Three-Mode Abstracts, Part S
With one can go to the index of
this part of the Abstracts, with
one can go to other
parts (letters) of the Abstracts.
|Sa | Sb |
Sc | Sd |
Se | Sf |
Sg | Sh |
Si | Sj |
Sk | Sl |
Sm | Sn |
So | Sp |
Sq | Sr |
Ss | St |
Su | Sv |
Sw | Sx |
Sy | Sz |
Saile, H. (1979).
Zur Struktur der Einschätzung von Lebensereignissen. Eine
Untersuching über Beurteilungsunterschiede mittels
dreimodaler Faktorenanalyse. Unpublished master thesis: University
of Trier, Trier, FRG.
Partially reported in Gräser et al., 1981.
Saldanha, T. C. B., De Araujo, M. C. U., & Neto, B. D. (1999).
Simultaneous multicomponent analysis by UV-VIS spectrophotometry.
Quimica Nova, 22, 847-853.
This review presents the evolution of simultaneous multicomponent
analysis by absorption spectrophotometry in the ultraviolet and visual regions in
terms of some qualitative and quantitative analysis techniques, otimization
methods, as well as applications and modern trends.
Sanchez, E., & Kowalski, B.R. (1990).
Tensorial resolution: A direct trilinear decomposition.
Journal of Chemometrics, 4, 29-45.
Trilinear arrays of data are known to have unique factor analysis decompositions
which correspond to the true physical factors that form the data, such that a
unique solution can be found in many cases for each order X, Y and
Z. This is in contrast to the well-known second-order bilinear data
factor analysis, where the abstract solutions obtained are not unique and at
best cannot be easily compared with the underlying physical factors owing to a
rotational ambiguity. This paper introduces a method for reducing the problem to
a rectangular generalized eigenvalue-eigenvector equation where the eigenvectors
are the contravariant form (pseudo-inverse) of the actual factors. It is shown
that the method works well when the factors are linearly independent in at least
two orders (e.g. Xir and Yjr are full rank
matrices). Finally, it is shown how trilinear decompositions relate to
multicomponent calibration, curve resolution and chemical analysis.
Sands, R. & Young, F.W. (1980).
Component models for three-way data: ALSCOMP3, an alternating
least squares algorithm with optimal scaling features.
Psychometrika, 45, 39-67.
An alternating least squares (ALS) method is proposed for the
weighted Euclidean (a three-mode three-way generalization of
the two-mode three-way INDSCAL model) and for the replicated
PCA model, where 'subjects' in the third mode are treated as
replications. The data may be defined at various measurement
levels with various measurement characteristics. It is the
only method which allows for other than metric data. Compared
with the other ALS methods (Lohmöller & Wold, 1980;
Kroonenberg & De Leeuw, 1980) the treated models are somewhat
less general. Illustrated with a Monte Carlo study, and data
on perception of political figures and roles.
Sanguineti, V., Laboissiere, R., & Payan, Y. (1997).
A control model of human tongue movements in
Biological Cybernetics, 77, 11-22.**
Tongue movements during speech production have
been investigated by means of a simple yet
realistic biomechanical model, based on a finite
elements modeling of soft tissues, in the
framework of the equilibrium point hypothesis
(x-model) of motor control. In particular, the
model has been applied to the estimation of the
"central" control commands issued to the
muscles, for a data set of mid-sagittal digitized
tracings of vocal tract shape, recorded by means
of low-intensity x-ray cineradiographies during
speech. In spite of the highly non-linear mapping
between the shape of the oral cavity and its
acoustic consequences, the organization of control
commands preserves the peculiar spatial
organization of vowel phonemes in acoustic space.
A factor analysis of control commands, which have
been decomposed into independent or "orthogonal"
muscle groups, has shown that, in spite of the
great mobility of the tongue and the highly
complex arrangement of tongue muscles, its
movements can be explained in terms of the
activation of a small number of independent muscle
groups, each corresponding to an elementary or
"primitive" movement. These results are
consistent with the hypothesis that the tongue is
controlled by a small number of independent
"articulators", for which a precise
biomechanical substrate is provided. The influence
of the effect of jaw and hyoid movements on tongue
equilibrium has also been evaluated, suggesting
that the bony structures cannot be considered as a
moving frame of reference, but, indeed, there may
be a substantial interaction between them and the
tongue, that may only be accounted for by a
"global" model. The reported results also define
a simple control model for the tongue and, in
analogy with similar modelling studies, they
suggest that, because of the peculiar geometrical
arrangement of tongue muscles, the central nervous
system (CNS) may not need a detailed
representation of tongue mechanics but rather may
make use of a relatively small number of muscle
synergies, that are invariant over the whole space
of tongue configurations.
Sato, M. & Sato, Y. (1994).
On a multicriteria fuzzy clustering method for 3-way data.
International Journal of Uncertainty, Fuzziness and Knowledge-Based
A fuzzy clustering procedure for three-mode data is presented in which a
clustering need not
be the same for attributes, so that it is a multicriteria optimisation
solutions in this case are Pareto efficient, but non-fuzzy are difficult
to find due to the
combinatorial character in contrast with fuzzy clustering. Illustrated
with artificial data
and growth curves of physical characteristics of Japanese boys.
Sato, M. & Sato, Y. (1997).
Generalized fuzzy clustering model for 3-way data. In
Proceedings of the International Conference on Fuzzy Logic (pp.
132-137). Zichron Yakov, Israel: Ministry of Science.
A method of classification for longitudinal asymmetric 3-way data is
proposed. A fuzzy
clustering method is proposed for asymmetric similarity data by using
operators. The clustering need not be the same for attributes, so that it
is a multicriteria
optimisation problem. Practical solutions in this case are Pareto
efficient, but non-fuzzy are
difficult to find due to the combinatorial character in contrast with
Weights are introduced for each occasion to show the salience of each
Sato-Ilic, M. & Sato, Y. (1998).
A dynamic additive fuzzy clustering model. In A. Rizzi, M. Vichi, &
H.-H. Bock (Eds.),
Advances in data science and classification (pp. 117-124).
A dynamic clustering model is presented in which clusters are constructed
in order to find the
features of dynamic change. This is done by introducing the concepts of
dynamic MDS and
dynamic PCA into an additive clustering model.
Saurina, J., Hernández-Cassou, S., & Tauler, R. (1995a).
Continuous-flow titration system for the generation of multivariate spectrophotometric data in the study of
Analytica Chimica Acta, 312, 189-198.
In the present work a continuous flow system to carry out spectrophotometric titrations is
developed. The titrant solution is generated on-line from mixing two different stock buffer solutions. The
composition of the titrant agent is sequentially varied along the titration by changing the ratio of flow
rates of both buffer channels, and therefore the pH can be modified. One spectrum is recorded at each pH
value when the absorbance achieves the steady state. The spectral data have been treated by means of a
recently developed self-modelling multivariate curve resolution method (SPFAC procedure). This method has
been applied to the study of the acid-base equilibria of 1,2-naphthoquinone-4-sulfonate (NQS). Four
titrations with concentrations of NQS ranging from 1.6 X 10(-4) to 7.3 X 10(-4) M have been performed,
and, in every case, 24 spectra at different pH have been registered. Three species are detected in the
range of pH studied (6.9-12.3). Their distribution plot with pH and their unit spectrum have been obtained.
Saurina, J., Hernández-Cassou, S., & Tauler, R. (1995b).
Multivariate curve resolution applied to
continuous-flow spectrophotometric titrations:
reaction between amino-acids and
Analytical Chemistry, 67, 3722-3726.**
A continuous-flow acid-base titration system has
been developed for the study and analytical
application of chemical reactions between amino
acids and 1,2-naphthoquinone-4-sulfonate. For each
titration, a set of spectra are obtained at pH
values from 6.5 to 12.5. Multivariate curve
resolution is applied to provide an optimal
estimation of concentration and spectra profiles
of the species formed during the chemical
reaction. Resolution of these chemical species is
greatly improved when several runs of different
spectrophotometric titrations of the same chemical
reaction system (multiple correlated data
matrices) are analyzed simultaneously, allowing
the quantitative determination of the
concentration of amino acid that has reacted in
Saurina, J., Hernández, S. & Tauler, R. (1997).
Multivariate curve resolution and trilinear decomposition methods
in the analysis of stopped-flow kinetic data for binary amino acid
Analytical Chemistry, 69, 2329-2336.
The kinetic development of the reaction between amino acids and
1,2-naphtoquinone-4-sulfonate (NQS) is carried out by a
stopped-flow methodology. Each kinetic run was monitored
spectrophotometrically by using a diode array detector, which
produced a set of spectra registered at different times during the
process. The resolution of the derivative species formed during
the kinetic reaction by multivariate curve resolution and the
quantitative determination of amino acids in unknown samples in the
presence of interferences were studied by both constrained
singular value decomposition (called ALS) and direct trilinear
decomposition (TLD) in order to compare the ability of both
methods in the resolution and quantification of such kinetic data.
Because the trilinearity required for TLD was not completely
fulfilled the ALS-based method outperformed TLD.
Saurina, J., Hernández-Cassou, S., Tauler, R., & Izquierdo-Ridorsa, A. (1998).
Multivariate resolution of rank-deficient spectrophotometric data from first-order kinetic decomposition
reactions. Journal of Chemometrics, 12, 183-203.
The effect of a rank deficiency upon curve resolution in simple kinetic
reaction-based systems is studied. Firstly, simulated rank-deficient spectrophotometric data
of a mixture of two reagents, each one yielding its own reaction product by a first-order kinetic
reaction, are analysed. Four different situations are considered according to the differences in
the spectral responses of the reaction constituents and to the differences in the rate constants
between the two kinetic processes. A variation of the rate constant between runs for a certain
kinetic process is also taken into account. Secondly, the resolution of a real rank-deficient data
system, corresponding to the study of the pH-dependent decomposition of 1,2-naphthoquinone-4-sulphonate,
is investigated. All these studies were carried out using a multivariate curve resolution method
based on the alternating least squares optimization of the kinetic and spectral profiles of the
species present in the system.
Saurina, J., Hernández-Cassou, S., Tauler, R., & Izquierdo-Ridorsa, A. (1999a).
Procedure for the quantitative determination of mixtures of nucleic acid components
based on multivariate spectrophotometric acid-base titrations.
Analytical Chemistry, 71, 126-134.
A new procedure for the quantitative
determination of mixtures of nucleic acid
components, based on continuous
spectrophotometric acid-base titrations and
multivariate curve resolution, is proposed, The
procedure simultaneously takes into account the
spectroscopic and acid-base properties of the
compounds, which leads to a higher selectivity.
