Three-Mode Abstracts, Part Z

INDEX

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• Zampronio, C. G., Gurden, S. P., Moraes, L. A. B., Eberlin, M. N., Smilde, A. K., & Poppi, R. J. (2002).
  Direct sampling tandem mass spectrometry (MS/MS) and multiway calibration for isomer quantitation. Analyst, 127, 1054-1060.
  Direct sampling tandem mass spectrometry (MS/MS) was used for the quantitation of mixtures of the isomers 2-, 3- and 4-ethyl pyridine. The similarity between the analytes and the second-order nature of MS/MS data require the use of multivariate calibration techniques capable of handling multiway data. Multilinear PLS (N-PLS) was applied here, as well as the alternative technique of unfolding the data and using standard two-way PLS. Particular attention was paid to the optimal type of spectral preprocessing. Due to the presence of heteroscedastic noise the logarithmic transform of the spectra prior to calibration gives the best results. Predictions errors of the order of 10-15% were obtained, which compare well with other results found in the literature.

• Zarzo, M., & Ferrer, A. (2004).
  Batch process diagnosis: PLS with variable selection versus block-wise PCR. Chemometrics and Intelligent Laboratory Systems, 73, 15-27.
  Data from a batch chemical process have been analysed in order to diagnose the causes of variability of a final quality parameter. The trajectories of 47 process variables from 37 batches have been arranged in a matrix by using alignment methods. Two different approaches are compared to diagnose the key process variables: PLS with variable selection and block-wise PCR. The application of Unfold Partial Least Squares Regression (U-PLS) leads to one significant component. By means of weight plots, the variables most correlated with the final quality are identified. Nevertheless, with observed data, it is not possible to know if correlation is due to causality (and hence related to a critical point) or is due to other causes. Pruning PLS models by using variable selection methods and technical information of the process has allowed the process variables most correlated with the final quality to be revealed. The application of Principal Component Regression to the trajectories of the process variables (block-wise PCR) has given straightforward results without requiring a deep knowledge of the process. The results obtained have been used to propose several hypotheses about the likely key process variables that require a better control, as a previous step to conducting further studies for process diagnosis and optimisation, like experimental designs.

         

• Zeng, Y., & Hopke, P.K. (1990).
  Methodological study applying three-mode factor analysis to three-way chemical data sets. Chemometrics and Intelligent Laboratory Systems, 7, 237-250.
  A multivariate data analysis method, three-mode factor analysis (TMFA), has primarily been employed in the social sciences. Although it has not been extensively used in the natural sciences, TMFA provides the opportunity to examine data that are collected in form of a three-way matrix. With TMFA, one can simultaneously examine system variations in the three dimensions to determine the causal factors that control the system. This approach has been applied to the receptor modeling problem that attempts to relate ambient air quality to sources of pollution. By simulating an air pollution system, the relationships between the results of TMFA and the underlying physical model are investigated. In this way, the physical interpretation of the results of TMFA has been found. The model can be generalized to suit many three-way chemical data sets. It is also found that varimax rotation of the initially derived factors greatly improves their interpretability. The rotated solution can reflect the nature of the underlying physical system.

• Zeng, Y., & Hopke, P.K. (1992a).
  A new receptor model: A direct trilinear decomposition followed by a matrix reconstruction. Journal of Chemometrics, 6, 65-83.
  In many cases, monitoring data for ambient airborne particles can be organized in the form of a three-way data table with one way for chemical species, one for sampling periods and one for sites. A direct trilinear decomposition followed by a matrix reconstruction (DTDMR) is developed to analyze such a data table as a whole. The three-way data set is composed into three two-way matrices by a direct trilinear decomposition (DTD). The column vectors of each of the matrices are called 'source profiles', 'emission patterns' and 'site coefficients' respectively. Particulate sources are identified by examining both their source profiles and emission patterns. After the sources have been identified, emission patterns and site coefficients are used to produce a three-way matrix that gives estimates of mass contributions of sources to the samples collected at every site in every period. By simulation study, not only has the method been verified, but a good indicator has been found that shows the number of factors (i.e. Sources) in the system. Unlike other receptor models, DTDMR does not require source profile data and does not involve trial-and-error procedures. Since DTDMR identifies sources based on variations in two dimensions, it has a higher potential to distinguish two sources that have similar chemical compositions. The DTDMR model has provided excellent results with simulated data and has been applied in a real world three-way data set.

