Three-Mode Abstracts, Part E

INDEX

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• Eckes, T., & Orlik, P. (1994).
  Three-mode hierarchical cluster analysis of three-way three-mode data. In H.H. Bock, W. Lenski, & M.M. Richter (Eds.), Information systems and data analysis (pp. 217-225). Berlin: Springer-Verlag.
  A method is proposed for the simultaneous hierarchical clustering of row, column, and block elements of a three-way three-mode data matrix. The procedure generalizes the two-mode error-variance approach (Eckes & Orlik, 1993) to the three-mode case. At each step of the agglomerative process, the algorithm merges those clusters whose fusion results in the smallest possible increase in an internal heterogeneity measure. Optionally, the procedure yields an overlapping cluster solution by assigning further row and/or column and/or block elements to a given number of clusters. An application to a data set drawn from object perception research illustrates the approach. Finally, several indications of three-mode clustering are discussed.

         

• Egelandsdal, B., Christiansen, K. F., Host, V., Lundby, F., Wold, J. P., & Kvaal, K. (1999).
  Evaluation of scanning electron microscopy images of a model dressing using image feature extraction techniques and principal component analysis. Scanning, 21, 316-325.
  Twelve dressing systems made by varying protein type, oil level, CaCl2, NaCl, and sucrose, were examined using scanning electron microscopy. Images from the 12 systems were quantitatively analysed using methods of feature extraction. These methods were based on vectorisations of the images followed by principal component analysis on the extracted vectors. These techniques were used to examine the reproducibility of the acquired images as well as to relate the images to theologic and sensory texture parameters. Two feature extraction methods were used: the angle measure technique (AMT) and the absolute difference method (ABDF). The ABDF method used fewer principal components to extract information from images relevant to the complex modulus/sensory viscosity of the system, but the information seemed equally well preserved by the two-feature extraction methods. The AMT was more efficient in classifying the images with respect to protein type. A fair correlation between images and complex modulus was obtained (R=0.73). It is suggested that a better correlation might be obtained by adding more systems, increasing the number of areas imaged for each system as well as avoiding systems of low viscosity.

     

• Einax, J.W., Aulinger, A., Van Tümpling, W., & Prange, A. (1999).
  Quantitative description of element concentrations in longitudinal river profiles by multiway PLS models. Fresenius Journal of Analytical Chemistry, 363, 655-661.
  Partial least squares (PLS) models were used to examine the relationships between the distributions of elements in different compartments of a river. These relationships, if existing, enabled predictions to be made of the element concentrations in one compartment by knowing the concentrations in another compartment. The subjects of the study were the element concentrations measured in the water and the sediment of the river Saale as well as in the water and the suspended matter of the river Elbe. Special emphasis was placed on a comparison between two-way and three-way PLS.

       

• Elomaa, M., Lochmuller, C. H., Kudrjashova, M., & Kaljurand, M. (2000).
  Classification of polymeric materials by evolving factor analysis and principal component analysis of thermochromatographic data. Thermochimica Actra, 362, 137-144.
  Thermal decomposition of different polymeric materials was investigated by thermochromatography (ThGC), a temperature programmed pyrolysis chromatographic method. ThGC produces two-dimensional results; the co-ordinates of which are the retention time and the pyrolysis temperature at the time of sampling. Therefore, principal component analysis (PCA), on results from evolving factor analysis (EFA) successfully applied would decompose the complete data of each run into two parts: 'thermograms' and 'chromatograms'. Factor analysis at this stage compresses the data, making it more convenient for further analysis of the data structure composed of a few dozen of samples. The aim of this stage of the data analysis process is to extract 'real thermograms' as close as possible to the corresponding 'thermograms' - answering the question "which products are evolved at each temperature." Combination of 'chromatograms' and related 'thermograms' obtained on the first stage were used as characteristic vectors in the further analysis. Sets of significant 'thermograms'-'chromatograms' were subjected to PCA. Mapping of the polymeric samples onto planes defined by factors allows one to identify clusters as related to different classes of polymers, as well as different mechanisms of their thermal decomposition. The data was proven to give a very good basis for characterization of the samples by their polymer content.