Furthermore, quantitative determination of an
analyte in a complex mixture is performed using a
synthetic solution as standard containing only
the analyte of interest. An intrinsic difficulty
in the analysis of spectrometric titration data
is the presence of rank deficiency due to closure
for the mixtures of two or more compounds. An
additional problem can be encountered in some
mixtures if species spectra or species
concentration profiles are practically identical
(rank overlap). However, even in the presence of
these rank difficulties, accurate quantitation
with prediction errors lower than 5% was
obtained, The presence of unknown and
uncalibrated interferences in the samples does
not affect the quantitative determination of the
analyte of interest. The proposed procedure was
successfully applied to the analysis of real
samples (pharmaceuticals) using synthetic
Saurina, J., Hernández-Cassou, S., Tauler, R., & Izquierdo-Ridorsa, A. (1999b).
Continuous-flow and flow injection pH gradients for spectrophotometric determinations
of mixtures of nucleic acid components.
Analytical Chemistry, 71, 2215-2220.
A procedure for the rapid determination of
mixtures of nucleic acid components from the
analysis of spectrophotometric multivariate data
obtained with continuous-flow and flow injection
pH-gradient systems is proposed. Three flow
systems have been developed and assayed in which
an on-line pH gradient is generated from the
mixing and controlled dispersion of acidic and
basic titrant solutions. Quantitative
determinations of any particular analyte in the
unknown samples in the presence of interferences
is performed with a single pure standard for this
analyte. They are carried out using an
alternating least squares multivariate curve
resolution procedure. The methods proposed have
been validated using synthetic and real sample
mixtures. The results obtained are concordant
with the labeled values, and the relative
prediction errors are around 5%.
Saurina, J. (2000a).
Analytical application of pH-gradients in flow injection analysis and related techniques.
Reviews in Analytical Chemistry, 19, 157-178.
pH gradients in flow systems have proved useful for
performing multiple analytical tasks. Although the reproducibility,
sampling frequency and degree of automation makes these
techniques highly attractive from an analytical point of view,
data generated often suffer from poor selectivity. From a
historical perspective, following their initial application at
the end of the seventies, these methods fell into disuse as a
consequence of interference problems. Today, the potentiality
of pH-gradients has greatly increased, mainly in combination
with mathematical procedures for data analysis addressed at
improving the selectivity. This paper describes the existing
systems for the generation of pH gradients and provides an
overview of applications dealing with the study of pH-dependent
processes, quantitative determinations and the calculation of
stability constants. The characteristics, advantages and
shortcomings of the different techniques are outlined.
Furthermore, a number of examples developed in our working
group are described in more detail.
Saurina, J., Hernández-Cassou, S., Izquierdo-Ridorsa,
A., & Tauler, R. (2000b).
pH-Gradient spectrophotometric data files from
flow-injection and continuous flow systems for
two- and three-way data analysis.
Chemometrics and Intelligent Laboratory Systems, 50, 263-
This paper describes a contribution to
Chemometrics and Intelligent Laboratory Systems
Elsevier's data base of files. Mixtures of
nucleosides and a pharmaceutical preparation
composed of cytosine and inosine-5'-monophosphate
are analyzed using three different pH-gradient
spectrophotometric flow-injection and continuous
flow systems. Results for one of the
flow-injection systems and for the
continuous-flow system are reported for the first
time in this paper. Resolution and quantitation
of the constituents in the mixtures are given
using a multivariate curve resolution method
based on a constrained alternating least squares
Saurina, J., Leal, C., Compano, R., Granados, M., Tauler, R. & Prat, M. D. (2000c).
Determination of triphenyltin in sea-water by excitation-emission matrix
fluorescence and multivariate curve resolution.
Analytica Chimica Acta, 406, 237-245.
A new method for the determination of
triphenyltin (TPhT) in sea-water is proposed. The
method is based on solid-phase extraction (SPE),
reaction with flavonol in a Triton X-100 micellar
medium to yield a fluorimetrically active
derivative and excitation-emission fluorescence
measurements. TPhT was quantified by an
alternating least squares (ALS)-multivariate
curve resolution (MCR) procedure and a single
synthetic standard. In order to select the
optimum conditions for the analysis, the
procedure was assessed using synthetic samples.
With the proposed method, TPhT was quantified in
sea-water samples at low ng l(-1) level with an
overall prediction error of around 12%.
Schenone, A., Firenze, F., Acquarone, F., Gambaro, M., Masulli, F., & Andreucci, L. (1996).
Segmentation of multivariate medical images via unsupervised clustering with ´adaptive resolution´.
Computerized Medical Imaging and Graphics, 20, 119-129.
The need for quantitative information is becoming increasingly important in the clinical field. In this
paper we present an interactive X11 based system, devoted to segmentation of multivariate medical images, including an
unsupervised neural network approach to clustering. The following steps are considered in the analysis sequence: feature
extraction, reduction of dimensionality, unsupervised data clustering, voxel classification, interactive postprocessing
refinement. The environment turns out to be extremely interactive, thus making the user able to display and modify data
during processing, to set parameters, to choose different methods and different tools for each step, and to define online
the whole analysis sequence.
Schiffman, S.S., Reynolds, M.L., & Young, F.W. (1981).
Introduction to multidimensional scaling. New York: Academic Press. (Review by P.M. Kroonenberg and W.A. van der
This book contains three parts:
1. Foundations of MDS and data suitable for MDS.
2. Methods and applications.
The following models and algorithms for individual differences multidimensional
scaling are presented: INDSCAL, ALSCAL, and MULTISCALE. Both program
descriptions and illustrative applications are provided. Young, Carroll and
Ramsay discuss the theory behind their own programs.
Schmitt, N., Coyle, B.W. & Saari, B.B. (1977).
A review and critique of analyses of multitrait-multimethod
matrices. Multivariate Behavioral Research,
T3 (Method III) is discussed as one of the techniques
appropriate for multi-trait multi-method matrices. A small
example constructed from the data of 310 persons being rated
on 7 traits by 4 raters is used as illustration. The unrotated
core matrix is nicely diagonal.
Schneider, J. F., & Krolak-Schwerdt, S. (1994).
Dreimodale Faktorenanalyse von Wertkonzepten: Ein
Methodenvorschlag für interkulturelle Vergleiche.
[Three-mode factor analysis of value concepts: Proposal of a method
for intercultural comparison].
Gruppendynamik, 25, 117-131.
The present paper shows the usefulness of various methods of three-mode factor analysis for the cross-cultural
comparisons of value concepts. Data were obtained from 300 German and 300 American students, using the Individual and
Organizational Values SYMLOG rating form. The comparative structural analyses of the samples made it apparent that the
SYMLOG rating forms used did not yield the expected correspondence to the theoretical three-dimensional value space. The
masons and consequences of these findings for further studies in this field are discussed. The methodological approach
outlined in this paper can supplement the criteria formulated Bales et al. (1997) for adaptation of SYMLOG rating items to
particular populations and cultural contexts and it provides more adequate procedures for data analysis.
Schönemann, P. H. (1972).
An algebraic solution for a class of subjective metrics models.
Psychometrika, 37, 441-451.
It is shown that an obvious generalization of the subjective metrics model by Bloxom, Horan, Carroll
and Chang has a very simple algebraic solution which was previously considered by Meredith in a different context.
This solution is readily adapted to the special case treated by Bloxom, Horan, Carroll and Chang. In addition to
being very simple, this algebraic solution also permits testing the constraints of these models explicitly. A
numerical example is given.
Schott, J. R. (1998).
Estimating correlation matrices that have common eigenvectors.
Computational Statistics & Data Analysis, 27, 445-459.
In this paper we develop a method for obtaining estimators of the correlation matrices from k
groups when these correlation matrices have the same set of eigenvectors. These estimators are obtained by
utilizing the spectral decomposition of a symmetric matrix; that is, we obtain an estimate, say P', of
the matrix P containing the common normalized eigenvectors along with estimates of the eigenvalues
for each of the k correlation matrices. It is shown that the rank of the Hadamard product, P' O P',
is a crucial factor in the estimation of these correlation matrices. Consequently, our procedure begins with
an initial estimate of P which is then used to obtain an estimate P' such that P' O P' has its
rank less than or equal to some specified value. Initial estimators of the eigenvalues of Q, the correlation matrix
for the ith group, are then used to obtain refined estimators which, when put in the diagonal matrix
D', as its diagonal elements, are such that P'D'P' has correlation-matrix structure.
Schulz, U. (1972).
Ein euklidisches Modell der Multidimensionalen Skalierung unter
Berücksichtigung individueller Differenzen [A Euclidean
model for individual differences multidimensional scaling].
In Bericht über den
28. Kongreß der Deutschen Gesellschaft für Psychologie, Band 2:
Psychologische methodik und mathematische psychologie (pp. 75-
A Euclidean MDS model is proposed in which the stimuli by subjects are
represented both in an individual space which is derived from a common group
space via a linear transformation. An algorithm is proposed and its properties
are investigated both theoretically and via a simulated example.
Schulz, U. (1975).
Zu einem Dekompositionsmodell der multidimensionalen Skalierung
mit individueller Gewichtung der Dimensionen. Psychologische
Beitrage, 17, 167-187.
A model for
multidimensional scaling is formulated in which the individual
differences of the subjects are regarded by means of respective
weighting of the dimensions of the group. In case of
faultlessness of data it is tried to find out under what
conditions a realization is existing. A method of construction is
mentioned for a special realization. Finally the author
investigates under what conditions there is only one realization
and what transformations can be permitted if there should be more
than one realization.
Schulz, U., & Pittner, P.M. (1978).
Zur multidimensionale Skalierung individueller Differenzen: Zwei
Modelle mit Rechenalgorithmen. Psychologische Beitrage,
The authors suggest two calculative algorithms for the
determination of solutions for two models of multi-dimensional
caling with regard to individual differences. The special
numerical problems are dealt with in great detail. On the basis
of an example taken from pertinent literature the properties of
algorithms are pointed out and brought in relation to existing
Seasholtz, M. B. (1999).
Making money with chemometrics.
Chemometrics and Intelligent Laboratory Systems, 45, 55-63.
Chemometricians have been formally employed at Dow Chemical since 1988. In that time, chemometric
methods have been applied in a number of analytical chemistry applications. These have resulted in making money
for the company in a variety of ways, and several recent case studies are presented. These applications have been
positive for the company in terms of (1) better process control, (2) faster verification of raw material
identification and quality, and (3) faster analysis of wastewater. The analytical methods used are NIR and NMR
spectroscopy. The chemometric methods include pattern recognition and multivariate calibration.
See, K., & Smith, E.P. (1996).
A graphical tool for three-factor experiments with one observation per cell.
Communications in Statistics. Part B, Simulation and Computation, 25, 709-732.
