ThreeMode Abstracts, Part D
With one can go to the index of
this part of the bibliography, with
one can go to other
parts (letters) of the bibliography.
INDEX
Da  Db 
Dc  Dd 
De  Df 
Dg  Dh 
Di  Dj 
Dk  Dl 
Dm  Dn 
Do  Dp 
Dq  Dr 
Ds  Dt 
Du  Dv 
Dw  Dx 
Dy  Dz 


Dahl, K.S., Piovoso, M.J. & Kosanovich, K.A. (1999).
Translating thirdorder data analysis methods to
chemical batch processes.
Chemometrics and Intelligent Laboratory Systems, 46, 161
180.
Measurements collected from batch processes
naturally produce a thirdorder or
threedimensional data form. The same structure
also results when multiple samples are measured
using hyphenated analysis techniques such as
liquid chromatography with diode array detection.
Analysis of thirdorder data by principal
components analysis (PCA) is achieved by a
nonunique rearrangement that produces a
twodimensional array. This preferentially models
only one of the three orders present. In
contrast, methods such as parallel factor
analysis (PARAFAC) apply a particular
decomposition that accounts for all three orders
explicitly. The results from either approach
should be related if data are to be interpreted
reliably for applications to batch processes such
as online monitoring and control. This work
compares these two approaches from an applied
point of view. To accomplish this objective,
exemplary methods are selected from each type of
analysis, parallel factor analysis (PARAFAC) and
multiway principal components analysis (MPCA).
These are employed to analyze data obtained
during the manufacture of a condensation polymer
in an industrial batch reactor.

Dahl, T., & Naes, T. (2004).
Outlier and group detection in sensory panels using hierarchical cluster analysis with the
Procrustes distance.
Food Quality and Preference, 15, 195208.
Generalised Procrustes analysis (GPA) is a muchused method for analysing
sensory profile data. In this paper, hierarchical clustering using the Procrustes
distance is proposed for situations where the data profiles are believed to come from a
nonhomogeneous group. This new approach to sensory panel analysis may be used at an
exploratory stage, in combination with GPA, to gain insight into the structures of the
data set. It can help the researcher detect outliers and subgroups, help him/her make
decisions regarding further analysis, and reduce the risk of erroneous inference about
the data.

Dai, K. (1982).
Application of the threemode factor analysis to industrial design
of chair styles. Japanese Psychological Review, 25,91103.
This paper presents a modified vrsion of Tucker's (1966)
method, which was applied to a practical problem of chair style image. One hundred
and fifty subjects rated photographs of twenty styles of chairs in market, with 28
scales.

Dai, K. (1985).
Application of a threemode factor analysis to brand images of whisky.
Reports of Statistical Application Research, 32, 1122.
New interpretation and calculation methods of Tucker's threemode factor analysis
are proposed. The most marked modification is the option, which mode is the theme
of factor analysis and which is not, depending on the purpose of the survey. The
score matrix, in which one mode is summarized into factors, is defined as "onemode
factor score matrix". Twomode factor score and threemode factor score are also
defined. This generalized threemode factor analysis was applied to a survey,
subjects numbering 2762, on brand images of whisky. An example of an interpretation
for onemode factor score and twomode factor score was presented.

Damiani, P. C., Nepote, A. J., Bearzotti, M., & Olivieri, A. C. (2004).
A test field for the secondorder advantage in bilinear leastsquares and parallel
factor analyses: Fluorescence determination of ciprofloxacin in human urine.
Analytical Chemistry, 76, 27982806.
The analytical performances of two algorithms, the recently introduced
bilinear leastsquares (BLLS) and the popular parallel factor analysis (PARAFAC), are
compared as regards secondorder fluorescence data recorded for the determination of the
fluoroquinolone antibiotic ciprofloxacin in human urine samples. The applied chemometric
methodologies employ different strategies for exploiting the socalled secondorder
advantage, which allows one to obtain individual concentrations of calibrated analytes
in the presence of any number of uncalibrated (urine) components. Analysis of a spiked
urine test set (in the analyte concentration range 0200 mg L1) showed that BLLS
provides results of slightly better quality than PARAFAC. Satisfactory results have
been obtained on comparing the concentrations predicted for a series of real urine
samples with those furnished by liquid chromatography. The limit of detection of the
fluorescencebased methods is similar to5 mg L1.

D'Ambra, L. (1989).
Least squares criterion for asymmetric dependence models in threeway
contingency tables. In E. Diday (Ed.), Data analysis, learning symbolic and
numeric knowledge (pp. 1520). New York: Nova Science.
This paper deals with logbilinear and logtrilinear models proposed by Goodman
for threeway contingency tables. The proposed approach allows to study the
dependence or association structure between two or three qualitative varibales.
The parameters of the models are estimated by means of the least squares
methods.

