method for multicomponent calibration using two data matrices simultaneously, one for the unknown and one for the calibration sample. In its most general form, the generalized rank annihilation method (GRAM), an eigenvalue problem has to be solved. In this first paper different formulations of gram are compared and a slightly different eigenvalue problem will be derived. The eigenvectors of this specific eigenvalue problem constitute the transformation matrix that rotates the abstract factors from principal component analysis (PCA) into their physical counterparts. This reformulation of GRAM facilitates a comparison with other PCA-based methods for curve resolution and calibration. Furthermore, we will discuss two characteristics common to all formulations of gram, i.e. The distinct possibility of a complex and degenerate solution. It will be shown that a complex solution-contrary to degeneracy-should not arise for components present in both samples for model data.

• Faber, N.M., Buydens, L.M.C., & Kateman, G. (1994b).
  Generalized rank annihilation method. II: Bias and variance in the estimated eigenvalues. Journal of Chemometrics, 8, 181-203.
  Rank annihilation factor analysis (RAFA) is a method for multicomponent calibration using two data matrices simultaneously, one for the unknown and one for the calibration sample. In its most general form, the generalized rank annihilation method (GRAM), an eigenvalue problem has to be solved. In this second paper expressions are derived for predicting the bias and variance in the eigenvalues of GRAM. These expressions are built on the analogies between a reformulation of the eigenvalue problem and the prediction equations of univariate and multivariate calibration. The error analysis will also be performed for Lorber's formulation of RAFA. It will be demonstrated that, depending on the size of the eigenvalue, large differences in performance must be expected. A bias correction technique is proposed that effectively eliminates the bias if the error in the bias estimate is not too large. The derived expressions are evaluated by Monte Carlo simulations. It is shown that the predictions are satisfactory up to the limit of detection. The results are not sensitive to an incorrect choice of the dimension of the factor space.

• Faber, N.M., Buydens, L.M.C., & Kateman, G. (1994c).
  Generalized rank annihilation method. III: Practical implementation. Journal of Chemometrics, 8, 273-285.
  In this paper we discuss the practical implementation of the generalized rank annihilation method (GRAM). The practical implementation comes down to developing a computer program where two critical steps can be distinguished: The construction of the factor space and the oblique rotation of the factors. The construction of the factor space is a least-squares (LS) problem solved by singular value decomposition (SVD), whereas the rotation of the factors is brought about by solving an eigenvalue problem. In the past several formulations for GRAM have been published. The differences essentially come down to solving either a standard eigenvalue problem or a generalized eigenvalue problem. The first objective of this paper is to discuss the numerical stability of the algorithms resulting from these formulations. It is found that the generalized eigenvalue problem is only to be preferred if the construction of the factor space is not performed with maximum precision. This is demonstrated for the case where the dominant factors are calculated by the non-linear iterative partial least-squares (NIPALS) algorithm. Several performance measures are proposed to investigate the numerical accuracy of the computed solution. The previously derived bias and variance are proposed to estimate the number of physically significant digits in the computed solution. The second objective of this paper is to discuss the relevance of theoretical considerations for application of gram in the presence of model errors.

• Faber, N.M., Ferreé, J., & Boqué, R. (2001).
  Iteratively reweighted generalized rank annihilation method 1. Improved handling of prediction bias. Chemometrics and Intelligent Laboratory Systems, 55, 67-90.
  The generalized rank annihilation method (CRAM) is a method for curve resolution and calibration that uses two bilinear matrices simultaneously, i.e., one for the unknown and one for the calibration sample. A GRAM calculation amounts to solving an eigenvalue problem for which the eigenvalues are related to the predicted analyte concentrations. Previous studies have shown that random measurement errors bring about a bias in the eigenvalues, which directly translates into prediction bias. In this paper, accurate formulas are derived that enable removing most of this bias. Two bias correction methods are investigated. While the first method directly subtracts bias from the eigenvalues obtained by the original GRAM, the second method first applies a weight to the data matrices to reduce bias. These weights are specific for the analyte of interest and must be determined iteratively from the data. Consequently, the proposed modification is called iteratively reweighted GRAM (IRGRAM). The results of Monte Carlo simulations show that both methods are effective in the sense that the standard error in the bias- corrected prediction compares favourably with the root mean squared error (RMSE) that accompanies the original quantity. However, IRGRAM is found to perform best because the increase of variance caused by subtracting bias is minimised, In the original formulation of GRAM only a single calibration sample is exploited. The error analysis is extended to cope with multiple calibration samples. (C) 2001 Elsevier Science B.V. All rights reserved.

