Three-Mode Abstracts, Part E
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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).
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
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.
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).
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
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
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).
decomposition of synchronous fluorescence spectra of mixtures of the major
metabolites of acetylsalicylic acid. The Analyst, 123, 2067-
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).
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
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Centre for Child and
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First version : 12/02/1997;