D'Ambra, L., & Kiers, H. (1990).
Analysis of logtrilinear models for a threeway contingency table
using
PARAFAC/CANDECOMP. In the Proceedings of the Study Days of the
Italian Statistical Society, 101114, Pescara, 1112 October.
This paper deals with logtrilinear models derived from the
models proposed by
Goodman (1986) for threeway contingency tables. The proposed
approach allows
to study the association structure between three qualitative
variables. The
parameters of the models are estimated by means of
PARAFAC/CANDECOMP
and the results are compared to those of a generalized singular
value
decomposition approach.

D'Ambra, L., & Lauro, N. (1989).
Non symmetrical analysis of threeway contingency tables. In R. Coppi &
S. Bolasco (Eds.), Multiway data analysis (pp. 301315). Amsterdam: Elsevier.
This paper deals with a non symmetrical analysis of threeway contingency tables
in order to study the structure of dependence among qualitative variables that play
a different role in the analysis. The proposed approach allows the decomposition
of non symmetric association indexes such as the GoodmanKruskal tau and its extension
dues to GrayWilliams.

Da Silva, J. C. G. E., & Novais, S. A. G. (1998).
Trilinear PARAFAC decomposition of synchronous fluorescence spectra of mixtures of the major
metabolites of acetylsalicylic acid.
Analyst, 123, 20672070.
Mixtures of the three major metabolites of acetylsalicylic acid (salicylic, gentisic
and salicyluric acid) were analyzed by synchronous molecular fluorescence spectroscopy. Threeway
data matrices were generated by acquisition of spectra as a function bf the pH (between 2 and 11) and
of different relative concentrations of the three components. The PARAFAC trilinear model, without
restrictions and using one factor per metabolite, was used in the data analysis. A full decomposition
of the data matrices into the spectra, concentration and pH profiles was obtained. This result shows
that molecular fluorescence spectroscopy can be used for the development of robust analytical methods
for th simultaneous determination of the three major metabolites of acetylsalicylic acid in complex
background samples.

Da Silva, J. C. G. E., & Oliveira, C. J. S. (1999).
Parafac decomposition of threeway kineticspectrophotometric spectral matrices corresponding
to mixtures of heavy metal ions.
Talanta, 49, 889897.
Binary and ternary mixtures of some of the following heavy metal ions Zn(II), NI(II),
Pb(II), Co(II) and Cd(II) were analyzed by a ligand substitution kinetic method. Threeway data
matrices were generated by acquisition of WVis spectra (332580 nm) as a function of the time of a
substitution reaction observed between the complex of the heavy metal ions with the non selective
metallochromic indicator 4(2pyridylazo) resorcinol (PAR) and EDTA, and of different relative
concentration of the metal ions (16 mM). The PARAFAC trilinear model, without restrictions, was used
in the data analysis. A full decomposition of the data matrices was obtained (spectra, concentration
and time profiles). It was shown that ligand substitution kinetic methods coupled to threeway
chemometric analytical methods can be used for the development of robust sensors for the analysis of
binary [Zn(II) + Ni(II), Pb(II) + Cd(II), Zn(II) + Pb(II)] or ternary [Zn(II) + Pb(II) + Co(II)]
mixtures of metal ions in the micromolar concentration range.

Da Silva, J. C. G. E., Leitao, J. M. M., Costa, F. S. & Ribeiro, J. L. A. (2002).
Detection of verapamil drug by fluorescence and trilinear decompositim techniques
Analytica Chimica Acta, 453, 105115.
A threeway analytical methodology experimentally based on fluorescence excitation
emission matrix (EEM) and in PARAFAC and TLD chemometric analysis was assessed for
the quantification of verapamil drug in a tablet formulation. A standard addition
procedure generates experimental information compatible with the chemometric data
analysis model allowing the estimation of verapamil with a detection limit of about
0.04 mg/l using methanol as solvent. The structure of the verapamil EEM follows a
trilinear model, but background signals (first and secondorder scatter bands)
did nota trilinear threefactor model is necessary to describe experimental datasets.
The comparison of a threefactor PARAFAC model with a United States Pharmacopoeia
(USP) standard chromatographic method showed similar results. (C) 2002 Elsevier
Science B.V. All rights reserved.

D'Aubigny, G., & Polit, E. (1989).
Some optimality properties of the generalization of the Tucker
method to the analysis of
nway tables with specified metrics. In R. Coppi & S. Bolasco
(Eds.),
Multiway data analysis (pp. 3952). Amsterdam: Elsevier.
A tensor space formulation of the TUCKER3 method results in the extension of this
approach to nway nmode data sets. The introduction of non identity metrics
attached to each mode yields a statistical modelling enrichment of this multivariate data analysis method. The evaluation of extended forms of the
usual optimality criteria, worked out by OKAMOTO (1969) in the 2way PCA case, is
presented in the general setting of the nPCA of the tensor structure (X,Q) of
order n, where X is derived from the observation and Q defines a Euclidean geometry
on the representation space. The lack of pairwise duality relations between modes
that characterizes the general (i.e. n>2) situation is shown to be responsible for the
falsity of the extension of several optimality properties in that case, while the introduction of non identity metrics is not influential. The
representation of a tensor of order n by one matrix is a combinatorial problem. So
it is of interest that representations induced by a bipartition of the modes
crosstabulating one mode with any combination of the others result in an intermediate
situation, preserving some optimality properties of twoway PCA.