• Faber, N.M., Ferreé, J., Boqué, R. & Kalivas, J. H. (2002).
  Second-order bilinear calibration: the effects of vectorising the data matrices of the calibration set. Chemometrics and Intelligent Laboratory Systems, 63, 107-116.
  In a groundbreaking paper, Linder and Sundberg [Chemometr. Intell. Lab. Syst. 42 (1998) 159] developed a statistical framework for the calibration of second-order bilinear data. Within this framework, they formulated three different predictor construction methods [J. Chemom. 16 (2002) 12], namely the so-called naive method, the bilinear least squares (BLLS) method, and a refined version of the latter that takes account of the calibration uncertainty. Elsewhere [J. Chemom. 15 (2001) 743], a close relationship is established between the naive method and the generalized rank annihilation method (GRAM) by comparing expressions for prediction variance. Here it is proved that the BLLS method can be interpreted to work with vectorised data matrices, which establishes an algebraic relationship with so-called unfold partial least squares (PLS) and unfold principal component regression (PCR). It is detailed how these results enable quantifying the effects of vectorising bilinear second-order data matrices on analytical figures of merit and variance inflation factors. (C) 2002 Elsevier Science B.V. All rights reserved.

• Faber, N.M., Ferreé, J., Boqué, R. & Kalivas, J. H. (2003).
  Quantifying selectivity in spectrophotometric multicomponent analysis. Trac-trends in Analytical Chemistry, 22, 352-361.
  According to the latest recommendation of the International Union of Pure and Applied Chemistry, "selectivity refers to the extent to which the method can be used to determine particular analytes in mixtures or matrices without interferences from other components of similar behavior". Because of the prime importance of selectivity as an analytical figure of merit, numerous proposals have been published on how to quantify it in spectrophotometric multicomponent analysis. We show that the criterion independently developed by Lorber [11,12] and Bergmann, von Oepen and Zinn [13] is the most suitable, because it directly relates to prediction uncertainty and allows for a consistent generalization to more complex systems of chemical analysis. (C) 2003 Published by Elsevier Science B.V.

• Faber, N.M., Lorber, A., & Kowalski, B.R. (1997a).
  Analytical figures of merit for tensorial calibration. Journal of Chemometrics, 11, 419-461.
  The subject of analytical figures of merit for tensorial calibration is critically reviewed. Tensorial calibration derives its name from tensor algebra, which provides a classification of calibration methods depending on the complexity of the data obtained for one chemical sample. Expressions for net analyte signal, sensitivity (classical model formulation), 'inverse sensitivity' (inverse model formulation), selectivity, signal-to-noise ratio and limit of detection (in signal space) are proposed for Nth-order data (N greater than or equal to 2) that are consistent with the accepted zeroth-order definitions and previously proposed definitions for first-order data. Useful relationships between the proposed figures of merit and prediction error variance are described. A selectivity-based rule of thumb is derived to compare data analysis across orders. Central to the currently proposed framework for analytical figures of merit is the reduction of a complex data structure to the scalar net analyte signal. This allows for the construction of a univariate calibration graph (classical or inverse model), independent of the complexity of the data. Enhanced visualization and interpretation are obtained that may help to bridge the gap between Nth-order calibration and the intuitive understanding of zeroth-order data. (c) 1997 John Wiley & Sons, Ltd.

• Faber, N.M., Lorber, A., & Kowalski, B.R. (1997b).
  Generalized rank annihilation method: Standard errors in the estimated eigenvalues if the instrumental errors are heteroscedastic and correlated. Journal of Chemometrics, 11, 95-109.
  The generalized rank annihilation method (GRAM) is a method for curve resolution and calibration that uses two data matrices simultaneously, i.e. One for the unknown and one for the calibration sample. The method is known to become an eigenvalue problem for which the eigenvalues are the ratios of the concentrations for the samples under scrutiny. Previously derived standard errors in the estimated eigenvalues of GRAM have very recently been shown to be based on unrealistic assumptions about the measurement errors. In this paper a systematic notation is introduced that enables the propagation of errors that are based on realistic assumptions concerning the data-generating process. The error propagation will be performed in detail for the case that one data order modulates the second one. Extensions to more complicated error models are indicated. (c) 1997 by John Wiley & Sons, Ltd.