The joint-plot graphical display is proposed as a data analytic tool for diagnosing
the type of model to fit to three-factor data. It is a three-way generalization of the biplot display
which is useful in graphically diagnosing models for two-way data joint-plots of the three-way
array have been used to help understand the underlying structure of the data when all of the
three ways or factors are of equal consideration from the view point of exploratory data analysis.
In this paper, it is shown that joint-plots can help in understanding the interactions between
factors in three factor experiments and in assessing the type of the model to fit. Illustrations from
physical and biological science show how to use diagnostic rules in search for models to describe the
See, K., & Smith, E. P. (1998).
Testing interaction in three-way ANOVA tables with a single
observation per cell.
Communications in Statistics. Part A, Theory and Methods, 27, 839-866.
A common approach in analyzing nonreplicated data is to omit
the highest order interaction and regard it as error. This
paper discusses the use of a multiplicative model, called a
quadrilinear model in order to separate variability due to the
three-factor interaction from random error, and also examines
its significance in nonreplicated three-factor experiments. The
quadrilinear model is a nonreplicated three-way multiplicative
model with quadrilinear terms. These estimated quadrilinear
terms can be obtained by performing a three-mode principal
component analysis of the residuals. in particular, we derive a
criterion to select an appropriate number of multiplicative
terms to describe significant three-factor interaction. A table
of degrees of freedom associated,with the three-factor
interaction term is constructed by applying Monte Carlo
simulations. An ANOVA table with estimated experimental error
variance and error degrees of freedom is provided. These
methods are appropriate when it is reasonable to assume that a
dominant principal component of the residuals exists. The
proposed methods are illustrated using a biological science
Selli, E., Zaccaria, C., Sena, F;.,Tomasi, G., & Bidoglio, G. (2004).
Application of multi-way models to the time-resolved fluorescence of polycyclic
aromatic hydrocarbons mixtures in water.
Water Research, 38, 2269-2276.
The time-resolved laser-induced fluorescence of a series of polycyclic
aromatic compounds (PAHs) and mixtures of these latter in aqueous solution was measured
by means of an apparatus equipped with optical fibers, which allows their real time in
situ monitoring. The potential of such spectroscopic technique, yielding 4-way fluorescence
data arrays, together with the application of multi-way models to the matricized data, was
tested for the resolution of complex aqueous mixtures containing low concentrations of PAHs,
as typical fluorescent pollutants in aquatic systems. PARAllel FACtors analysis was employed
for the qualitative resolution of PAHs mixtures and for calculating the fluorescence
lifetimes of single PAHs; n-way partial least squares analysis was applied for evaluating
the concentration of the single PAHs in the aqueous mixtures.
Sena, M.M., Fernandes, J.C.B., Rover, L., Poppi, R.J. & Kubota,L.T. (2000).
Application of two- and three-way chemometric methods in the study of
acetylsalicylic acid and ascorbic acid mixtures using ultraviolet
Analytica Chimica Acta, 409, 159-170.
In this work, mixtures of acetylsalicylic acid (ASA) and ascorbic acid (AA)
were studied by ultraviolet spectrophotometry using parallel factor
analysis (PARAFAC) and partial least square (PLS). Parafac was used for
spectra deconvolution. The estimated first pKa was equal
to 3.41 and 4.10 for ASA and AA, respectively. Multivariate calibration
models using PLS at different pH and N-way PLS were elaborated for
simultaneous determination of ASA and AA in pharmaceutical samples. The
best models for the system were obtained with N-way PLS2 and PLS2 at
Sena, M. M., Fernandes, J. C. B., Rover, L., Poppi, R. J. & Kubota, L. T. (2000b).
Evaluation of the use of chemometric methods in soil analysis.
Quimica Nova, 23, 547-556.
One of the major interests in soil analysis is the
evaluation of its chemical, physical and biological parameters, which are
indicators of soil quality (the most important is the organic matter).
Besides there is a great interest in the study of humic substances and on
the assessment of pollutants, such as pesticides and heavy metals, in
soils. Chemometrics is a powerful tool to deal with these problems and can
help soil researchers to extract much more information from their data. In
spite of this, the presence of these kinds of strategies in the literature
has obtained projection only recently. The utilization of chemometric
methods in soil analysis is evaluated in this article. The applications
will be divided in four parts (with emphasis in the first two): (i)
descriptive and exploratory methods based on Principal Component Analysis
(PCA); (ii) multivariate calibration methods (MLR, PCR and PLS); (iii)
methods such as Evolving Factor Analysis and SIMPLISMA; and (iv)
artificial intelligence methods, such as Artificial Neural
Sena, M. M., & Poppi, R. J. (2004).
N-way PLS applied to simultaneous spectrophotometric determination of
acetylsalicylic acid, paracetamol and caffeine. Journal of
Pharmaceutical and Biomedical Analysis, 34, 27-34.
In this work, a simple and rapid analytical procedure was
proposed for simultaneous determination of acetylsalicylic acid (ASA),
paracetamol (PRC, also known as acetaminophen) and caffeine (CAF) in
pharmaceutical formulations based on multivariate calibration and UV
spectrophotometric measurements (210-300 nm). The calibration set was
constructed with nine solutions in the concentration ranges from 10.0 to
15.0 mug ml(-1) for ASA and PRC and from 2.0 to 6.0 mug ml(-1) for CAF,
according to an experimental design. The procedure was repeated at four
different pH values: 2.0, 3.0, 4.0 and 5.0. Partial least squares (PLS)
models were built at each pH and used to determinate a set of synthetic
mixtures. The best model was obtained at pH 5.0. An N-way PLS model was
applied to a three-way array constructed using all the pH data sets and
enabled better results. This calibration model provided root mean squares
errors of prediction (RMSEP) from 11.5 to 35% lower than those obtained
with PLS at pH 5.0, depending on the analyte. The results achieved for the
determination of these drugs in commercial tablets were in agreement to
the values specified by the manufactures and the recovery was between 94.7
Sena, M. M., Trevisan, M. G., & Poppi, R. J. (2005).
PARAFAC: A chemometric tool for multi-dimensional data treatment.
Applications in direct determination of drugs in human plasma by spectrofluorimetry.
Quimica Nova, 28, 910-920.
Since the last decade, the combined use of chemometrics
and molecular spectroscopic techniques has become a new alternative for
direct drug determination, without the need of physical separation. Among
the new methodologies developed, the application of PARAFAC in the
decomposition of spectrofluorimetric data should be highlighted. The first
objective of this article is to describe the theoretical basis of PARAFAC.
For this purpose, a discussion about the order of chemometric methods used
in multivariate calibration and the development of multi-dimensional
methods is presented first. The other objective of this article is to
divulge for the Brazilian chemical community the potential of the
combination PARAFAC/spectrofluorimetry for the determination of drugs in
complex biological matrices. For this purpose, two applications aiming at
determining, respectively, doxorrubicine and salicylate in human plasma
Serneels, S., Moens, M., Van Espen, P. J., & Blockhuys, F. (2004).
Identification of micro-organisms by dint of the electronic and trilinear partial
least squares regression.
Analytica Chimica Acta, 516, 1-5.
Ventilator-associated pneumonia is one of the most lethal infections
occurring in intensive care units of hospitals. In order to obtain a faster method of
diagnosis, we proposed to apply the electronic nose to cultures of the relevant
micro-organisms. This allowed to halve the time of the analysis. In the current paper,
we focus on the application of some chemometrical tools which enhance the performance of
the method. Trilinear partial least squares (tri-PLS) regression is used to perform
calibration and is shown to produce satisfactory predictions. Sample specific prediction
intervals are produced for each predicted value, which allows us to eliminate erroneous
predictions. The method is applied to an external validation set and it is shown that
only a single observation out of 22 is being wrongly classified, so that the method is
acceptable for inclusion in the clinical routine.
Shaffer, R. E., Rose-Pehrsson, S. L., & McGill R. A. (1998).
Multiway anaysis of preconcentrator-sampled surface acoustic wave chemical sensor array data.
Field Analytical Chemistry and Technology, 2, 179-192.
New data processing methods for preconcentrator-sampled surface acoustic wave (SAW)
sensor arrays are described. The preconcentrator-sampling procedure is used to collect and
concentrate analyte vapors on a porous solid sorbent, Subsequent thermal desorption provides a crude
chromatographic separation of the collected vapors prior to exposure to the SAW array. This article
describes experiments to test the effects of incorporating retention information into the
pattern-recognition procedures and to explore the feasibility of multiway classification methods.
Linear discriminant analysis (LDA) and nearest-neighbor (NN) pattern-recognition models are built to
discriminate between SAW sensor array data for four toxic organophosphorus chemical agent vapors and
one agent simulant collected under a wide variety of conditions. Classification results are obtained
for three types of patterns: (a)first-order patterns; (b) first-order patterns augmented with the
time of the largest peak; and (c) second-order patterns with the use of the SAW frequency for each
sensor over a broad time window. Classification models for the second-order patterns are also
developed with the use of unfolded and multiway partial least-squares discriminants (uPLSD and mPLSD)
and NN and LDA of the scores from unfolded and multiway principal-component analysis (uPCA and mPCA),
It is determined that classification performance improves when information about the desorption time
is included, Treating the preconcentrator-sampled SAW sensor array as a second-order analytical
instrument and using a classification model based upon either uPLSD, uPCA-LDA, or NN results in the
correct identification of 100% of the patterns in the prediction set. With the second-order patterns,
the other pattern-recognition algorithms only do slightly worse.
Shapiro, A., & Ten Berge, J. M. F. (2002).
Statistical inference of Minimum Rank Factor Analysis.
Psychometrika, 67, 79-94.
For any given number of factors, Minimum Rank Factor Analysis yields
optimal communalities for an observed covariance matrix in the sense that the unexplained
common variance with that number of factors is minimized, subject to the constraint that
both the diagonal matrix of unique variances and the observed covariance matrix minus
that diagonal matrix are positive semidefinite. As a result, it becomes possible to
distinguish the explained common variance from the total common variance. The percentage
of explained common variance is similar in meaning to the percentage of explained observed
variance in Principal Component Analysis, but typically the former is much closer to 100
than the latter. So far, no statistical theory of MRFA has been developed. The present
paper is a first start. It yields closed-form expressions for the asymptotic bias of the
explained common variance, or, more precisely, of the unexplained common variance, under
the assumption of multivariate normality. Also, the asymptotic variance of this bias is
derived, and also the asymptotic covariance matrix of the unique variances that define a
MRFA solution. The presented asymptotic statistical inference is based on a recently
developed perturbation theory of semidefinite programming. A numerical example is also
offered to demonstrate the accuracy of the expressions.
Shaywitz, B.A., Shaywitz, S.E., Pugh, K.R., Constable, R.T.,
Skudlarski, P., Fulbright, R.K., Bronen, R.A., Fletcher,
J.M., Shankweiler, D.P., Katz, L., & Gore, J.C. (1995).