     

• Engelsen, S. B., & Bro, R. (2003).
  PowerSlicing. Journal of Magnetic Resonance, 163, 192-197.
  Recently, a new technique for unique non-iterative multi-exponential fitting of time domain NMR data was proposed. The method was termed SLICING, because an intrinsic part of the method consisted of taking different parts (slices) of the original matrix data and rearranging the slices into a three-way box of data. Subsequently, a directly calculated model of this box provided T-2-estimates and corresponding amplitudes. The most critical part of this method is the choice of how to slice the original data. In this paper, a new general scheme for this slicing is proposed which (1) is shown to provide more accurate T2-estimates and (2) leads to a significant speed improvement compared to earlier approaches. The method is called POWERSLICING, because it takes slices of lag 2(x) (x = 0, 1,...,N) where 2(N) less than or equal to J/2 and J is the number of bins on the time axis. This approach ensures a reasonably high amount of direct constraints and an appropriate representation of both short and long time decays in the decomposition.

         

• Eriksson, L., Gottfries, J., Johansson, E., & Wold, S. (2004).
  Time-resolved QSAR: an approach to PLS modelling of three-way biological data. Chemometrics and Intelligent Laboratory Systems, 73, 73-84.
  This paper outlines a novel approach to the analysis of three-way Y-data in quantitative structure-activity relationship (QSAR) modelling. The new method represents a modification of an existing approach for multivariate modelling of batch process data. It is based on unfolding the three-way Y-matrix into a two-way matrix according to a sequential order of an external variable. In QSAR, time, pH, or temperature at which the biological data were gathered, are conceivably such external variables. Thus, unfolding can be done differently depending on the objective of the investigation, thereby shifting the focus of the QSAR analysis. The ensuing multivariate data analysis uses two levels of modelling. (1) On the lower (observation) level a projections to latent structures (PLS) model is developed between the unfolded biological data and the external variable. This model will identify compounds with biological data being sensitive to changes in the external variable (like time, pH, or temperature). (2) The scores of the lower level model are then re-arranged to enable the upper (QSAR) level model. In this model. a battery of structure descriptors (X) is related to the Y-matrix of scores of the lower level model. As an example, a series of 35 compounds and their anti-microbial activity towards the bacterial strain Escherichia coli CCM2260 is used. This biological activity has been determined at different times (2 to 10 h) and pH-values (pH 5.6 to 8.0).

   

• Esbensen, K.H., & Geladi, P. (1989).
  Strategy of multivariate image analysis (MIA). Chemometrics and Intelligent Laboratory Systems, 7, 67-86.
  Bilinear decomposition (soft modelling using principal component analysis) of multivariate imagery results in: score and loading plots, score images, classification projections and residual images in the scene space. Feature space score plots are used as a starting point for pixel class delineations, followed by iterative scene space evaluation. This is a reversal of traditional image processing practice, which selects training samples in the scene space. The present feature space class definitions can be shown to have certain optimality characteristics with respect to traditional scene space delineations. After problem-dependent relevant pixel class delineations have been obtained, one can compute corresponding local class PC-models that serva as an alternative basis for problem-dependent classification and sequential segmentation. Multivariate image analysis (MIA) allows interactive exploration and classification of most types of technical multivariate imagery. We present a general strategy for multivariate image analysis, illustrated by a remote sensing showcase.

  

• Esbensen, K. H., Geladi, P., & Grahn, H. F. (1992).
  Strategies for multivariate image regression. Chemometrics and Intelligent Laboratory Systems, 14, 357-374.
  We present multivariate image regression (MIR) as a set of typically problem-dependent strategies for image decomposition guided by the nature of the Y variable and/or training data set delineation in the (X, Y) image domains. Regression techniques common in chemometrics may be applied also to the image regimen (in this paper we treat mainly two-dimensional images). We present applications of both IMPCR and IMPLS-DISCRIM in an effort to delineate the various possibilities for image regression. IMPCR builds directly on our earlier bilinear multivariate image analysis projection approach, while IMPLS-DISCRIM is trained on scene space binary classification masking with subsequent off-screen partial least squares analysis; the results are back-projected as images in the original scene space. Regression may either be carried out for modelling purposes and/or for subsequent prediction purposes. In the image domain this duality is accompanied by several optional training data set delineations in the scene space and/or in the spectral domain. We try to cover as complete a survey as possible of typical, representative regression problem types. We illustrate some of these MIR strategies with an MR-imaging example as well as a simple didactic MIR calibration from analytical chemistry.