• Faber, N.M., Meinders, M.J., Geladi, P., Sjöström, M., Buydens, L.M.C., & Kateman, G. (1995).
  Random error bias in principal component analysis. Part II. Application of theoretical predictions to multivariate problems. Analytica Chimica Acta, 304, 273-283.
  In the first part of this paper expressions were derived for the prediction of random error bias in the eigenvalues of principal component analysis (PCA) and the singular values of singular value decomposition (SVD). The main issues of Part I were to investigate the question whether adequate prediction of this bias is possible and to discuss how the validation and evaluation of these predictions could proceed for a specific application in practice. The main issue of this second part is to investigate how random error bias should be taken into account. This question will be treated for a number of seemingly disparate multivariate problems. For example, the construction of confidence intervals for the bias-corrected quantities will be discussed with respect to the estimation of the number of significant principal components. The consequences of random error bias for calibration and prediction with ordinary least squares (OLS), principal component regression (PCR), partial least squares (PLS) and the generalized rank annihilation method (GRAM) will also be outlined. Finally, the derived bias expressions will be compared in detail with the corresponding results for OLS and GRAM.

• Fabricius, W. V., Nagoshi, C. T., & Mackinnon, D. P. (1997).
  Concepts of drugs: differences in conceptual structure across groups with different levels of drug expercience. Addiction, 92, 847-858.
  Seventy seven college students varying in degree of drug use experience rated the perceived similarities of all possible combinations of 16 drug classes (cigarettes, other tobacco, alcohol, marijuana, barbiturates, minor and major tranquilizers, amphetamines, amphetamine derivatives, cocaine, heroin, opiates, hallucinogens, inhalants, PCP, anti depressants). Multi dimensional scaling (INDSCAL) and network models (PFNET) indicated that abstainers had only one pharmacological category involving sedatives/depressants, and that they attached more importance to whether drugs were licit vs. illicit than to whether they were depressants vs. stimulants. Conceptions became more coherent, differentiated and based on pharmacological properties for more experienced drug users. In line with previous work, groups with greater experience with drugs had more sophisticated conceptions not only about the drugs they had used, but also about drugs they had not used These findings suggest that early on in drug behavior sophisticated and interrelated concepts are developing that should be taken into account when designing interventions and information campaigns.

• Fabrizius, M.A., Cooper, M., & Basford, K.E. (1997).
  Genetic analysis of variation for grain yield and protein concentration in two wheat crosses. Australian Journal of Agricultural Research, 48, 605- 614.**
  Grain yield and protein concentration are two of the more important criteria for wheat breeding in Queensland. Three aspects of the inheritance of both of these traits can have an impact on achieving genetic progress: (i) the magnitude and form of the genetic correlation between the traits, (ii) the magnitude of genetic variation and genotype × environment interactions, and (iii) the importance of epistasis in genetic variation. These 3 factors were examined for 2 crosses in a multi-environment trial conducted in Queensland in 1989. Negative genetic correlations were found between. Grain yield and protein concentration in both crosses. Genetic variation and genotype × environment interactions were found to be important for both traits. There was little evidence for the existence of significant additive × additive epistasis for either trait and the genotype × environment interactions were predominantly additive × environment in nature. From both crosses, progeny combining the high yield and high protein levels of the parents were identified. This suggests that there was a degree of independent segregation of the genes controlling grain yield and protein concentration in both crosses. Therefore, simultaneous genetic progress for yield and protein concentration is possible in Queensland environments.

• Fachin, S., Shea, D. G., & Vichi, M. (2002).
  Exploring 3D datasets: a factorial matrices analysis of the US industry in the 1980s. Applied Economics, 34, 295-304.
  In this paper a Factorial Matrices technique suitable for exploratory analysis of multivariate, disaggregated time series is presented and applied to a data set covering 19 US manufacturing industries over the years 1979 to 1990. The empirical analysis confirms that the technique is a powerful tool, allowing otherwise difficult extraction of stylized facts from multidimensional datasets. In this case: (i) there are no signs of deindustrialization induced by growing import penetration, and, (ii), employment decline has generally not been associated to substitution of capital to labour.