Davis, E.E. & Grobstein, N.N. (1966).
Multimode factor
analysis of interpersonal perceptions. (Technical Report No. 36),
UrbanaChampaign: University of Illinois, Department of Psychology.
88 white/black, male/female students scored 28 complex person
stimuli designated mainly in terms of race, sex, religion
and occupation on 15 behavioral differential scales. The T3
solution was varimaxed for scales and students. The stimuli
components were rotated to agree closely with the discriminant
functions, emerging from an analysis on the components. The
counterrotated core matrix was interpreted but did not
provide obvious subject component interpretations.

Davis, J. W. & Gao, H. (2003).
An expressive threemode principal components model of human action style
Image and Vision Computing, 21, 10011016.
We present a threemode expressivefeature model for representing and recognizing
performance styles of human actions. A set of style variations for an action are
initially arranged into a threemode data representation (body pose, time, style)
and factored into its threemode principal components to reduce the data dimensionality.
We next embed tunable weights on trajectories within the subspace model to enable
different contextbased style estimations. We outline physical and perceptual
parameterization methods for choosing style labels for the training data, from
which we automatically learn the necessary expressive weights using a gradient
descent procedure. Experiments are presented examining several motioncapture walking
variations corresponding to carrying load, gender, and pace. Results demonstrate a
greater flexibility of the expressive threemode model, over standard squarederror
style estimation, to adapt to different style matching criteria.

Davis, J. W. & Gao, H. (2004).
An expressive threemode principal components model for gender recognition.
Journal of Vision, 4, 363377.
We present a threemode expressivefeature model for recognizing gender (female, male) from
pointlight displays of walking people. Prototype female and male walkers are initially decomposed
into a subspace of their threemode components (posture, time, and gender). We then apply a weight
factor to each pointlight trajectory in the basis representation to enable adaptive, contextbased
gender estimations. The weight values are automatically learned from labeled training data. We
present experiments using physical (actual) and perceived (from perceptual experiments) gender
labels to train and test the system. Results with 40 walkers demonstrate greater than 90%
recognition for both physically and perceptually labeled training examples. The approach has a
greater flexibility over standard squarederror gender estimation to successfully adapt to different
matching contexts.

Daws, J.T. (1996).
The analysis of freesorting data: Beyond pairwise
cooccurrences.
Journal of Classification, 13, 5780.
Freesorting data are obtained when subjects are given a set of
objects
and are asked to divide them into subsets. Such data are usually
reduced by counting, for each pair of objects, how many subjects
placed
both of them into the same subset. The present study examines the
utility of a group of additional statistics, the cooccurrences of
sets
of three objects. Because there are dependencies among the pair and
triple cooccurrences, adjusted triple similarity statistics are
developed. Multidimensional scaling and cluster analysis  which
usually
use pair similarities as their input data  can be modified to
operate
on threeway similarities to create representations of the set of
objects. Such methods are applied to a set of empirical sorting
data:
Rosenberg and Kim's (1975) fifteen kinship terms.

Dawson, M.R.W., & Harshman, R.A. (1986).
The multidimensional analysis of asymmetries in alphabetic confusion matrices:
Evidence for globaltolocal and localtoglobal processing.
Perception & Psychophysics, 40, 370383.
This study examined the ability of an asymmetric multidimensional scaling program
(DEDICOM) to reveal information about letterperception processes. To demonstrate
its potential, we applied it to the controversy concerning localtoglobal versus
globaltolocal letter perception. These two theories lead to different predictions
about stimulus confusion asymmetries. Since DEDICOM is capable of recovering the
structure of asymmetric or directional patterns, it should reveal whether a
stimulusresponse confusion matrix contains patterns of asymmetry more consistent
with one or the other perceptual theory. This was tested using two data sets. The
first (from Lupker, 1979) revealed an additive hierarchy of asymmetry strongly
consistent with globaltolocal processing, although unexpected additional structure
and reliable anomalies indicated the need for a more refined theoretical account.
The second (a full alphabetic confusion matrix combining data from Gilmore
et al., 1979; Loomis, 1982; and Townsend, 1971) revealed five distinct patterns,
each consisting of transformations attributable to the failure to detect specific
local letter features. This solution strengthened support for localtoglobal
processing, in sharp contrast to the first analysis. Possible reasons for this
divergence are discussed, including differences in the stimuli, exposure durations,
and a hypothetical twostage process of perception. Despite their differences, both
solutions demonstrated how asymmetric scaling can reveal structure in asymmetries,
which is relevant to perceptual theory and which would have been difficult to recover
by other means.