• Esbensen, K.H., Wold, S., & Geladi, P. (1988).
  Relationships between higher-order data array configurations and problem formulations in multivariate data analysis. Journal of Chemometrics, 3, 33-48.
  A scaffold for detailed understanding of the concept 'dimensionality' in data analysis is furnished by a systematic classification of higher-order data array configurations. Three major types of problem formulation in multivariate data analysis can be characterized for relevant data classes: 1) Data description, 2) Classification and 3) correlation, regression. The relationship between these three categories of data analytical problem formulation and the fundamental data array classification is exposed. These relations are augmented to include the general casse of data arrays of order R, and R-way data analysis with the use of bilinear projections is presented. Based upon this, some possible directions for the future development of data analysis may be imagined.

• Esbensen, K. H., & Höskuldsson, A. (2003).
  Multivariate data analysis: quo vadis? I. Object-oriented data modelling (OODM). Journal of Chemometrics, 17, 34-44.
  

• Esbensen, K. H., & Höskuldsson, A. (2003).
  Multivariate data analysis: quo vadis? II. Levels of data-modelling objectives and possibilities. Journal of Chemometrics, 17, 45-52.
  

• Escandar, G. M., Gonzáles Gomez, D., Espinosa Mansilla, A., Muñoz de la Peña, A., & Goicoechea, H. C. (2004).
  Determination of carbamazepine in serum and pharmaceutical preparations using immobilization on a nylon support and fluorescence detection. Analytica Chimica Acta, 506, 161-170.
  A novel approach is presented for the spectrofluorimetric determination of the powerful anticonvulsant carbamazepine and its main metabolite in human serum. The strategy consists in the support of both compounds on a nylon membrane, and their subsequent determination through a solid-surface fluorescence methodology combined with a suitable chemometric analysis. The novelty of the present method lies in the fact that while carbamazepine does not fluoresce neither in solution nor supported on a variety of surfaces, significant emission signals are observed when it is supported on the nylon matrix, a property which has not been previously exploited by analysts. Multivariate calibration analysis was performed on three-way excitation- emission matrix data. The algorithms applied were: parallel factor analysis (PARAFAC), self-weighted alternating trilinear decomposition (SWATLD) and N-way partial least-s quares regression (N-PLS). The results were compared with two-way calibration data analysed with partial least-squares regression (PLS-1). The methodology is highly specific, and it appears to be suitable for the routine monitoring of serum concentrations in patients receiving chronic therapy. In addition, the technique was satisfactorily applied to the determination of carbamazepine in pharmaceutical formulations.

• Escofier, B., & Pagès, J. (1994).
  Multiple factor analysis (AFMULT package). Computational Statistics & Data Analysis, 18, 121-140.
  Multiple Factor Snalysis (MFA) studies several groups of variables (numerical and/or categorial) defined on the same set of individuals. MFA approaches this kind of data according to many points of view already used in others methods as: factor analysis in which groups of variables are weighted, canonical analysis, Procrustes analysis, STATIS, INDSCAL. In MFA, these points of view are considered in a unique framework. This paper presents the different outputs provided by MFA and an example about sensory analysis of wines.

  

• Espinosa-Mansilla, A., De la Pena, A. M., Goicoechea, T. C. & Olivieri, A. C. (2004).
  Two Multivariate strategies applied to three-way kinetic spectrophotometric data for the determination of mixtures of the pesticides carbaryl and chlorpyrifos. Applied Spectroscopy, 58, 83-90.
  Two pesticides, carbaryl and chlorpyrifos, have been simultaneously determined using second-order kinetic spectrophotometric measurements upon alkaline oxidative degradation. In spite of the complexity of the system and of the serious spectral overlap among the reagents and products, calibration and prediction is possible thanks to the power of second-order multivariate techniques. Strategies such as parallel factor analysis (PARAFAC) and multivariate curve resolution coupled to alternating least-squares (MCR-ALS) have been employed, which adequately exploit the second-order advantage. They allow for a correct determination of the analytes both in synthetic binary samples and in a commercial formulation, in this latter case even in the presence of unmodeled interferents. Multi-way partial least-squares (n-PLS) produced good results only on synthetic binary mixtures but could not be applied to a commercial sample because it contained an uncalibrated component.