• Fah, D., & Koch, K. (2002).
  Discrimination between earthquakes and, chemical explosions by multivariate statistical analysis: A case study for Switzerland. Bulletin of the Seismological Society of America, 92, 1795-1805.
  A data set of 43 confirmed earthquakes and 42 explosions (1.3 +/- M-L less than or equal to 3.8) is analyzed by multivariate statistical analysis. The explosion events include quarry blasts and explosions detonated for seismic experiments as well as an explosion of an ammunition storage site. The events of this training data set are mainly located in the Alpine mountains and Central Switzerland, with the seismic sources having excellent distance (R < 300 km) and azimuthal coverage for the recording stations. Multivariate statistical analysis is used to derive general discriminant functions based on regional waveform data for the training set. The discriminant functions are then tested for consistency on the events of the training data set, with the result that 97% of these events are correctly identified by the multivariate discriminant functions. Of the total training data set, 17% is classified as ambiguous cases, based on marginal discriminant functions. The method is subsequently applied to an extended data set including nighttime events from 1992-1996, which are hence regarded as earthquakes, and a set of presumed explosions from the years 1984-1997. For Central Switzerland, the events of the extended data set can clearly be identified with the discriminant functions derived from the training data set. The identification rate is lower for other regions in Switzerland, which can be related to tectonic units. For these regions, considered to have a laterally homogeneous crust, a linear correction term in the discriminant function providing for station corrections can be found that significantly decreases the misidentification rate.

         

• Ferreira, M. M. C. (2003).
  Multivariate QSAR. Journal of the Brazilian Chemical Society, 13, 742-753.
  In this work, the chemometric techniques most frequently used in QSAR (quantitative structure-activity relationships) studies are reviewed. They are introduced in chronological order, beginning with Hansch analysis and the exploratory data analysis methods of principal components and hierarchical clustering (PCA and HCA). Principal component regression and partial least squares regression methods (PCR and PLS) are discussed, followed by the pattern recognition methods (KNN and SIMCA). Different applications are presented to illustrate these chemometric techniques. The methodology used for regression in 3D-QSAR is presented ( unfolding PLS). Finally, the higher order method called Multilinear PLS, already used in analytical chemistry but not yet explored by the QSAR community, is introduced. This method maintains the multiway structure of the data and has several advantages over bilinear PLS including speed in calculation, simplicity and stability, since the number of parameters to be estimated can be greatly reduced.

• Ferreira, M.M.C., Brandes, M.L., Ferreira, I.M.C., Booksh, K.S., Dolowy, W.C., Gouterman, M., & Kowalski, B.R. (1995).
  Chemometric study of the fluorescence of dental calculus by trilinear decomposition. Applied Spectroscopy, 49, 1317-1325.
  Chemometric techniques have been applied to the unresolved second-order porphyrinic emission-excitation fluorescent spectra of several animal dental calculus deposits dissolved in HCl. A singular value decomposition (SVD) procedure was used for preliminary indication of the number of fluorescent species present in the samples. The trilinear decomposition (TLD) method was applied to resolve component spectra, resulting in three porphyrinic spectral profiles for both canines and felines.

• Ferrer, R., Beltrán, J. L., & Guiteras, J. (1999).
  Multivariate calibration applied to synchronous fluorescence spectrometry. Simultaneous determination of polycyclic aromatic hydrocarbons in water samples. Talanta, 45, 1073-1080.
  Synchronous fluorescence spectra of mixtures containing ten polycyclic aromatic hydrocarbons (anthracene, benz[a]anthracene, benzo[a]pyrene, chrysene, fluoranthene, fluorene, naphthalene, perylene, phenanthrene and pyrene) have been used for the determination of these compounds by Partial Least Squares Regression (PLSR), using both PLS-1 and PLS-2. Different procedures have been used for the pretreatment of the data in order to obtain better models, and the size of the calibration matrix has also been studied. The best models have been used for the determination of the above mentioned PAHs in spiked natural water samples at concentration levels between 4 and 20 ng ml(-1). Recoveries ranged from 80 to 120% in most cases, although fluorene gave significantly lower results.