• Zeng, Y.S., & Hopke, P.K. (1992b).
  The application of three-mode factor analysis (TMFA) to receptor modeling of scenes particle data. Atmospheric Environment, 26A, 1701-1711.
  In the previous applications of eigenvector mathematical methods such as factor analysis, principal components analysis, and empirical orthogonal function analysis, the analysis has been made on a two-dimensional set of data. These data sets could be the chemical composition of a series of particle samples taken at a single location over time or the concentration of a single species measured over multiple locations at multiple times. However, there have not been methods previously available to examine a data set of chemical compositions measured at multiple sites over a series of sampling time intervals. Three-mode factor analysis permits the reduction of a three-dimensional data set into three two-dimensional matrices and a three-dimensional core matrix that presents how the system variance is partitioned among the three modes (chemical species, location and time). The technique will be illustrated with data from the scenes program that is measuring particle compositions at a number of sites in the southwestern united states.

• Zenisek, T.J. (1978).
  Three-mode factor analysis via a modification of Tucker's computational method-III. Educational and Psychological Measurement, 38, 787-792.
  Description of program based on Tucker's (1966) Method III for large data sets.

• Zenisek, T.J. (1980).
  The measurement of job satisfaction: a three-mode factor analysis. Unpublished doctoral thesis, Ohio State University. ( Dissertation Abstracts International, 1980, 41 (1-A), 75).
  Eight operational measures, each consisting of 23 common job facets were administered to 304 operatives, clerical and first line managers in four widely dispersed steel fabricating plants in order to replicate current finding the literature as well as test the efficacy of three-mode factor analysis as a data analytic technique.

  
       

• Zhang, T., & Golub, G.H. (2001).
  Rank-one approximation to high order tensors. Siam Journal on Matrix Analysis and Applications, 23, 534-550.
  The singular value decomposition (SVD) has been extensively used in engineering and statistical applications. This method was originally discovered by Eckart and Young (Psychometrika, 1 (1936), pp. 211-218), where they considered the problem of low-rank approximation to a matrix. A natural generalization of the SVD is the problem of low-rank approximation to high order tensors, which we call the multidimensional SVD. In this paper, we investigate certain properties of this decomposition as well as numerical algorithms.

• Zheng, Y. L., McAvoy, T. J., Huang, Y. B., & Chen, G. (2001).
  Application of multivariate statistical analysis in batch processes. Industrial & Engineering Chemistry Research, 40, 1641-1649.
  Multivariate statistical analysis methods such as principal component analysis (PCA) and partial least squares (PLS) are powerful tools for chemical process modeling and monitoring. This paper applies PCA/PLS techniques and their variants, multiway PCA/PLS and orthogonal PCA, to an industrial batch process. The study utilizes an existing large historical process data set and combines multivariate statistical methods with batch time optimization calculations to identify possibilities for process improvement. The objective is to increase throughput by shortening the batch reaction time. The batch time optimization calculations provide feasible setpoint operational suggestions while maintaining the underlying data correlation structure. A pseudo-setpoint approach is also proposed to investigate the reaction period during which the setpoint profiles remain constant. Results for an industrial reactor indicate that the batch time can be shortened by approximately 4.3%.

• Zheng L., Hasegawa-Johnson, M., & Pizza, S. (2003).
  Analysis of the three-dimensional tongue shape using a three-index factor analysis model. Journal of the Acoustical Society of America, 113, 478-486.
  Three-dimensional tongue shape during vowel production is analyzed using the three-mode PARAFAC (parallel factors) model. Three-dimensional MRI images of,five speakers (9 vowels) are analyzed. Sixty-five virtual fleshpoints (13 segments along the rostral-caudal dimension and 5 segments along the right-left direction) are chosen based on the interpolated tongue shape images. Methods used to adjust the alignment of MRI images, to set up the fleshpoints, and to measure the position of the fleshpoints are presented. PARAFAC analysis of this 3D coordinate data results in a stable two-factor solution that explains about 70% of the variance.

• Zhou, Y-X., Xu., L., Wu, Y-P., & Liu, B-L. (1999).
  A QSAR study of the antiallergic activities of substituted benzamides and their structures. Chemometrics and Intelligent Laboratory Systems., 45, 95-100.
  Multiple regression analysis (MRA) and comparative molecular field analysis (CoMFA) have been used in studies of the correlation between the antiallergic activities of substituted benzamides and their structures. The results achieved using CoMFA based on 3D factors are much better than those obtained using MRA based on mainly 2D structural information. The CoMFA results reveal that the steric effects are more important than the electrostatic effects for the activities of substituted benzamides.