• Esteves da Silva, J.C.G., & Novais, S.A.G. (1998).
  Trilinear PARAFAC decomposition of synchronous fluorescence spectra of mixtures of the major metabolites of acetylsalicylic acid. The Analyst, 123, 2067- 2070.
  Mixtures of the three major metabolites of acetylsalicylic acid were analyzed by synchronous molecular fluorescence spectroscopy. Three-way data matrices were generated by acquisition of spectra as a function of the pH (between 2 and 11) and of different relative concentrations of the three components. The PARAFAC trilinear model, without restrictions and using one factor per metabolite, was used in the data analysis. A full decomposition of the data matrices into the spectra, concentration and pH profiles was obtained. This result shows that molecular fluorescence spectroscopy can be used for the development of robust analytical methods for the simultaneous determination of the three major metabolites of acetylsalicylic acid in complex background samples.

• Esteves da Silva, J.C.G., & Oliveira, C.J.S. (1999).
  Parafac decomposition of three-way kinetic-spectrophotometric spectral matrices corresponding to mixtures of heavy metal ions. Talanta, 49, 889-898.
  Binary and ternary mixtures of some of the following heavy metal ions Zn(II), Ni(II), Pb(II), Co(II) and Cd(II) were analyzed by a ligand substitution kinetic method. Three-way data matrices were generated by acquisition of UV-Vis spectra (332-580 nm) as a function of the time of a substitution reaction observed between the complex of the heavy metal ions with a non selective metallochromic indicator and EDTA, and of different relative concentration of the metal ions (1-6 mM). The PARAFAC trilinear model, without restrictions, was used in the data analysis. A full decomposition of the data matrices was obtained (spectra, concentration and time profiles). It was shown that ligand substitution kinetic methods coupled to three-way chemometric analytical methods can be used for the development of robust sensors for the analysis of binary or ternary mixtures of metal ions in the micromolar concentration range.

• Estienne, F., Matthijs, N., Massart, D.L., Ricoux, P., & Leibovici, D. (2001a).
  Multi-way modelling of high-dimensionality electroencephalographic data. Chemometrics and Intelligent Laboratory Systems, 58, 59-72.
  The aim of this study is to investigate whether useful information can be extracted from an electroencephalographic (EEG) data set with a very high number of modes, and to determine which model is the most appropriate for this purpose. The data was acquired during the testing phase of a new drug expected to have effect on the brain activity. The implemented test program (several patients followed in time, different doses, conditions, etc....) led to a six-way data set. After it was confirmed that the exploratory analysis of this data set could not be handled with classical principal component analysis (PCA), and it was verified that multidimensional structure was present, multi-way methods were used to model the data. It appeared that Tucker 3 was the most suited model. It was possible to extract useful information from this high-dimensionality data. Non-relevant sources of variance (outlying patients for instance) were identified so that they can be removed before the in-depth physiological study is performed.

• Estienne, F., Heyden, Y. V., & Massart, D. L. (2001b).
  Cemometrics and modeling. Chimia, 55, 70-80.
  Chemometrics is a chemical discipline in which mathematical and statistical techniques are applied to design experiments or to analyze chemical data. An important part of chemometrics is modeling, in which one tries to relate two or more characteristics in such a way that the obtained model represents reality as closely as possible. In this article some less known but useful regression methods such as orthogonal least squares. inverse and robust regression are introduced and compared with the well-known classical least squares regression method. Genetic algorithms are described as a means of carrying out feature selection for multivariate regression. Regression methods such as principal component regression and partial least squares are introduced as well as the use of N-way principal components.

               

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