Sex-differences in the functional-organization of
the brain for language.
Nature, 373, 607-609.**
A much debated question is whether sex differences
exist in the functional organization of the brain
for language(1-4). A long-held hypothesis posits
that language functions are more likely to be
highly lateralized in males and to be represented
in both cerebral hemispheres in females(5,6), but
attempts to demonstrate this have been
inconclusive(7-17). Here we use echo-planar
functional magnetic resonance imaging(18-21) to
study 38 right-handed subjects (19 males and 19
females) during orthographic (letter recognition),
phonological (rhyme) and semantic (semantic
category) tasks. During phonological tasks, brain
activation in males is lateralized to the left
inferior frontal gyrus regions; in females the
pattern of activation is very different, engaging
more diffuse neural systems that involve both the
left and right inferior frontal gyrus. Our data
provide clear evidence for a sex difference in the
functional organization of the brain for language
and indicate that these variations exist at the
level of phonological processing.
Shikiar, R. (1974a).
An empirical comparison of two individual differences
multidimensional scaling models. Educational and
Psychogical Measurement, 34,
For each of five similarity judgment tasks (8-20 stimuli; 115
(student) judges), the INDSCAL and three-mode scaling object
space solutions were compared, and found to be very similar.
The comparisons of the subject spaces were less similar due to
largely unexplained reasons.
Shikiar, R. (1974b).
The perception of politicians and political issues: a
multidimensional scaling approach. Multivariate
Behavioral Research, 9, 461-477.
Similarity judgments among all possible pairs of the 8
candidates for the 1972 presidency election (USA), among the
12 attributes, and among all candidate-attribute combinations
were analysed using Tucker (1972). The components were
validated by regression analyses using additional
Siciliano, R. (1992).
Reduced-rank models for dependence analysis of contingency tables.
Statistica Applicata, 4, 481-501.
In the framwork of contingency table analysis, the present
paper overviews some of the contributions by the French,
Anglo-Saxon, Italian and Dutch schools. Special attention in
Italy is given to dependence analysis for the case that a set of
response variables can be distinguished from a set of exploratory
variables. Dependence models which provide a reduced-rank
decomposition of a (transformed) matrix of conditional
probabilities are discussed.
Siciliano, R., & Mooijaart, A. (1997).
Three-factor association models for three-way contingency tables.
Computational Statistics & Data Analysis, 24, 337 -
A general formulation of association models is introduced for the
analysis of contingency tables. The two-factor and three-factor
interaction matrices are decomposed into matrices of lower rank.
In particular, the three-factor interaction is decomposed by the
PARAFAC model. Various conditional models can be used to validate
special assumptions for the data such as departures from
conditional independence in the context of sets of contingency
tables. The problem of identification is discussed. Two sets of
data are analysed to illustrate the versatility in the
interpretaiton and the advantages of the models developed here.
Sidiropoulos, N.D., & Bro, R. (1999).
Mathematical programming algorithms for regression-based nonlinear
filtering in N-dimensional real space. IEEE Transactions on
processing, 47, 771-782.
This paper is concerned with regression under a "sum" of partial order
include locally monotonic, piecewise monotonic, runlength constrained,
and unimodal and
oligomodal regression. These are of interest not only in nonlinear
filtering but also in
density estimation and chromatographic analysis. It is shown that under a
error criterion, these problems can be transformed into appropriate
finite problems, which
can then be efficiently solved via dynamic programming techniques.
Although the result does
not carry over to least squares regression, hybrid programming algorithms
can be developed to
solve least squares counterparts of certain problems in the
Sidiropoulos, N.D., & Bro, R. (2000).
On the uniqueness of multilinear decomposition of N-way arrays.
Journal of Chemometrics, 14, 229-239.
We generalize Kruskal's fundamental result on the uniqueness of trilinear
decomposition of three-way arrays to the case of multilinear decomposition of
four- and higher-way arrays. The result is surprisingly general and simple and
has several interesting ramifications.
Sidiropoulos, N.D., Bro, R., & Giannakis, G.B. (2000).
Parallel factor analysis in sensor array processing. IEEE Transactions on
Signal Processing, 48, 2377-2388.
This paper links multiple invariance sensor array processing (MI-SAP) to
parallel factor (PARAFAC) analysis, which is a tool rooted in Psychometrics and
Chemometrics. PARAFAC is a common name for low-rank decomposition of three- and
higher way arrays. This link facilitates the derivation of powerful
identifiability results for MI-SAP, shows that the uniqueness of single- and
multiple-invariance ESPRIT stems from uniqueness-of low-rank decomposition of
three-way arrays, and allows tapping on the available expertise for fitting the
PARAFAC model. The results are applicable to both data-domain and subspace MI-
SAP formulations. The paper also includes a constructive uniqueness proof for a
special PARAFAC model.
Sidiropoulos, N.D., Giannakis, G.B., & Bro, R. (2000).
Blind PARAFAC receivers for DS-CDMA systems. IEEE Transactions on Signal
Processing, 48, 810-823.
This paper links the direct-sequence
code-division multiple access ( DS-CDMA) multiuser
separation-equalization-detection problem to the
parallel factor (PARAFAC) model, which is an
analysis tool rooted in psychometrics and
chemometrics. Exploiting this link, it derives a
deterministic blind PARAFAC DS-CDMA receiver with
performance close to nonblind minimum
mean-squared error (MMSE). The proposed PARAFAC
receiver capitalizes on code, spatial, and
temporal diversity-combining, thereby supporting
small sample sizes, more users than sensors,
and/or less spreading than users. Interestingly,
PARAFAC does not require knowledge of spreading
codes, the specifics of multipath (interchip
interference), DOA-calibration information,
finite alphabet/constant modulus, or statistical
independence/whiteness to recover the
information-bearing signals. Instead, PARAFAC
relies on a fundamental result regarding the
uniqueness of low-rank three-way array
decomposition due to Kruskal (and generalized
herein to the complex-valued case) that
guarantees identifiability of all relevant
signals and propagation parameters. These and
other issues are also demonstrated in pertinent
Sidiropoulos, N. D., & Liu, X. (2001).
Identifiability results for blind beamforming in incoherent multipath with small delay spread.
IEEE Transactions on Signal Processing, 49, 228-236.
Several explicit identifiability results are derived for deterministic blind
beamforming in incoherent multipath with small delay spread. For example, it is
shown that if the sum of spatial and fractional sampling diversities exceeds two
times the total number of paths, then identifiability can be guaranteed even for
one symbol snapshot. The tools come from the theory of low-rank three-way array
decomposition (commonly referred to as parallel factor analysis (PARAFAC) and data
smoothing in one and two dimensions, New results regarding the Kruskal-rank of certain
structured matrices are also included, and they are of interest in their own right.
Simons, S. J. R., Ni, X., Tabe, H. T., West, R. M., & Williams, R. A. (1999).
Reduction of tomographic data for use in control of multiphase processes.
Chemical Engineering Communications, 175, 99-115.
Tomograhic sensors are ideally suited to the on-line control of multiphase processes. Little work
to date however has been undertaken to determine what type and style of information is required from an image to
provide effective process control. In this paper, a possible strategy is presented; namely, a combination of
Principal Component Analysis (PCA) and Neural Networks (NN) is used to convert multivariate data from tomographic
images into useful information suitable for the control and optimization of chemical processes.
Sinha, A. E., Fraga, C. G., Prazen, B. J. & Synovec, R. E. (2004a).
Trilinear chemometric analysis of two-dimensional comprehensive gas
chromatography-time-of-flight mass spectrometry data.
Journal of Chromatography A, 1027, 269-277.
Two-dimensional comprehensive gas chromatography (GC x GC) is a powerful instrumental
tool in its own right that can be used to analyze-complex mixtures. generating
selective data that is applicable to multivariate quantitative analysis and pattern
recognition. It has been recently demonstrated that by coupling GC x GC to time-of-flight
mass spectrometry (TOFMS), a highly selective technique is produced. One separation
on a GC x GC[TOFMS provides retention times on two chromatographic columns and a
complete mass spectrum for each component within the mixture. In this manuscript,
we demonstrate how the selectivity of GC x GC/TOFMS combined with trilinear chemometric
techniques such as trilinear decomposition (TLD) and parallel factor analysis (PARAFAC)
results in a powerful analytical methodology. Using TLD and PARAFAC. partially resolved
components in complex mixtures can be deconvoluted and identified using only one
data set without requiring either signal shape assumptions or fully selective mass
signals. Specifically, a region of overlapped peaks in a complex environmental sample
was mathematically resolved with TLD and PARAFAC to demonstrate the utility of these
techniques as applied to GC x GC/TOFMS data of a complex mixture. For this data,
it was determined that PARAFAC initiated by TLD performed a better deconvolution
than TLD alone. After deconvolution. mass spectral profiles were then matched to
library spectra for identification. A standard addition analysis was performed on
one of the deconvoluted analytes to demonstrate the utility of TLD-initiated PARAFAC
for quantification without the need for accurate retention time alignment between
sample and standard data sets. (C) 2003 Elsevier B.V. All rights reserved.
Sinha, A. E., Hope, J. L., Prazen, B. J., Fraga, C. G., Nilsson, E. J., & Synovec, R. E. (2004b).
Multivariate selectivity as a metric for evaluating comprehensive two-dimensional gas
chromatography-time-of-flight mass spectrometry subjected to chemometric peak deconvolution.
Journal of Chromatography A, 1056, 145-154.
Two-dimensional gas chromatography (GC x GC) coupled to time-of-flight
mass spectrometry (TOFMS) [GC x GC-TOFMS)] is a highly selective technique well suited
to analyzing complex mixtures. The data generated is information-rich, making it
applicable to multivariate quantitative analysis and pattern recognition. One separation
on a GC x GC-TOFMS provides retention times on two chromatographic columns and a complete
mass spectrum for each component within the mixture. In this report, we demonstrate how
GC x GC-TOFMS combined with trilinear chemometric techniques, specifically parallel
factor analysis (PARAFAC) initiated by trilinear decomposition (TLD), results in a
powerful analytical methodology for multivariate deconvolution. Using PARAFAC, partially
resolved components in complex mixtures can be deconvoluted and identified without.
Requiring a standard data set, signal shape assumptions or any fully selective mass
signals. A set of four isomers (iso-butyl, sec-butyl, tert-butyl, and n-butyl benzenes)
is used to investigate the practical limitations of FARAFAC for the deconvolution of
isomers at varying degrees of chromatographic resolution and mass spectral selectivity.