• Ferrer, R., Guiteras, J. & Beltrán, J.L. (1999).
  Artificial neural networks (ANNs) in the analysis of polycyclic aromatic hydrocarbons in water samples by synchronous fluorescence. Analytica Chimica Acta, 384, 261-269.
  Backpropagation artificial neural networks, principal component regression and partial least squares have been compared in order to establish the best multivariate calibration models for the analysis of mixtures of polycyclic aromatic hydrocarbons containing 10 of these compounds (anthracene, benz[a]anthracene, benzo[a]pyrene, chrysene, fluoranthene, fluorene, naphthalene, perylene, phenanthrene and pyrene). The synchronous fluorescence spectra (recorded at wavelength increments of 50 and 100 nm) of 85 standards, with concentrations ranging from 0 to 20 ng ml^-1, have been used for this purpose.

         

• Fillipan, N., Bezemer, E., Burke, J., & Rutan, S. C. (2004).
  Studies of liquid-phase complexes in acetonitrile/water solutions by attenuated total reflection infrared spectroscopy with acetaldehyde as a model solute. Applied Spectroscopy, 58, 1187-1194.
  Chemometric methods combined with infrared (IR) spectroscopy, using attenuated total reflectance (ATR) sampling, are employed here to characterize the stoichiometry of complexes of solvent molecules in the liquid phase. The spectral information provides insight into the liquid microstructure present in liquid chromatographic mobile phases. This information should make it easier to understand and predict the effects of changes in mobile phase composition on the results of chromatographic separations. In this paper, mobile phases consisting of 0 mol % to 100 mol % acetonitrile in water were studied, with the addition of acetaldehyde as a model solute at concentrations ranging from 3 to 8 mol %. Using three-way multivariate curve resolution by the alternating least squares method (MCR-ALS) it was possible to resolve eight unique spectra: four mobile phase components, and four unique spectra of acetaldehyde solvated in different environments. The directions of the shifts of the important acetaldehyde infrared bands show good correlation with those predicted by gas-phase ab initio calculations of small solvated clusters.

• Field, A.S, & Graupe, D. (1991)
  Topographic component (parallel factor) analysis of multichannel evoked potentials: practical issues in trilinear spatiotemporal decomposition. Brain Topography, 3, 407-423.
  An application of PARAFAC (called the trilinear topographic components model (after Möcks 19**) to the decomposition of multichannel evoked potentials (MEP's). Practical guidelines and procedures for applying PARAFAC to MEP decomposition are provided. Preprocessing, orthogonality constraints, and validation of solutions in a complete PARAFAC analysis were used for the first time using actual MEP data. The PARAFAC model is shown to be superior to the traditional bilinear principal components model in terms of data reduction, confirming the advantage of PARAFAC added assumptions. The model is then shown to provide a unique spatiotemporal decomposition that is reproducible in different subject groups. The components are shown to be consistent with spatial/temporal features evident in the data, except for an artificial component resulting from latency jitter. Subject scores on this component are shown to reflect peak latencies in the data, suggesting a new aspect to statistical analyses based on subject scores. In general, the results support the conclusion that the PARAFAC model is a promising alternative to principal components for data reduction and analysis of MEP's.

  

• Firth, P.M. & Snyder Jr, C.W. (1979).
  Three-mode factor analysis of self-reported difficulty in assertiveness. Australian Journal of Psychology, 31, 125-135.
  Difficulty in Assertiveness Inventory (Leah et al., 1979). Tucker's Method III (1966) with image factor analysis is used. Replication of Leah's results on students and hospital workers. Referent and response class factors similar, individual differences and core matrix far less so.

• Fischel, J.E. (1982).
  The organization of human newborn sucking and movement during auditory stimulation. Infant Behavior and Development, 5, 45-61.
  Many of the newborn human's earliest interactions occur during episodes of sucking, but there is little understanding of how sucking may interact with responsiveness to other social and physical stimuli. In the present study, levels of body movement, or activity, and characteristics of nonnutritive sucking were evaluated for two groups of newborns; one receiving brief presentations of a complex sound as they initiated sucking bursts, and a second group receiving the same sound during pauses between their suking bursts. A control group for comparison received no sound stimulation. Infants stimulated during pausing showed significantly higher activity levels and more rapid habituation of movement than those stimulated during bursting. Sound during bursting was less likely to cause a shift to pausing than sound during pausing was to cause a shift to sucking. These differences suggested that bursting and pausing were not similar contexts for responding to sound stimulation. Potential mechanisms underlying differential responsiveness during sucking are suggested.