De Belie, N., Sivertsvik, M., & De Baerdemaeker, J. (2003).
Differences in chewing sounds of drycrisp snacks by multivariate data analysis.
Journal of Sound and Vribration, 266, 625643.
Chewing sounds of different types of drycrisp snacks (two types of
potato chips, prawn crackers, cornflakes and low calorie snacks from extruded starch)
were analysed to assess differences in sound emission patterns. The emitted sounds were
recorded by a microphone placed over the ear canal. The first bite and the first
subsequent chew were selected from the time signal and a fast Fourier transformation
provided the power spectra. Different multivariate analysis techniques were used for
classification of the snack groups. This included principal component analysis (PCA) and
unfold partial leastsquares (PLS) algorithms, as well as multiway techniques such as
threeway PLS, threeway PCA (Tucker3), and parallel factor analysis (PARAFAC) on the
first bite and subsequent chew. The models were evaluated by calculating the classification
errors and the root mean square error of prediction (RMSEP) for independent validation sets.
It appeared that the logarithm of the power spectra obtained from the chewing sounds could
be used successfully to distinguish the different snack groups. When different chewers
were used, recalibration of the models was necessary. Multiway models distinguished
better between chewing sounds of different snack groups than PCA on bite or chew
separately and than unfold PLS. From all threeway models applied, NPLS with three
components showed the best classification capabilities, resulting in classification
errors of 1418%. The major amount of incorrect classifications was due to one type of
potato chips that had a very irregular shape, resulting in a wide variation of the
emitted sounds.

Defays, D. (1979).
Tree representation of ternary relations. Journal of Mathematical Psychology, 19,
208218.
In this paper, trees are constructed from ternary relations; the model represents
each object of an empirical set by a node of a tree so that a betweenness relation
among the nodes (the node b is on the path from the node a to the
node c) in the graph reflects a ternary relation among the objects. Various
systems of formal properties that lead to three different kinds of tree representation
are investigated.

De Jong, S. (1998).
Short communication regression coefficients in multipilinear PLS.
Journal of Chemometrics, 12, 7781.
Three alternative approaches are discussed for finding the final calibration model
(regression coefficients) in PLS regression of kway Y on Nway X. The simplest approach is to skip
the deflation of the Xdata. From the observation that the specific deflation used in multiway PLS is
inconsequential, it also follows that Bro's triPLS is equivalent to Ståhle's linear threeway decomposition
(LTD).

De Jong, S., & Farebrother, R. W. (1994).
Extending the relationship between ridgeregression and continuum regression.
Chemometrics and Intelligent Laboratory Systems, 25, 179181.
Recently, a close relationship has been
established between ridge regression (RR) and a
special case of continuum regression (CR).
Attention was restricted to the usual positive
range of values for the ridge parameter. This
restriction identifies the trajectory lying
between ordinary least squares (OLS) and partial
least squares (PLS) regressions, leaving the
trajectory between PLS and principal component
regression (PCR) untouched. In this note we
demonstrate that the relationship between CR and
RR can be extended to the full range of methods,
OLS <> PLS <> PCR, identified by the CR
technique. For this purpose one has to admit a
nonstandard variant of the RR technique in which
the ridge parameter becomes negative.

De Juan, A., & Rutan, S. C., & Tauler, R., Massart, D. L. (1998).
Comparison between the direct trilinear decomposition and the multivariate curve
resolutionalternating least squares methods for the resolution of threeway data sets.
Chemometrics and Intelligent Laboratory Systems, 40, 1932.
Direct trilinear decomposition (DTD) and multivariate curve resolutionalternating least squares
(MCRALS) methods are two of the most representative threeway resolution procedures. The former, noniterative,
is based on the resolution of the generalized eigenvector/eigenvalue problem and the latter, iterative, is focused on the
optimization of initial estimates by using data structure and chemical constraints. DTD and MCRALS have been tested
on a variety of threeway simulated data sets having common sources of variation in real response profiles, such as signal
shift, broadening or shape distortions caused by noise. The effect of these factors on the resolution results has been
evaluated through the analysis of several parameters related to the recovery of both qualitative and quantitative
information and to the quality of the overall data description. Conclusions inferred from the simulated examples help to
clarify the performance of both methods on a real example and to provide some general guidelines to understand better
the potential of each method.