In this report, multivariate selectivity was tested as a metric for evaluating GC x
GC-TOFMS data that is subjected to PARAFAC peak deconvolution. It was found that
deconvolution results were best with multivariate selectivities over 0.18. Furthermore,
the application of GC x GC-TOFMS followed by TLD/PARAFAC is demonstrated for a plant
metabolite sample. A region of GC x GC-TOFMS data from a complex natural sample of a
derivatized metabolic plant extract from Huilmo (Sisyrinchium striatum) was analyzed
using TLD/PARAFAC, demonstrating the utility of this analytical technique on a natural
sample containing overlapped analytes without selective ions or peak shape assumptions.
Sjöberg, L. (1977).
Choice frequency and similarity. Scandinavion Journal
of Psychology, 18, 103-115.
T3 (Tucker, 1966, Method III) was used to analyse the
judgments of 215 students about 7 Swedish political parties
using 18 rating scales. The judgments were requested as part
of a larger study. The three component spaces for the scales
and the parties were each varimax rotated, the latter yielded
an (unrecognized?) three-dimensional 'horse shoe'.
Sjöberg, L. (1984).
Interests, effort, achievement and vocational preference.
British Journal of Educational Psychology, 54,
The components of interest in natural sciences and technology were studied in
100 students in the science and technology divisions of the Swedish secondary
school. Structural analysis of the relationships between interest and
achievement related variables using Kroonenberg's TUCKALS3 program suggested
that effort was mainly directed towards school subjects which students rated as
important in which they perceived a high degree of ability.
Skolnick, A. (1981).
Married lives: Longitudinal perspectives on marriage. In D.H.
Eichorn, J.A. Clausen, N. Haan, M.P. Honzik, & P.H. Mussen. (Eds.),
Present and past in middle life (pp. 269-298). New York: Academic
This paper uses the six dimensions resulting from a PARAFAC analysis performed
on Q sort data of 136 persons at several time points. The PARAFAC analyses are
described in Harshman &
Multivariate calibration of reversed-phase chromatographic
systems. Unpublished doctoral thesis, University of Groningen.
Part 1. Statistical introduction.
1. The choice of markers; 2. The linear model; 3. Biased estimation; 4.
Experimental design considerations.
Part 2. Reversed-phase chromatic introduction.
5. The mobile phase; 6. The stationary phase; 7. Calibration of reversed-phase
chromatographic systems; 8. New calibration strategies aimed at prediction of
retention on new chromatographic systems.
Part 3. Calibration of various types of stationary phases.
9. Experimental design; 10. Two-way approach: the induced-variance criterion;
11. Two-way approach: the determinant criterion; 12. Two-way approach: other
marker choices; 13. Three-way approaches.
Part 4. Calibration of octadecyl stationary phases of different batches.
14. Experimental design; 15. Two-way approaches; 16. Three-way
Smilde, A.K. (1992).
Three-way analyses: Problems and prospects. Chemometrics and
Intelligent Laboratory Systems, 15, 143-157.
Three-way methods are multivariate data analysis tools that
compress and visualize simultaneous variation of combinations of
variables and objects. Unfolding, Tucker and PARAFAC models are
examples of such methods. The interest in such tools is
increasing in chemometrics. The history of three-way methods is
sketched and the basic theory is presented, together with
chemical applications. Problems in the three-way analyses area re
summarized. Some prospects for future use of three-way methods
Smilde, A.K. (1997).
Comments on multilinear PLS. Journal of Chemometrics,
In 1996 Bro published a paper on Multilinear Partial Least Squares
(PLS) in which he proposed a generalisation of PLS to multiway
situations, called multilinear PLS, which is a mixture of a
trilinear model (PARAFAC) and PLS. However, Bro does not give the
equations for the prediction step. In this paper these prediction
equations are given in both their full and closed forms. The
least squares properties of the proposed multilinear PLS are
established and a more comprehensive notation is given. Using
this notation, it is clear that some other multiway analysis
methods such as PARAFAC and Tucker1 models can be combined with
PLS. Multiway methods such as Tucker2 and Tucker3 need a
different approach. A framework is given for general two-block
Smilde, A.K. (2001a).
Comments on three-way analyses used for batch process data. Journal of
Chemometrics, 15, 19-27.
Recently, several papers have appeared concerning the use of three-way
models for batch process data. In these papers a number of points are
raised. This paper discusses some of these points and illustrates some
pitfalls. More specifically, some theoretical aspects of using different
three-way models for batch process data and some practical consequences
are discussed. The topics of cross-validation and data preprocessing are
also discussed. These issues will be discussed using small simulated
examples and theoretical arguments.
Smilde, A.K., & Doornbos, D.A. (1992).
Simple validatory tools for judging the predictive
performance of Parafac and three-way PLS.
Journal of Chemometrics, 6, 11-28.
The methods Parafac and three-way PLS are compared
with respect to their ability to predict
reversed-phase retention values. Special attention
is paid to simple validatory tools, the meaning
and use of which are explained.
The simple validatory tools consist of percentages
of explained variation in the training set and
those that can be calculated with the use of
markers. These markers are special (reference)
solutes, the retention values of which are used to
gain information about a new object for which
predictions are wanted. Different validatory tools
can be calculated with the use of these marker
retention values: Percentages of used variation
and mean sum of squared residuals after applying
the model to these marker retention values. The
validatory tools are evaluated on their power to
estimate their test set counterparts: The
percentages of explained variation in the test set
and mean sum of squared prediction errors in the
Two different data sets from reversed-phase
chromatography are used to evaluate the validatory
tools. The first data set has a high
signal-to-noise ratio and is measured under the
same measurement conditions. The second data set
has a low signal-to-noise ratio and is measured
under different measurement conditions. Some of
the simple validatory tools seem to have relevance
to their test set counterparts, even in the case
of the second data set.
Smilde, A. K., Hoefsloot, H. C. J., Kiers, H. A. L., Bijlsma, S., & Boelens, H. F. M. (2001b).
Sufficient conditions for unique solutions within a certain class of curve resolution models.
Journal of Chemometrics, 15, 405-411.
Curve resolution is a class of techniques concerned with estimating profiles underlying a set of
measurements of time-evolving chemical systems. In general, the estimated profiles are not unique. Both intensity
and rotational ambiguities exist in the solutions of these problems. Constraints can be imposed on the solution to
decrease the ambiguity. Some chemical systems show closure. It is proven that imposing a closure constraint is
sufficient to solve the intensity ambiguity but not the rotational ambiguity. Some curve resolution techniques are
concerned with estimating reaction rate or equilibrium constants from measurements of evolving systems. Then a
kinetic model is imposed on the measured data. It is proven that imposing a certain class of kinetic models is
sufficient to solve both the rotational and the intensity ambiguity.
Smilde, A.K., & Kiers, H.A.L. (1999).
Multiway covariates regression models. Journal of Chemometrics,
An abundance of methods exist to regress a y variable on a set of
x variables collected in a matrix X. In the chemical sciences a
growing number of problems translate into arrays of measurements X
and Y, where X and Y are three-way
arrays or multiway arrays. In this paper a general model is described for
regressing such a multiway Y on a multiway X, while
taking into account three-way structure in X and Y.
A global least squares optimization problem is formulated to estimate the
parameters of the model. The model is described and illustrated with a real
industrial example from batch process operation. An algorithm is given in an
Smilde, A. K., Tates, A. A., Boelens, H. F. M., Oerlemans, P., & Ruitenberg, G. (2001c).
Systematic investigation of process and product variations in a spindraw-winding process.
Chemical Engineering Science, 56, 4993-5002.
The variation in product quality of industrial poly-ethylene terephthalate (PET) produced in a
spindraw-winding process was related to on-line measured process variables. An experimental design in three
process variables was used to introduce meaningful variation. Using standard multivariate data analysis techniques
the relation between the variation of the product quality and the process variation could be modeled. The adequacy
of these models was judged by comparing the modeling error to the known measurement error of the quality variables.
It Could be established that the three process variables that were used in the experimental design are responsible
for almost all variation in product quality. This shows the feasibility of the multivariate approach to systematically
analyze the variation in product quality of industrial processes.
Smilde, A.K., Tauler, R., Henshaw, J.M., Burgess, L.W., &
Multicomponent determination of chlorinated hydrocarbons
using a reaction-based chemical sensor. 3. Medium-rank second-order
calibration with restricted Tucker models. Analytical Chemistry,
The calibration of a chemical sensor for chlorinated hydrocarbon
analytes based on the Fujiwara reaction is described. This sensor
generates a particular type of data: medium-rank second-order data.
With this type of data it is possible to calibrate the sensor in
such a way that quantitation for the analytes in the presence of
unknown interferents is possible. The calibration method developed
is a new approach based on so-called restricted Tucker models that
utilize all available chemical information.
Smilde, A.K., Tauler, R., Saurina, J., & Bro, R. (1999).
Calibration methods for complex second-order data. Analytica Chimica Acta,
In this paper, different three-way methods are
tested for their power and shortcomings to solve
complex second-order calibration problems. The
generic calibration problem is quantifying for an
analyte in the presence of an unknown
interferent: A second-order calibration problem.
Due to rank restrictions of the data, standard
second-order calibration methods like generalized
rank annihilation cannot be used to solve the
type of complex second-order calibration problems
shown in this paper. Different real examples are
tested in which it is shown that the three-way
methods can, to a certain extent, deal with the
complex calibrations. This stresses the fact that
all second-order calibration methods should be
regarded as three-way methods, and when put in
this framework, can be compared with respect to
Smilde, A.K., Van der Graaf, P.H., Doornbos, D.A., Steerneman, T.,
& Sleurink, A. (1990).
Multivariate calibration of reversed-phase chromatographic systems:
Some designs based on three-way data analysis. Analytica
Chimica Acta, 235, 41-51.
When retention measurments are available for a set of solutes
on different stationary phases, with varying mobile phase
compositions, the resulting data set can be used to calibrate a
new stationary phase. Two models are tested for this purpose:
three-way partial least squares and parallel factor analysis.
Smilde, A.K., Wang, Y., & Kowalski, B.R. (1994).
Theory of medium-rank second-order calibration with
Journal of Chemometrics, 8, 21-36.
If an analytical instrument or instrumental method
gives a response matrix when analyzing a pure
analyte, the instrument or instrumental method is
called a second-order method. Second-order methods
that generate a response matrix for a pure analyte
of rank one are called rank-one second-order
methods. If the response matrix of a pure analyte
is not rank one, essentially two cases exist:
Medium rank (between two and five) and high rank
(greater than five). Subsequently, medium- and
high-rank second-order calibration tries to use
medium- and high-rank second-order methods to
analyze for analytes of interest in a mixture. a
particular advantage of second-order methods is
the ability to analyze for analytes of interest in
a mixture which contains unknown interferences.
Keeping this advantage is the challenge on moving
away from rank-one second-order calibration
methods. In this paper a medium-rank second-order
calibration method is proposed based on
least-squares restricted Tucker models. With this
method the second-order advantage is retained.
Smilde, A.K., Westerhuis, J.A., & Boqué, R. (2000).