  
       

• Flaten, G. R., Grung, B., & Kvalheim, O. M. (2004).
  Quantification of pollution levels by multiway modelling. Journal of Chemometrics,18, 173-182.
  Environmental surveys are performed regularly in environmental monitoring of possible industrial pollution. The seabed pollution from industry in or near water, e.g. offshore oil production, can be biologically monitored as benthic species, and their diversity can be used as indicators of pollution. The community disturbance index (CDI) was recently proposed as a quantitative measure of pollution calculated from the benthic data. However, the CDI and other measurements are not optimal for quantifying the changes in level of environmental stress over several years. In this work it is suggested that the total environmental stress over several monitoring surveys can be determined by modelling the natural variation for a set of non-polluted sites. The suggested approach uses a multiway method (Tucker3) to describe the natural variation, and the three-way extension of CDI to quantify the pollution. Implicitly, the traditional soft independent modelling of class analogies (SIMCA) classification is extended to its three-way counterpart. The proposed method is tested on the data from four subsequent surveys performed at the North Sea oil field Embla.

• Flores-Cerrillo, J., & MacGregor, J.F. (2004).
  Multivariate monitoring of batch processes using batch-to-batch information. Aiche Journal, 50, 1219-1228.
  Multiway principal component analysis (MPCA) and multiway partial-least squares (MPLS) are well-established methods for the analysis of historical data from batch processes, and for monitoring the progress of new batches. Direct measurements made on prior batches can also be incorporated into the analysis by monitoring with multiblock methods. An extension of the multiblock MPCA/MPLS approach is introduced to explicitly incorporate batch-to-batch trajectory information summarized by the scores of previous batches, while keeping all the advantages and monitoring statistics of the traditional MPCA/MPLS. However, it is shown that the advantages of using information on prior batches for analysis and monitoring are often small. Its main advantage is that it can be useful for detecting problems when monitoring new batches in the early stages of their operation., the approach and benefits are illustrated with condensation polymerization and emulsion polymerization systems, as examples.

• Flôres Jr, R.G. (1988b).
  Classical approaches to cubic tables. Cahiers du Centre d'Etudes et de Recherche Opérationelle, 30, 39-46.
  This paper presents two methods for the exploratory analysis of cubic tables. Emphasis is given to the modelling stages involved in these and similar techniques, what motivates the concept of symmetric and asymmetric procedures. The information losses at each stage are evaluated, for both methods, in terms of chi-square differences. A discussion with other existing viewpoints and a brief example are also included.

• Flury, B.N. (1984).
  Common principle components in k groups. Journal of the American Statistical Association, 79,892-898. This article generalizes the method of principal components to so-called "common principal components" as follows: Consider the hypothesis that the covariance matrices sigma_i for k populations are simultaneously diagonalizable. That is, there is an orthogonal matrix beta such that beta'sigma_ibeta is diagonal for i = 1,..., k. I derive the normal-theory maximum likelihood estimates of the common component sigma_i matrices and the log-likelihood-ratio statistics for testing this hypothesis. The solution has some favorable properties that do not depend on normality assumptions. Numerical examples illustrate the method. Applications to data reduction, multiple regression, and nonlinear discriminant analysis are sketched.

• Flury, B. (1990).
  Principal points. Biometrika, 77, 33-41.
  The k principal points of a p-variate random variable X are defined as those points Ea,....,Ek wich minimize the espected squared distance of X from the hearest of the Ej. This paper presents result on the principal points of univariate symmetric distributions, the univariate and bivariate normal distribution, multivariate elliptical distributions, and multivariate distributions in general. In the cases of normal and elliptical distributions, the relationship between principal points and principal components is studied.

       

• Foss, M.A., Fabiani, M., Mane, A.M., & Donchin, E. (1989).
  Unsupervised practice: The performance of the control group. Acta Psychologica, 71, 23-51.
  40 male university students practiced the Space Fortress game, a task used to examine acquisition of complex skills previously described by Mane and Donchin, for 10 1-hr sessions. Performance data were evaluated using three-mode principal component analysis. Ss showed a general improvement in performance throughout training; however, individual differences were found in the Ss' initial capacity, in their rate of learning, and in the strategies they adopted to achieve their final performance.