De Juan, A., & Tauler, R. (2001).
Comparison of 3way resolution methods for nontrilinear data sets.
Journal of Chemometrics, 15, 749772.
Resolution of threeway chemical data sets can be tackled using two families
of chemometric methods: those assuming trilinear structure in the data set,
such as direct trilinear decomposition (DTD) or parallel factor analysis (PARAFAC);
and those which decompose the threeway data set according to a model lacking
this structure, such as TUCKER3 or multivariate curve resolutionalternating
least squares (MCRALS). The first group of methods provides unique solutions,
whereas the second group gives solutions subject to rotational ambiguities.
DTD and PARAFAC are thus the choice to deal with chemical data sets with trilinear
structure. However, in the analysis of chemical data with nontrilinear structure,
which is most commonly found in practice, the more ambiguous solutions given
by TUCKER3 and MCRALS could be balanced by the major flexibility in the modelling
of profiles. To assess this possibility, threeway resolution methods from
the two mentioned families are applied to simulated and real data sets designed
to show typical nontrilinear chemical situations, caused by shifts and shape
changes in profiles.

De Juan, A., & Tauler, R. (2003).
Chemometrics applied to unravel multicomponent processes and mixtures  Revisiting
latest trends in multivariate resolution.
Analytica Chimica Acta, 500, 195210.
Progress in the analysis of multicomponent processes and mixtures relies on the
combination of sophisticated instrumental techniques and suitable data analysis
tools focused on the interpretation of the multivariate responses obtained. Despite
the differences in compositional variation, complexity and origin, the raw
measurements recorded in a multicomponent chemical system can be very often
described with a simple model consisting of the compositionweighted sum of the
signals of their pure compounds.Multivariate resolution methods have been the
tools designed to unravel this pure compound information from the nonselective
mixed original experimental output. The evolution of these chemometric approaches
through the improvement of exploratory tools, the adaptation to work with complex
data structures, the ability to introduce chemical and mathematical information
in the algorithms and the better quality assessment of the results obtained is
revisited. The active research on these chemometric area has allowed the successful
application of these methodologies to chemical problems as complex and diverse as
the interpretation of protein folding processes or the resolution of spectroscopic
images.

De Juan, A., Tauler, R., Dyson, R., Marcolli, C., Rault, M. & Maeder, M. (2004).
Spectroscopic imaging and chemometrics: a powerful combination for global and local sample analysis.
Tratrends in Analytical Chemistry, 23, 7079.
Merging spectroscopic imaging and chemometrics enhances the outcomes of
instrumental technology and data analysis. Multivariate exploratory and resolution
methods can be adapted to image analysis and provide global and local information about
pure compounds in an imaged sample. Knowing in detail how the chemical compounds are
distributed over the scanned surface gives valuable information about essential issues
in the manufacture and the characterization of products, such as evenness of composition
and, therefore, homogeneity of the sample. The power to detect and to locate impurities
is also greatly enhanced because these unwanted compounds could show locally large
concentrations (and signals), even though their abundance on the surface is very low.
The capabilities of this combination are shown in an example of pharmaceutical product
control, where analysis of the end product requires chemical characterization and
quantitative information at global and local levels. The approach used and the kind
of information obtained is general and can be applied to the analysis of images in
other fields.

De Lathauwer, L.(2004a).
Firstorder perturbation analysis of the best
rank(R1, R2, R3) approximation in multilinear algebra.
Journal of Chemometrics, 18, 211.
In this paper we perform a firstorder perturbation analysis of the least squares approximation of a
given higherorder tensor by a tensor having prespecified nmode ranks. This work generalizes the
classical firstorder perturbation analysis of the matrix singular value decomposition. We will show
that there are important differences between the matrix and the higherorder tensor case. We
subsequently address (1) the best rank1 approximation of supersymmetric tensors, (2) the best
rank(R1, R2, R3) approximation of arbitrary tensors and (3) the best rank(R1, R2, R3) approximation
of arbitrary tensors.

De Lathauwer, L. (2006).
A link between the canonical decomposition in multilinear algebra and simultaneous matrix diagonalization.
SIAM Journal on Matrix Analysis and Applications, Vol28, 642666.
Canonical decomposition is a key concept in multilinear algebra. In this paper we consider the decomposition of
higherorder tensors which have the property that the rank is smaller than the greatest dimension. We derive a new and relatively
weak deterministic sufficient condition for uniqueness. The proof is constructive. It shows that the canonical components can be
obtained from a simultaneous matrix diagonalization by congruence, yielding a new algorithm. From the deterministic condition we
derive an easytocheck dimensionality condition that guarantees generic uniqueness.

De Lathauwer, De Moor, B, & Vandewalle, J. (2000a).
An introduction to independent component analysis.
Journal of Chemometrics, 14, 123149.
This paper is an introduction to the concept of
independent component analysis (ICA) which has
recently been developed in the area of signal
processing. ICA is a variant of principal
component analysis (PCA) in which the components
are assumed to be mutually statistically
independent instead of merely uncorrelated. The
stronger condition allows one to remove the
rotational invariance of PCA, i.e. ICA provides a
meaningful unique bilinear decomposition of
twoway data that can be considered as a linear
mixture of a number of independent source
signals. The discipline of multilinear algebra
offers some means to solve the ICA problem. In
this paper we briefly discuss four orthogonal
tensor decompositions that can be interpreted in
terms of higherorder generalizations of the
symmetric eigenvalue decomposition.