Multiway multiblock component and coveriates regression models. Journal of
Chemometrics, 14, 301-331.
In this paper the general theory of multiway multiblock component and covariates
regression models is explained. Unlike in existing methods such as multiblock
PLS and multiblock PCA, in the new proposed method a different number of
components can be selected for each block. Furthermore, the method can be
generalized to incorporate multiway blocks to which any multiway model can be
applied. The method is a direct extension of principal covariates regression and
therefore works in a simultaneous fashion in which a clearly defined objective
criterion is minimized. It can be tuned to fulfil the requirements of the user.
Algorithms to calculate the components will be presented. The method will be
illustrated with two three-block examples and compared to existing approaches.
The first example is with two-way data and the second example is with a three-
way array. It will be shown that predictions are as good as with the existing
methods, but because for most blocks fewer components are required, diagnostic
properties of the method are improved.
Smilde, A. K., Westerhuis, J. A., & de Jong, S. (2003).
A framework for sequential multiblock component methods.
Journal of Chemometrics, 17, 323-337.
Multiblock or multiset methods are starting to be used in chemistry and biology to study complex
data sets. In chemometrics, sequential multiblock methods are popular; that is, methods that
calculate one component at a time and use deflation for finding the next component. In this paper
a framework is provided for sequential multiblock methods, including hierarchical PCA (HPCA; two
versions), consensus PCA (CPCA; two versions) and generalized PCA (GPCA). Properties of the
methods are derived and characteristics of the methods are discussed. All this is illustrated with a
real five-block example from chromatography. The only methods with clear optimization criteria are
GPCA and one version of CPCA. Of these, GPCA is shown to give inferior results compared with
Smolinski, A., & Walczak, B.(2002a).
Exploratory analysis of chromatographic data-sets with missing elements.
Initialization of the expectation-maximization algorithm.
Acta Chromatographica, 12, 30-48.
The main goal of the work presented in this paper was comparison
of different methods of initialization of missing elements in chromatographic
data-sets to speed up convergence of the expectation-maximization (EM) algorithm.
The EM algorithm can be built into different computational procedures used for
exploratory analysis, for example principal component analysis (PCA) and its
generalization for N-way data, i.e. the Tucker3 model.
Smolinski, A., Walczak, B. & Einax, J. W. (2002b).
Exploratory analysis of data sets with missing elements and outliers.
Chemosphere, 49, 233-245.
The main goal of the presented paper was to develop a general strategy allowing
exploration of contaminated data sets with missing elements, based on application
of robust PLS for initial estimation of missing elements. Using robust distance,
the outlying elements were identified. After their identification and replacing
by missing elements, the expectation-maximization algorithm (which can be built
in into different computational procedures, such as principal component analysis
and its generalisation to the N-way data-the TUCKER3 model) was used for construction
of the final model. (C) 2002 Elsevier Science Ltd. All rights reserved.
Snyder Jr, C.W. (1970).
Intrinsic individual differences in disjunctive conceptual
behavior: three-mode factor analysis. Unpublished doctoral thesis,
University of Pennsylvania. ( Dissertation Abstracts
International, 1970, 32 (1-B), 544.)
Snyder Jr, C.W. (1976).
Multivariate analysis of intrinsic individual differences in
disjunctive conceptual behavior. Multivariate Behavioral Research,
T3 with multitrait-multimethod matrix (Tucker (1966), Method
III) with learning data (40 subjects, 10 trial blocks, and 4
response measures). Relatively clear core matrix.
Snyder Jr, C.W. (1988).
Multimode factor analysis. In J.R. Nesselroade and R.B. Cattell
(Eds.), Handbook of multivariate experimental psychology
(second edition) (pp. 289-316). New York: Plenum Press.
Multimode factor-analytic methods are designed to systematize and represent the
relations in data that are classified by more than two entity sets.
Unfortunately, the mathematical and conceptual extension of factor analysis to
the multimode case is not straightforward. This chapter reviews the difficulties
associated with multimode analysis and outlines some suggested analytic
resolutions. An application in affect assessment, entailing a three-mode
structural hypothesis, will be used to illustrate the different
Snyder Jr, C.W., Bridgman, R.P., & Law, H.G. (1981).
Three-mode factor analytic reference curves for concept
identification. Personality and Individual Differences,
T2 (common FA model on a Multi measure and multiblock matrix
was used to explore the intrinsic individual differences in a
figural, disjunctive conceptual behavior task. 38 students
were scored on 4 response measures during 10 trial blocks.
Trial blocks were varimax, the core matrix counter rotated.
Rather complex core matrix, the interpretation of which was
compared to individual solutions.
Snyder Jr, C.W. and Law, H.G. (1979).
Three-mode common factor analysis: Procedure and computer
programs. Multivariate Behavioral Research,
T3 (Method III) is described in step-by-step format for easy
comprehension. The described procedure uses the SPSS package,
subprogram FACTOR, interfaced with specialized programs
written by the authors.
Snyder Jr, C.W., & Law, H.G. (1981).
Three-mode models for road research. In: J.M. Morris (Ed.),
Proceedings of a Seminar on measuring so cial
behavior in road research. Vermont South, Vic., Australia:
Australian Road Research Board (pp. 39-48).*
Factor analytic and multidimensional scaling models which can
be used on three-way categorised data sets are reviewed in
terms of their usefulness for road researchers. These models
include Harshman's PARAFAC, Tucker's three-mode common factor
analysis, Carroll & Chang's INDSCAL, and Takane, Young & De
Leeuw's ALSCAL. Enough of the formalities associated with each
model is presented to clarify the particular approach to data
analysis. The results are characterised in terms of a
hypothetical road research project on traffic noise.
Snyder Jr, C.W., Law, H.G. & Pamment, P.R. (1979).
Calculation of Tucker's three-mode common factor analysis.
Behavior Research Methods & Instrumentation,
The working of three programs is described. They were written
to interface with the SPSS FACTOR routine to calculate a
solution for T3 by Tucker's methode III (1966).
Snyder, F.W. (1968).
A unique variance model for three-mode factor analysis.
Department of Psychology, University of Illinois, Urbana, Illinois
(also doctoral thesis, 1969). (Dissertation
Abstracts International, 1969, 30
A 'true' T3 factor model is presented which allows for unique
variances for two of the modes and for their combinations. It
extends the model presented in Tucker (1966). The model is a
precursor of Bentler & Lee's (1979) model. The computational
procedure seems complex and cumbersome. Two illustrations: (1)
40 measures on 3 different sets of administrative tasks for
232 school administrators; (2) in each of 6 semesters 18
character and work traits of 222 students of an aviation
school were rated by their teachers. Detailed numerical
Snyder, F.W., & Tucker, L.R. (1970).
Interpretation of the core matrix in three-mode factor
analysis. Paper presented at the Psychometric Society Meeting.
A special interpretation of the core array is developed. After suitable scaling
and rotations and after averaging over the markers of each mode, the core array
is the three-way average of the original data points. Marker variables have a
score of 1 on one component and 0 on all other components. The theoretical
treatment is illustrated with a hypothetical example.
Snyder, F.W. & Wiggins, N. (1973).
Affective meaning systems: a multivariate approach.
Multivariate Behavioral Research, 5,
T3 was applied to the semantic differential ratings of 20 con-
cepts by 100 subjects on 76 bipolar adjectival scales. The 4
scale and 5 concept factors were varimax rotated, the concept
dimensions were given somewhat questionable names, and the
subject dimensions were rotated by hand. An interpretation was
attempted of the rather jumbled core matrix.
Sogon, S., & Doi, K. (1990).
Three-mode factor analysis of
emblematic gesture and body manipulation viewed from the dorsal
perspective. Shinrigaku-Kenkyu, 60, 356-362.
This paper focuses on emblematic gesture and manipulation of body
movements. Subjects viewed from the dorsal perspective the body
movements depicting emotions displayed by two actors/actresses.
Three-mode factor analyses were applied to the data. Three
factors were found in the emotion-mode, three in the scene-mode,
and two factors in the subjects-mode. The emotion-mode and
scene-mode factors were found to correspond to a high degree. The
core matrix and subjects' factor scores were correlated with a
response tendency in terms of subjects' evaluations rather than
their accuracy of judgment.
Soli, S.D., Arabie, P., & Carroll, J.D. (1986).
Discrete representation of perceptual structure underlying
consonant confusions. Journal of the Acoustical
Society of America, 79, 826-837.
The perceptual representation of speech is generally assumed to be
discrete rather than
continuous, pointing to the need for general discrete analytic models to
perceptual similarities among speech sounds. The INDCLUS (INdividual
model and algorithm [J.D. Carroll and P.
Arabie] can provide this generality, representing symmetric three-way
(stimuli × stimuli × conditions) as an additive combination
of overlapping, and
generally not hierarchical, clusters whose weights (which are numerical
values gauging the
importance of the clusters) vary both as a function of the cluster and
considered. INDCLUS was used to obtain a discrete representation of
structure in the Miller and Nicely consonant confusion data [G.A. Miller
and P.E. Nicely
(1955)]. A 14-cluster solution accounted for 82.9% of total variance
across the 17 listening
conditions. The cluster composition and the variations in cluster weights
as a function of
stimulus degredation were interpreted in terms of the common and unique
of the consonants within each cluster. Low-pass filtering and noise
degraded unique attributes, especially the cues for place of
articulation, while high-pass
filtering degraded both unique and common attributes. The clustering
results revealed that
perceptual similarities among consonants are accurately modeled by
additive combinations of
their specific and discrete acoustic attributes whose weights are
determined by the nature of
the stimulus degradation.
Soltanian-Zadeh, H., & Peck, D. J. (2001).
Feature space analysis: Effects of MRI protocols.
Medical Physics, 28, 2344-2351.
We present a method for exploring the relationship between the image segmentation results obtained
by an optimal feature space method and the MRI protocols used. The steps of the work accomplished are as follows.
(1) Patients with brain tumors were imaged on a 1.5 T General Electric Signa MRI System using multiple protocols
(T1 and T2-weighted fast spin-echo and FLAIR). T1-weighted images were acquired before and after gadolinium injection.
(2) Image volumes were co-registered. and images of a slice through the center of the tumor were selected for
processing. (3) For each patient, several image sets were defined by selecting certain MR images (e.g., 4T2's +
1T1, 4T2's + FLAIR. 2T2's + 1T1). (4) Using each image set, the optimal feature space was generated and images
were segmented into normal tissues and different tumor zones. (5) Segmentation results obtained using the
different MRI sets were compared. Based on the analysis results from 27 image sets. we found that the locations
of the clusters for the tumor zones and their corresponding regions in the image domain changed as a function of
the MR images (MRI protocols) used. However. the segmentation results for the total lesion and normal tissues
remained relatively unchanged.