• Zhu, X., Zhang, L., Che, X., & Wang, L. (1999).
  The classification of hydrocarbons with factor analysis and the PONA analysis of gasoline. Journal of Chemometrics and Intelligent Laboratory Systems, 45, 147-155.
  The feasibility of classification of hydrocarbons by factor analysis was studied. The difference between the retention indices of 191 hydrocarbons on stationary phases DB-1 and DB-5 at the same temperature and their temperature coefficients on each column were processed with Varimax orthogonal rotation and Promax oblique rotation. The hydrocarbons were successfully classified into paraffins (P), olefins (O), naphthenes (N) and aromatics (A). A gasoline sample was analyzed and the PONA value was obtained with the above method. The correctness of this method was fully proved by gas chromatographymass spectrometry.

   

• Zielman, B. (1991).
  Three-way scaling of asymmetric proximities. Unpublished master's thesis. Department of Data Theory, Leiden University.
  1. Introduction
  2. Overview of multidimensional scaling
  3. Other approaches to asymmetry in MDS
  4. Modelling asymmetry by skew symmetric functions
  5. The algorithm
  Improved estimation for Okada's algorithm; the algorithm for three-way scaling.
  6. Estimation of the asymmetric component
  Estimation of the asymmetry parameters for fixed weights; finding weights for fixed radii.
  7. The SMACOF theory
  8. Examples
  9. Discussion

• Zielman, B. (1993).
  Directional analysis of three-way skew-symmetric matrices. In O. Opitz, B. Lausen, & R. Klar, Information and classification: Concepts, methods and applications (pp. 156-161). Berlin: Springer.
  Asymmetry is a problem in multidimensional scaling because these models predict symmetric values. A common way to solve this problem is to average the observations across the diagonal and then analyze the symmetrized component. In this paper a method for analyzing the departures from symmetry is extended to handle three-way tables. The departures from symmetry are skew-symmetric and this property is reflected in the model as a direction. An alternating least squares algorithm is presented for estimating the parameters of the model.

• Zijlstra, B. J. H., & Kiers, H. A. L. (2002).
  Degenerate solutions obtained from several variants of factor analysis. Journal of Chemometrics, 16, 596-605.
  Degenerate solutions occur in several models, such as the shifted multiplicative model, a model for component analysis of multitrait-multimethod matrices, the directly fitted Parafac-2 model, the indirectly fitted Parafac-2 model and a constrained variant of the Tucker-3 model. Comparing degenerate solutions reported in the literature with simulated ones, two-factor degenerate solutions seemed to share the same three properties. Moreover, all analyses produce rotationally unique components, but models which do not do so were shown not to produce degenerate components.

• Zissis, K. D., Brereton, R. G., & Scott, R. (1998).
  Partial least-squares calibration of two-way diode-array high-performance liquid chromatograms: influence of calibration design, noise and peak separation. Analyst, 123, 1165-1173. An approach for the calibration of two-way diode-array high-performance liquid chromatograms is described, involving unfolding a three-way data matrix and performing partial least-squares (PLS) calibration. The properties of loadings summed over time and wavelength are discussed. The influence of calibration design, noise levels and peak separation are investigated, using pseudosimulations, both by calculating prediction and test errors and by graphical representation of the summed loadings. The importance of using an independent test set is emphasized. Calibration design is shown to have a major effect both on the appearance of the loadings and on the PLS errors.

• Zissis, K.D., Brereton, R.G., Dunkerley, S. & Escott, R.E.A. (1999).
  Two-way, unfolded three-way and three-mode partial least squares calibration of diode array HPLC chromatograms for the quantitation of low-level pharmaceutical impurities. Analytica Chimica Acta, 384, 71-81.
  A series of two-way diode array chromatograms were recorded at 0.1-0.5% and 1-5% of 3-hydroxypyridine impurity coeluting with 2-hydroxypyridine, recorded at pH 4.9 (good resolution) and 5.0 (poor resolution). Four methods for PLS calibration, namely, using summed spectral profiles, summed elution profiles, unfolded three-way PLS and true three-way PLS were applied to the data sets, both using auto-predictions and cross-validation. It was found that it was possible to accurately quantify low levels of impurities. Three-way methods often performed worse than two-way methods using the summed spectral profile probably due to irreproducibility of elution times.

                                   

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