De Lathauwer, L., De Moor, B., & Vandewalle, J. (2000b).
A multilinear singular value decomposition.
Siam Journal on Matrix Analysis and Applications, 21, 1253
1278.
A multilinear generalization of the
singular value decomposition is discussed. There is a strong
analogy between several properties of the matrix
and the higherorder tensor decomposition;
uniqueness, link with the matrix eigenvalue
decomposition, firstorder perturbation effects,
etc., are analyzed. It is then investigated how tensor
symmetries affect the decomposition and propose a
multilinear generalization of the symmetric
eigenvalue decomposition for pairwise symmetric
tensors.

De Lathauwer, L., De Moor, B., & Vandewalle, J.
(2000c).
On the best rank1 and rank(R_{1}, R_{2},…,
R_{N}) approximation of higherorder tensors. SIAM
Journal on Matrix Analysis and Applications, 21, 13241342.
In this paper we discuss a multilinear generalization of the best rankR
approximation problem for matrices, namely, the approximation of a given higher
order tensor, in an optimal leastsquares sense, by a tensor that has
prespecified column rank, row rank value, etc. For matrices, the solution
is conceptually obtained by truncation of the singular value decomposition
(SVD); however, this approach does not have a straightforward multilinear
counterpart. We discuss higherorder generalizations of the power method and the
orthogonal iteration method.

De Lathauwer, L., De Moor, B., & Vandewalle, J. (2000d).
A multilinear singular value decomposition. SIAM Journal on
Matrix Analysis and Applications, 21, 12531278.
We discuss a multilinear generalization of the singular value decomposition. There is
a strong analogy between several properties of the matrix and the higherorder tensor decomposition;
uniqueness, link with the matrix eigenvalue decomposition, .rstorder perturbation e.ects, etc., are
analyzed. We investigate how tensor symmetries a.ect the decomposition and propose a multilinear
generalization of the symmetric eigenvalue decomposition for pairwise symmetric tensors.

De Lathauwer, L., & Vandewalle, J. (2004b).
Dimensionality reduction in higherorder signal processing and rank(R1, R2, ..., RN) reduction in multilinear algebra.
Linear Algebra and its Applications, 391, 3155.
In this paper we review a multilinear generalization of the singular value decomposition
and the best rank(R1, R2,..., RN) approximation of higherorder tensors. We show that they are
important tools for dimensionality reduction in higherorder signal processing. We discuss applications in
independent component analysis, simultaneous matrix diagonalization and subspace variants of algorithms
based on higherorder statistics.

De Lathauwer, L., & Vandewalle, J. (2004c).
Dimensionality reduction in ICA and rank(R1, R2, ..., RN) reduction in multilinear algebra.
Independent Component Analysis and Blind Signal Separation, 3915, 295302.
We show that the best rank(R1, R2,..., RN) approximation in multilinear algebra is a
powerful tool for dimensionality reduction in ICA schemes without prewhitening. We consider the application
to different classes of ICA algorithms.

De la Pena, A. M., Mansilla, A. E. Gomez, D. G., Olivieri, A. C., &
Goicoechea, H. C. (2003).
Interferencefree analysis using threeway fluorescence data and the parallel
factor model. Determination of fluoroquinolone antibiotics in human serum.
Analytical Chemistry, 75, 26402646.
Threeway fluorescence data and multivariate calibration based on
parallel factor analysis (PARAFAC) are combined for the simultaneous quantitation of
three fluoroquinolone anitibiotics (norfloxacin, enoxacin, and ofloxacin) in human serum
samples. The three analytes can be adequately determined with limits of detection of 0.2,
3.0, and 0.5 mug L1, respectively, with minimum experimental effort. The selected
analytical methodology fully exploits the socalled secondorder advantage of the employed
threeway data, allowing obtaining individual concentrations of calibrated analytes in
the presence of any number of uncalibrated (serum) components. In contrast to PARAFAC,
less satisfactory results were obtained with a multidimensional partial leastsquares
(nPLS) model trained with the same calibration set.