Soltanian-Zadeh, H., Windham, J. P., & Peck, D. J. (1996).
Optimal linear transformation for MRI feature extraction.
IEEE Transactions on Medical Imaging, 15, 749-767.
This paper presents development and application of a feature extraction method for magnetic
resonance imaging (MRI), without explicit calculation of tissue parameters. A three-dimensional (3-D) feature
space representation of the data is generated in which normal tissues are clustered around prespecified target
positions and abnormalities are clustered elsewhere. This is accomplished by a linear minimum mean square error
transformation of categorical data to target positions. From the 3-D histogram (cluster plot) of the transformed
data, clusters are identified and regions of interest (ROI's) for normal and abnormal tissues are defined. These
ROI's are used to estimate signature (prototype) vectors for each tissue type which in turn are used to segment
the MRI scene. The proposed feature space is compared to those generated by tissue-parameter-weighted images,
principal component images, and angle images, demonstrating its superiority for feature extraction and scene
segmentation. Its relationship with discriminant analysis is discussed. The method and its performance are
illustrated using a computer simulation and MRI images of an egg phantom and a human brain.
Soltanian-Zadeh, H., Windham, J. P., Peck, D. J., & Mikkelsen, T. (1998).
Feature space analysis of MRI.
Magnetic Resonance in Medicine, 40, 443-453.
This paper presents an MRI feature-space image-analysis method and its application to brain tumor
studies. The proposed method generates a transformed feature space in which the normal tissues (white matter,
gray matter, and CSF) become orthonormal. As such, the method is expected to have site-to-site and patient-to-patient
consistency, and is useful for identification of tissue types, segmentation of tissues, and quantitative measurements
on tissues, The steps of the work accomplished are as follows: (1) Four T-2-weighted and two T-1-weighted images
(before and after injection of gadolinium) were acquired for 10 tumor patients. (2) Images were analyzed by an
image analyst according to the proposed algorithm, (3) Biopsy samples were extracted from each patient and were
subsequently analyzed by the pathology laboratory. (4) Image-analysis results were compared with the biopsy results.
Pre- and postsurgery feature spaces were also compared, The proposed method made it possible to visualize the MRI
feature space and to segment the image. In all cases, the operators were able to find clusters for normal and
abnormal tissues. Also, clusters for different zones of the tumor were found. The method successfully segmented
the image into normal tissues (white matter, gray matter, and CSF) and different zones of the lesion (tumor, cyst,
edema, radiation necrosis, necrotic core, and infiltrated tumor). The results agreed with those obtained from the
biopsy samples. Comparison of pre- with postsurgery and radiation feature spaces illustrated that the original
solid tumor was not present in the second study, but a new tissue component appeared in a different location of
the feature space. This tissue could be radiation necrosis generated as a result of radiation.
Soltanian-Zadeh, H., Windham, J. P., Peck, D. J., & Yagle, A. E. (1992).
A comparative-analysis of several transformations for enhancement and segmentation of magnetic-resonance
image scene sequences.
IEEE Transactions on Medical Imaging, 11, 302-318.
We compare the performance of the eigenimage filter to that of several other filters, applied to
magnetic resonance image (MRI) scene sequences for images enhancement and segmentation. Comparisons are made with
principal component analysis, matched, modified-matched, maximum contrast, target point, ratio, log-ratio, and
angle image filters. Signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), segmentation of a desired feature
(SDF), and correction for partial volume averaging effects (CPV) are used as performance measures. For comparison,
analytical expressions for SNRs and CNRs of filtered images are derived, and CPV by a linear filter is studied.
Properties of filters are illustrated through their applications to simulated and acquired MRI sequences of a
phantom study and a clinical case; advantages and weaknesses are discussed. Our conclusion is that the eigenimage
filter is the optimal linear filter that achieves SDF and CPV simultaneously.
Sorenson, L. (1986).
Factor analysis of open-field behavior in rats: Using the
three-way PARAFAC model for longitudinal data. Paper presented
at the Annual Meeting of the Canadian Psychological Association,
Recognition of the fact that single variable approaches to the study of
animal behavior are
often inadequate has led to the suggestion that "behavioral profiles"
multivariate measurement techniques might better describe a behavioral
phenomenon. In the
experiment reported here we examined one such application of multivariate
subjecting a longitudinal data set obtained during open-field testing of
rats to a
PARAFAC analysis. The PARAFAC procedure allows one to directly analyze
three-way arrays and is this very appropriate for longitudinal data.
two-way factor analytic models that provide many possible solutons because
the factors can be
arbitrarily rotated, the PARAFAC model provides a unique factor
a data set. A PARAFAC analysis thus provides an empirically grounded basis
selecting the best candidates for "real" factors within a given domain.
measures were collected for twenty-six rats tested during four sessions
spaced 48-hours apart.
The PARAFAC analysis extracted two factors, the first reflecting emotional
and the second reflecting exploration. These two factors change in
temporal prominence with
animals showing greater emotional reactivity on the first test session and
greater levels of
exploration on the third and fourth test sessions. These results are in
general accord with
previous findings using more conventional approaches and suggest that
such as these may be of great value to researchers in the behavioral
SOUPAC program descriptions. Computing Services
Offices, University of Illinois, Urbana, Ill., 1973.
Describes implementations of Tucker's (1966) methods I and II
for three-mode factor analysis.
Spanjer, M.C. (1984).
Substituent interaction effects and mathematical-statistical
description of retention in liquid chromatography. Unpublished
doctoral thesis, University of Utrecht.
I. Substituent interaction effects in aromatic molecules in reversed-phase
II. Substituent interaction effects in aromatic molecules in RP-HPLC with
acetonitrile-water and tetrahudrofuran-water eluents.
III. A comparison of some linear substituent free energy relationships.
IV. Simultaneous description of the influence of solvent, reaction type and
substituent on equilibrium constants by means of three-mode factor
V. Three-mode factor analysis of data on the retention in normal-phase
Ståhle, L. (1989).
Aspects of the analysis of three-way data. Chemometrics and
Intelligent Laboratory Systems, 7, 95-100.
An algorithm is developed for linear three-way decomposition
(LTD) of three- way tables for the case of one dependent block of
variables and one independent, predictor block. The algorithm is
a generalization of the two-block partial least- squares (PLS)
algorithm. Using simulation and real data LTD is compared with
multi-way PLS with and without decomposition of the eight matrix.
LTD and PLS with a one-dimensional decomposition of the weight
matrix gives essentially the same results. By means of the
cross-validation criterion it is shown that, in practice, optimal
prediction may be obtained with a model that is neither
completely trilinear nor bilinear. The multi-way PLS method with
decomposition of the weight matrix to give the minimum
cross-validation perdiction error is preferred.
Ståhle, L. (1991).
Relating multivariate time-seris by linear 3-way decomposition (LTD) and partial least-squares (PLS) analysis.
Journal of Pharmaceutical and Biomedical Analysis, 9, 671-678.
The problem of relating multivariate time-series which is common in drug development is considered.
The mathematical and statistical problems involve relating two three-way tables. These tables have objects and
time-points in common while the variables to be related are unique for each table. A modification is presented of
the linear three-way decomposition (LTD) algorithm which directly incorporates the information that both objects
and time-points are common to the two tables. A comparison is made with partial least squares (PLS) analysis both
at the theoretical level and in their application to three sets of real data. Limitations of LTD are discussed,
in particular the constraint imposed by the trilinearity requirement, and areas for future development are proposed.
Stanimirova, I., Walczak, B., Massart, D. L., Simeonov, V.,
Saby, C. A., & Di Crescenzo, E. (2004).
STATIS, a three-way method for data analysis. Application to environmental data.
Chemometrics and Intelligent Laboratory Systems, 73, 219-233.
The present paper deals with the data exploration of three-way
environmental data with the use of "Structuration des Tableaux A Trois Indices de la
Statistique" (STATIS). The performance of the method is compared with Tucker3 and
PARAFAC2, two more commonly used methods in chemometric N-way data analysis. The
features of STATIS are demonstrated on real data sets. Due to its robust properties,
lack of special requirements for data preprocessing and ability to deal with sets of
two-way tables (matrices) that do not have the same dimension for columns or rows,
STATIS appears as a very attractive three-way exploratory tool.
Stankov, L., & Chen, K. (1988).
Can we boost fluid and crystallised intelligence? A structural
modelling approach. Australian Journal of Psychology,
The invariant factor structure model for
multimode data (
McDonald, 1984)was fitted, with LISREL, to
data obtained from two groups of high-school students. The
experimental group was exposed to extensive training in creative
problem solving over a three-year period. The control group
attended normal school activities. The same battery of eight
intelligence tests was administered three times: at the beginning
of the experiment, at the end of training, and one year after the
end of training. The results indicate that, at the last testing
session, the experimental group performed better than the control
group on both fluid and crystallised intelligence factors. In
addition, by employing both invariant factor analysis and
simultaneous factor analysis it was possible to conclude that
fluid intelligence is affected slightly more by training than
Stedmon, C. A., Markager, S. & Bro, R. (2003).
Tracing dissolved organic matter in aquatic environments using a new approach to
fluorescence spectroscopy. Marine Chemistry, 82, 239-254.
Dissolved organic matter (DOM) is a complex and poorly understood mixture of organic
polymers that plays an influential role in aquatic ecosystems. In this study we have
successfully characterised the fluorescent fraction of DOM in the catchment of a
Danish estuary using fluorescence excitation-emission spectroscopy and parallel
factor analysis (PARAFAC). PARAFAC aids the characterisation of fluorescent DOM by
decomposing the fluorescence matrices into different independent fluorescent components.
The results reveal that at least five different fluorescent DOM fractions present
(in significant amounts) in the catchment and that the relative composition is dependent
on the source (e.g. agricultural runoff, forest soil, aquatic production). Four
different allochthonous fluorescent groups and one autochthonous fluorescent group
were identified. The ability to trace the different fractions of the DOM pool using
this relatively cheap and fast technique represents a significant advance within
the fields of aquatic ecology and chemistry, and will prove to be useful for catchment
Steeby, J. A., Hargreaves, J. A., & Tucker, C. S. (2004).
Factors affecting sediment oxygen demand in commercial channel catfish ponds.
Journal of the World Aquaculture Society, 35, 322-334.