  

• Foucart, Th. (1985a).
  Application de l'analyse factorielle des correspondances. [Application of correspondence factor analysis]. Statistique et Analyse de Données, 10, 54-64.
  The method used here to describe a sequence of boards is based upon Correspondence Factor Analysis. First we will explain particular procedures we have had to use, and second we will present the result obtained with this method in the analysis of the common data.

• Foucart, Th. (1985b).
  Application de la méthode RAS. [Application of the RAS method] Statistique et Analyse de Données, 10, 65-82.
  The algorithm RAS is a classical method to adjust a table to fixed margins. We generalize it to describe a sequence of boards, each of them being adjusted to the margins of the next one and use this approach to study common data.

  
       

• Franc, A. (1989).
  Multiway arrays: Some algebraic remarks. In R. Coppi & S. Bolasco (Eds.), Multiway data analysis (pp. 19-29). Amsterdam: Elsevier.
  This paper is divided into three parts: * First, the main good properties that underly PCA are recalled. * Second, some PCA techniques for three-way arrays are looked on as PCA of linear maps nested on a particaular lattice structure on the tensor algebra. This is easily extended to n-way arrays. * Third: some of the choices to be done to keep some good properties of PCA for its extension to three way arrays are sketched out on examples.

• Frederiksen, N. (1972).
  Toward a taxonomy of situations. American Psychologist, 27, 114-123.
  F. cites in some detail T3 research of Levin (1965), Tucker (1964) and Frederikson et al. (1972).

• Frederiksen, N., Jensen, O. & Beaton, A.E. (1972).Prediction of organizational behavior. Elmsford N.Y.: Pergamon Press.
  As part of a project to study the performance of managers in various work situations, the performance of 118 subjects was scored on 11 composite performance variables for each of 37 'in-basket' items. Although an in-depth discussion is given of the substantive results (after equimax rotations to simple structure of the factor matrices). The methodological informa- tion is rather scanty.

  

• Frenich, A. G., Galera, M. M., Vidal, J. L. M., Massart, D. L., Torres-Lapasio, J. R., De Braekeleer, K., Wang, J. H., & Hopke, P. K. (2000).
  Resolution of multicomponent peaks by orthogonal projection approach, positive matrix factorization and alternating least squares. Analytica Chimica Acta, 411, 145-155.
  The application of orthogonal projection approach (OPA), alternating least squares (ALS), and positive matrix factorization (PMF) to resolve HPLC-DAD data into individual concentration profiles and spectra is discussed. OPA was initially described as a purity method but the inclusion of an ALS procedure allows its application as a curve resolution method. PMF is a least square approach to factor analysis that in this study has been used as a tool to tackle the problem of curve resolution. OPA, ALS and PMF have been applied using a single matrix (two-way data) or an augmented matrix containing several data matrices simultaneously. The results obtained with the different resolution methods are compared and evaluated using measures of dissimilarity between the real and the estimated spectra. The study is performed in three data subsets, obtained by segmentation of the original data matrix. Within each data subset, there is a reduced number of species present which makes the resolution easier.

• Frenich, A. G., Galera, M. M., Garcia, M. D. G., Vidal, J. L. M., Catasus, M., Marti, L., & Mederos, M. V.(2001).
  Resolution of HPLC-DAD highly overlapping analytical signals for quantitation of pesticide mixtures in groundwater and soil using multicomponent analysis and neural networks. Journal of Liquid Chromatography & Related Technologies, 24, 651-668.
  Along with the development of hyphenated chromatography techniques, such as high performance liquid chromatography (HPLC) with diode array detection (DAD), three-dimensional data matrix for each sample can be easily obtained. In this paper, a comparative study of three methods using this type of data is presented. The capabilities of inverse calibration through ordinary least squares (OLS), partial least squares (PLS), and an artificial neural network (ANN) model, have been investigated for the simultaneous multicomponent analysis of synthetic mixtures of iprodione, procymidone, chlorothalonil, folpet, and triazophos when highly overlapping analytical signals are present. Also, the methods have been satisfactorily applied to the determination of the pesticides in groundwater and soil samples, although the ANN gave the best results.