De la Pena, A. M., Mansilla, A. E., Valenzuela, M. I. A.,
Goicoechea, H. C., & Olivieri, A. C. (2002).
Comparative study of net analyte signalbased methods and partial
least squares for the simultaneous determination of amoxycillin and
clavulanic acid by stoppedflow kinetic analysis.
Analytica Chimica Acta, 463, 7588.
A comparative study about advantages and limitations of net analyte signal
(NAS)based methods (NBMs) and partial least squares (PLS) calibration in kinetic analysis
has been performed. The different multivariate calibration methods were applied to the
determination of binary mixtures of amoxycillin and clavulauic acid, by stoppedflow kinetic
analysis. The reactions of oxidation of these compounds with cerium(IV), in sulphuric acid
medium, were monitored by following the changes on the fluorescence of the oxidation products,
in stoppedflow mode. The differences on the kinetic profiles obtained at lambda(ex) = 256 nm
and lambda(em) = 351 nm, were used to determine mixtures of both compounds by multivariate
calibration of the kinetic data, using PLS1, a modification of hybrid linear analysis (HLA)
and net analyte preprocessing combined with classical least squares (NAP/CLS) methods. The NBMs
allowed the selection of optimal time data regions by calculating the minimum error indicator
function (EIF), improving the results and making NBMs very convenient for the analysis. In
addition, the use of the net analyte signal concept allows the calculation of the analytical
figures of merit, limit of detection (LOD), sensitivity and selectivity, for each component.

De la Torre, F., & Black, M. J. (2003).
A framework for robust subspace learning.
International Journal of Computer Vision, 54, 117142.
Many computer vision, signal processing and statistical problems can be
posed as problems of learning low dimensional linear or multilinear models. These models
have been widely used for the representation of shape, appearance, motion, etc., in
computer vision applications. Methods for learning linear models can be seen as a special
case of subspace fitting. One drawback of previous learning methods is that they are
based on least squares estimation techniques and hence fail to account for "outliers"
which are common in realistic training sets. We review previous approaches for making
linear learning methods robust to outliers and present a new method that uses an
intrasample outlier process to account for pixel outliers. We develop the theory of
Robust Subspace Learning (RSL) for linear models within a continuous optimization
framework based on robust Mestimation. The framework applies to a variety of linear
learning problems in computer vision including eigenanalysis and structure from motion.
Several synthetic and natural examples are used to develop and illustrate the theory and
applications of robust subspace learning in computer vision.

De la Vega, A.J., & Chapman, S.C. (2001).
Genotype by environment interaction and indirect selection for yield in sunflower.
II. Threemode principal component analysis of oil and biomass yield across
environments in Argentina. Field Crops Research, 72, 3950.
The genotype by environment (G x E) interactions observed for sunflower oil
yield in different regions of Argentina can be analyzed in terms of differences
among genotypes in individual environments for its components grain number, grain
weight, and oil content (yield analysis). Similarly, G x E interactions observed
for oilcorrected grain yield can be analyzed in terms of its determinants total
biomass and harvest index (physiological analysis). Threemode (genotypes x
environments x attributes) principal component analysis was applied to 10 x 21 x 4
and 10 x I I x 3 matrices, for each of the first and the second analyses,
respectively, to collectively interpret the changes in these attributes in a
sunflower genotypeenvironment system, and to assess the relative importance
of each trait as underlying determinant of the observed G x E interaction for
oil yield. The 3 x 2 x 3 and 4 x 4 x 2 (genotypes x environments x attributes)
principal component models explained about 65% of the variation computed
for first and second approaches, respectively.
For the yield analysis, the first environment component (54% of the variation)
explained the common pattern of oil yield over environments and showed that
oil content was highly positively correlated to oil yield, while grain number
and grain weight showed lack of association with oil yield and were negatively correlated.
The second environment component (11% of the variation) contrasted northern and
central environments and showed that grain number is the main underlying determinant
of the observed G x E interactions between these two megaenvironments for oil yield.
In the physiological analysis, the first environment component (29% of the
variation) explained the common pattern of oilcorrected grain yield over environments and
showed that harvest index was more strongly positively correlated to oilcorrected
grain yield, but not to total oilcorrected biomass. The second environmental
component (19% of the variation) contrasted northern and central environments
and showed that oilcorrected biomass is the physiological attribute that is
largely responsible for the G x E interactions for oilcorrected grain yield.

De la Vega, A. J., Hall, A. J., & Kroonenberg, P. M. (2002).
Investigating the physiological bases of predictable and unpredictable
genotype by environment interactions using threemode pattern analysis.
Field Crops Research, 78, 165183.
Understanding of the underlying physiology of the genotypespecific responses
to predictable and unpredictable environmental variation would improve the efficiency of
selection within a complex target population of environments. Threemode principal component
analysis (PCA) can be used for interpreting the complex threeway (genotypes, environments,
attributes) trial datasets from which this understanding should emerge. The efficiency of this
method largely depends on the right combination between the biological and statistical models
used, especially on the attributes selected to describe the genotypic responses and the centring
of the threeway input data. In this study, we assessed the scope of yield determination models
and doublecentring of input data for generating some physiological understanding of the genotype
x environment (G x E) interactions observed in a sunflower genotypeenvironment system and for
developing ideotypebased breeding strategies. Doublecentring of the threeway arrays permitted
the separation of predictable and unpredictable G x E interactions. This, in combination with the
use of models that explain the physiological bases of yield variation among genotypes, has served
to identify three relevant sources of genotypic variation for use in a breeding program, namely:
(i) attributes that can be selected to achieve specific adaptation to the target environment by
emphasising predictable interactions (e.g. duration of grain filling, a trait associated with
canopy stay green); (ii) attributes that allow the unpredictable G x E interactions to be
accommodated, improving the linkage between managedenvironments and target production
environments (e.g. grain set); and (iii) genotypes of similar response pattern for yield but
contrasting relative behaviour for the primary and secondary yield determinants. Breeding
projects involving crosses between these genotypes could generate better opportunities for yield
improvements for individual megaenvironments.