Sediment oxygen demand (SOD) measured in 45 commercial channel catfish
ponds in northwest Mississippi using in situ respirometry (N = 167) ranged from 63 to
1,038 mg/m(2) per h. Mean SOD in this study (359 mg/m(2) per h) was greater than that
reported previously for catfish ponds but was similar to SOD in semi-intensive marine
shrimp ponds. Nine variables were selected and measured to assess their relative
importance in accounting for variation in SOD. Six variables were included in multiple
regression models that explained slightly more than half of the variation in SOD. These
variables were: dissolved oxygen concentration at the beginning of respirometry
incubation;, particulate organic matter concentration in water above the sediment
surface; organic carbon concentration at the immediate sediment-water interface
(flocculent or F-layer) combined with the upper 2 cm of sediment (Slayer); organic
carbon concentration in the mature (M) underlying sediment layer; water temperature;
and total depth of accumulated sediment. Sediment oxygen demand was most sensitive to
changes in dissolved oxygen concentration in the overlying water, particulate organic
matter concentration in the water, and the concentration of organic carbon in the
combined flocculent and upper sediment (F+S) layer. Models for SOD in this research
predict that the mass of sediment below the upper 2-cm surface layer on average
contributes only similar to20% of total SOD. Stratification and normal daily fluctuation
of dissolved oxygen concentration in eutrophic culture ponds likely limit expression of
sediment oxygen demand. Maintaining aerobic conditions at the sediment-water interface
will minimize accumulation of organic matter in pond sediment.
Stefanov, Z. I. & Hoo, K. A.(2003).
Hierarchical multivariate analysis of cockle phenomena. Journal of Chemometrics,
The phenomena called cockle are small wrinkles on the paper surface that appear
during paper production. This condition poses significant economic and operability
problems in the production of magazine paper, as it deteriorates the printabilty
of the paper. There are many and varied sources that can lead to cockle, and their
detection is often very complicated. In this work a multivariate hierarchical approach
is proposed to analyze the cause of cockle. The hierarchy has two levels, the first
of which is a three-way decomposition and analysis of the data collected from sections
of a paper machine. The second level is a two-way decomposition and analysis between
the combined loadings from the three-way decomposition and the measured cockle data.
The results show that this approach is capable of identifying the important process
sections and process variables, in spite of the large dimensionality of the problem.
Data analyzed from two real industrial paper machines, involving several grades of
paper, are used to demonstrate the proposed hierarchical approach.
Stellman, C. M., Booksh, K. S., Muroski, A. R., Nelson, M. P., & Myrick, M. L. (1998).
Principal component mapping applied to Rman microspectroscopy of fiber-reinforced polymer composites.
Science and Engineering of Composite Materials, 7, 51-80.
We describe the development and implementation of a spectroscopic Raman imaging system using
Principal Component data analysis. Raman microspectroscopy followed by multivariate data analysis and principal
component mapping has been used to investigate the spacial variations of chemical and physical properties at
interfaces in glass-reinforced composites on the micrometer scale. A protocol for monitoring chemical and
physical variances via multivariate statistics has been developed and a preliminary study of a "real world"
glass-reinforced composite is presented. It is demonstrated that multivariate Raman imaging is more precisely
interpretable than traditional univariate methods and that by appropriately choosing distinct spectral regions
(such as a cure sensitive epoxide band) for PCA, subtle compositional changes like local cure percentage may be
Stewart, T.R. (1971).
The relation between three-mode factor analysis and
multidimensional scaling of personality trait profiles.
Unpublished doctoral thesis, University of Illinois, Urbana-
Champaign, Ill. (Dissertation Abstracts
International, 1971, 32 (2-B), 1197.)
(see Stewart, 1974)
Stewart, T.R. (1974).
Generality of multidimensional representations. Multivariate
Behavioral Research, 9, 507-519.
Proposes to compare the MDS solution of combination mode
similarity matrices (15 personality descriptions judged in
pairs by 98 subjects), and a PCA solution of a combination-
mode three-mode matrix (judgement on 4 rating scales of 81
hypothetical people by the same 98 subjects) in search for
'generality' of the multidimensional configuration. Although
the usage of Tucker (1972) is claimed for the MDS, only the
combination-mode aspect of it is used.
Stone, M., & Jonathan, P. (1994).
Statistical thinking and technique for QSAR and related studies.
Part II: Specific methods.
Journal of Chemometrics, 8, 1-20.
Twenty-two contrasting statistical methods are reviewed for their
applicability to QSAR studies and similar prediction-oriented fields. Each method is
concisely specified prior to explanatory or critical comment.
Stone, M., & Lundberg, A. (1996).
Three-dimensional tongue surface shapes of English
consonants and vowels.
Journal of the Acoustical Society of America, 7, 7.**
This paper presents three-dimensional tongue surfaces
reconstructed from multiple coronal cross-sectional slices of the tongue.
Surfaces were reconstructed for sustained vocalizations of the American
English sounds /i, i, e, epsilon, ae, a, reverse c, o, upsilon, labda, sic,
l, s, integral, theta, n, eta/. Electropalatography (EPG) data were also
collected for the sounds to compare tongue surface shapes with
tongue-palate contact patterns. The study was interested also in whether
3-D surface shapes of the tongue were different for consonants and vowels.
Previous research and speculation had found that there were differences in
production, acoustics, and linguistic usage between the two groups. The
present study found that four classes of tongue shape were adequate to
categorize all the sounds measured. These classes were bent raising,
complete groove, back raising, and two-point displacement. The first and
third classes have been documented before in the midsagittal plane [cf. R.
Harshman, P. Ladefoged, and L. Goldstein, J. Acoust. Sec. Am. 62, 693-707
(1976)]. The first three classes contained both vowels and consonants, the
last only consonants. Electropalatographic patterns of the sounds indicated
three categories of tongue-palate contact: Bilateral, cross-sectional, and
combination of the two. Vowels used only the first pattern, consonants used
all three. The EPG data provided an observable distinction in contact
pattern between consonants and vowels. The ultrasound tongue surface data
did not. The conclusion was that the tongue actually has a limited
repertoire of shapes and positions them against the palate in different
ways for consonants versus vowels to create narrow channels, divert
airflow, and produce sound.
Stone, M., Shawker, T. H., Talbot, T. L., & Rich, A. H.
Cross-sectional tongue shape during the production of vowels.
Journal of the Acoustical Society of America, 83, 1586-1596.
This study used ultrasound imaging to examine the
cross-sectional shape of the tonque during the production of the ten
English vowels in two consonant contexts - /p/ and /s/- and at two scan
angles - anterior and posterior. Results were compared with models of
sagittal tongue shape. A newly built transduder holder and head testraint
maintained the ultrasound transducer in a fixed position inverior to the
mandible at a chosen location and angle. The transducer was free to move
only in a superior/inferior direction, and demonstrated reliable tracking
of the jaw. Since the tongue is anisotrophic along its length, anterior
and posterior scan angles were examined to identify differences in tongue
shape. Similarly, the coarticulatory effects of the sibilant /s/ versus
the bilabial /b/ were examined, to assess variability of intrinsic tongue
shape for the vowels. Results showed that the subject's midsagittal tongue
grooving was almost universal for the vowels. Posterior grooves were
deeper than anterior grooves. In /s/ context, posterior tongue grooves for
low vowels. Cross-sectional tongue shape varied with tongue position
similarly to sagittal tongue shape.
Stoop, I. (1980).
Sekundaire analyse van de "Van jaar tot jaar data" met behulp van
niet-lineaire multivariate technieken: Verschillen in de
schoolloopbaan van meisjes en jongens. Research Bulletin, RB
001-80, Department of Data Theory, University of Leiden, Leiden,
As part of a reanalysis of the data from a longitudinal study
of the school and vocational carreer of Dutch children,
TUCKALS2 (Kroonenberg & De Leeuw, 1977, 1980, 1981c) was
applied. Also the merits of the technique in relation to
INDSCAL, and some problems with the preliminary version of the
program were discussed. The data consisted of correlation
matrices (boys and girls, resp.) based on 26 variables in the
first analysis and of 7 correlation matrices (one for each
occupational class of the father) based on the same 26
Strordrange, L., Rajalahti, T, & Libnau, F. O. (2004).
Multiway methods to explore and model NIR data from a batch process.
Chemometrics and Intelligent Laboratory Systems, 70, 137-145.
Multiway methods are tested for their ability to explore and model
near-infrared (NIR) spectra from a pharmaceutical batch process. The study reveals that
blocking of data having a nonlinear behaviour into higher-order array can improve the
predictive ability. The variation in each control point is independently modelled and
N-way techniques overcome the nonlinearity problem. Important issues as variable
selection and how to fill in for missing values have been discussed. Variable selection
was shown to be essential to be able to perform multiway modelling. For spectra not yet
monitored, use of mean spectra from calibration set gave close to the best results.
Decomposing the spectra by N-way techniques gave additional information about the
chemical system. To support the results simulated data sets were used.
Sundberg, R. (1999).
Multivariate calibration - Direct and indirect regression methodology.
Scandinavian Journal of Statistics, 26, 161-191.
This paper tries first to introduce and motivate the methodology of multivariate
calibration. Next a review is given, mostly avoiding technicalities, of the somewhat messy theory
of the subject. Two approaches are distinguished: the estimation approach (controlled calibration)
and the prediction approach (natural calibration). Among problems discussed are the choice of
estimator, the choice of confidence region, methodology for handling situations with more variables
than observations, near-collinearities (,vith countermeasures like ridge type regression, principal
components regression, partial least squares regression and continuum regression), pretreatment of
data, and cross-validation vs true prediction. Examples discussed in detail concern estimation of the
age of a rhinoceros from its horn lengths (low-dimensional), and nitrate prediction in waste-water
from high-dimensional spectroscopic measurements.
Swartzman, L. C., Harshman, R. A., Burkell, J., & Lundy, M. E. (2002).
What accounts for the appeal of complementary/alternative medicine, and
what makes complementary/alternative medicine "alternative"?
Medical Decision Making, 22, 431-150.
The goal of this study was to elucidate the basis for the appeal
of complementary/alternative medicine (CAM) and the basis upon which people
distinguish between CAM and conventional medicine. Undergraduates (N = 173) rated
19 approaches to the treatment of chronic back pain on 16 rating scales. Data
were analyzed via 3-mode factor analysis, which extracted conceptual dimensions
common to both the scales and the treatments. A 5-factor solution was judged to
give the best description of the raters' perceptions. One of these 5 factors
clearly reflected the distinction between conventional versus CAM approaches,
and a 2nd factor clearly referred to treatment appeal. The other 3 factors were
invasiveness, health care professional versus patient effort, and "druglikeness."
To the extent that treatment was seen as a CAM treatment (as opposed to a
conventional treatment), it was seen to be more appealing, less invasive, and
less druglike. Simple and partial correlations of the dimension weights indicated
that both the appeal of CAM and the distinction between CAM and conventional
medicine were largely driven by the view that CAM is less invasive than conventional
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Algemene en Gezinspedagogiek - Datatheorie
Centre for Child and
Family Studies |
Department of Education |
The Three-Mode Company |
Education and Child Studies, Leiden University
Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
Tel. *-31-71-5273446/5273434 (secr.); fax *-31-71-5273945
First version : 12/02/1997;