• Frenich, A.G., Zamora, D.P. Galera, M.M. & Vidal, J.L.M.
  Application of GRAM and TLD to the resolution and quantitation of real complex multicomponent mixtures by fluorescence spectroscopy Analytical and Bioanalytical Chemistry, 375, 974-980.
  The application of the generalised rank annihilation method (GRAM) and the trilinear decomposition (TLD) method to the resolution and quantitation of fluorescence excitation-emission matrices of a ternary mixture of pesticides, carbendazim, fuberidazole, and thiabendazole, with overlapped spectra is described. The results obtained with both methods are compared and evaluated using measures of similarity (correlation coefficients) between the real and estimated spectra. Both approaches have been tested using augmented data matrices containing only two samples, but none of these methods succeeded completely in resolution of the system. When TLD was applied to augmented data matrices containing more than two samples better performance was achieved. To illustrate the application of both algorithms to real samples, they were used in the analysis of water samples containing the target pesticides. Again, TLD had an advantage over GRAM because the ability to analyse data from multiple (more than two) samples simultaneously allowed the resolution of the mixtures.

• Frenich, A. G., Vidal, J. L. M., & Galera, M. M.(1999).
  Use of the cross-section technique linked with multivariate calibration methods to resolve complex pesticide mixtures. Analytical Chemistry, 71, 4844-4850.
  The potential of the cross-section (CS) approach in combination with the partial least squares (PLS) and principal component regression (PCR)was assessed in the resolution of a complex pesticide mixture showing twelve overlapped components in High Performance Liquid Chromatography with Diode Array Detection (HPLC-DAD). Careful selection of the CS through the three-dimensional (3D) (A, lambda, t) data matrix gave two-dimensional (2D) signals with the best sensitivity for the determination of each pesticide. In all cases, the application of the PLS method demonstrated a better quantitative prediction ability than that of the PCR method. The CS-PLS approach is a powerful analytical tool. Ten pesticides were well-resolved, while for the other two pesticides of the mixture prediction ability was poor, and they could not be determined, probably due to their low net analytical signal. The CS-PLS model was evaluated by predicting the concentrations of independent test set samples. Finally, the proposed model was successfully applied for the determination of these pesticides in groundwater.

  
  

• Frisvad, J. C. (1994).
  Correspondence, principal coordinate and redundancy analysis used on mixed chemotaxonomical qualitative and quantitave data. Chenometrics and Intelligent Laboratory Systems, 23, 213-229.
  A mixed type data matrix consisting of 11 quantitative carbohydrate variables and 23 binary secondary metabolites data measured in 5-8 isolates of 7 species of Penicillium was analyzed using different multivariate statistical methods. This kind of data matrix is common in numerical taxonomy and has formerly been analyzed by consensus methods based on the separate analysis of the quantitative and qualitative data matrix, by using Gower's general similarity coefficient for mixed data or by location models. For the initial data treatment the chi2, Bray-Curtis and Canberra distance coefficients were useful for cluster analysis and minimum spanning trees (MSTs) combined with principal coordinate analysis (PCO). The multivariate ordination methods hitherto recommended for chemotaxonomic data, principal component analysis (PCA) and its constrained ordination equivalent partial least squares (PLS) analysis (using dummy variables for each species) gave seven quite diffuse clusters with some overlap in two-dimensional ordination plots, while correspondence analysis (CA) gave seven very clear clusters. The results indicate that qualitative data strongly dominate quantitative data and that these qualitative data are best represented in plots by correspondence analysis. However, in physiological studies the quantitative data may be considered the most important, PCA and CA are preferred for the analysis of mixed data. Dummy constrained PLS may be used to select quantitative variables that are species specific rather than related to climatic conditions. In classification studies at the species level it is recommended to use cor-respondence analysis on mixed chemotaxonomical data. In the latter studies variables based on differentiation, such as the biosynthetic families of secondary metabolites used here, give clear species separations, and can be used for further cladistic analyses.

  
  

• Fruchter, B. (1969).
  A comparison of two-mode and three-mode factor analysis of psychomotor learning performance. In H. R. Wijngaarden (Pres.), Proceedings of the XVIth International Congress of Applied Psychology, (pp. 600-607). Amsterdam: Swets & Zeitlinger.
                 

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