De Leeuw, J. & Pruzansky, S. (1978).
A new computational
method to fit
the weighted Euclidean distance model. Psychometrika,
43, 479490.
Deals mainly with fitting the weighted Euclidean distance
model, (INDSCAL), but also includes a discussion of threemode
scaling, and ways to rotate the results of that procedure to
INDSCAL form (see also MacCallum, 1976; Cohen, 1974, 1975)

De Ligny, C.L., Spanjer, M.C., Van Houwelingen, J.C,
& Weesie, H.M. (1984).
Threemode factor analysis of data on retention in normalphase
highperformance liquid chromatography. Journal of
Chromatography, 301, 311324.
It is shown that the Snyder equation is not quite satisfactory for fitting
retention data in
normalphase highperformance liquid chromatography (HPLC) on chemically
bonded phases. This
equation is a special case of the mathematicalstatistical threemode
factor analysis model.
This model, in its general form, has been used to fit two sets of
literature data on the
retention in normalphase HPLC for 19 solutes on six adsorbents with two
eluents, and for 39
solutes on three adsorbents with two eluents, respectively. This study
represents the first
application of threemode factor analysis with missing data, and also the
first application of
threemode factor analysis in the field of the natural sciences. The
accuracy of the fit of
the observations and of the prediction of the missing data, for various
numbers of extracted
factors, is discussed.

Demir, C., & Brereton, R.G. (1997).
Calibration of gas chromatographymass
spectrometry of twocomponent mixtures using
univariate regression and two and threeway
partial least squares.
Analyst, 122, 631638.
Univariate calibration and twoway and threeway
partial least squares (PLS) were applied to a
series of GCMS results for 21 mixtures of two
closely eluting compounds, salbutamol and
clenbuterol. Steps in the analysis, including
baseline correction, alignment of chromatograms,
mass selection, unfolding (for threeway data),
standardizing and centring, are described,
appropriately modified for the problem in hand.
Both mass spectral and, for threeway data, time
dependent loadings can be calculated. The quality
of quantitative predictions was determined using a
leave one out cross validation method. For PLS
slightly better predictions were obtained compared
with the best predictions for univariate single
ion monitoring. Threeway PLS provides a wealth of
extra information.

Denis, J.B., & Dhorne, T. (1989).
Orthogonal tensor decomposition of 3way tables. In R. Coppi and S.
Bolasco (Eds.), Multiway data analysis (pp. 3137).
Amsterdam: Elsevier.
The authors' interest in 3way tables is concerned when all of
the three entries
are of equal consideration from the view point of exploratory data
analysis.
Moreover they look for an exhaustive and 3way symmetrical
decomposition. In
a first part, counterexamples of natural extensions of good
properties concerning
singular value decomposition of matrices are shown. In a second
part, a reduced
form of 3way tables named "rocket form" is proposed, it can be
seen as an
extension of the singular value decomposition of matrices.

De Rooij, M. (2001).
Distance models for transition frequency data. Unpublished doctoral
thesis, Leiden University, Leiden The Netherlands.
1. Transition frequency data
Contingency tables; Loglinear analysis of transition frequency data; Distance
models; Overview of this monograph
2. Multinomial logit models: with and without weights
Review of sequential data analysis; Imagery play therapy; Regression models
for contingency tables; Data analysis: Lag1 and lag2 transitions;
Forecasting new behavior through the use of weights; Data analysis: Forecasting
new behavior; Discussion
3. Distance association models for twoway data
Distance association models; The odds ratio; Identification of degrees of
freedom; Data analysis; Comparison to RC(M)model and discussion
4. Asymmetric triadic distance models
Asymmetric triadic distance models; Data analysis; Comparison and discussion
5. Distance models and threeway association
Models for threeway transition tables and distance restrictions; Triadic
distance models; Threeway distance models; Discussion
6. Distance association models for K twoway transition tables
The model; MLestimation; Data analysis; Discussion
7. Conclusion
The answer summarized; Some considerations

De Rooij, M., (2001).
Distance association models for the analysis of repeated transition frequency
tables. Statistica Neerlandica, 55, 157181.
The present paper is concerned with the analysis of repeated transition frequency
tables, for example, occupational mobility data measured in different cohorts.
The association present in such a table will be modeled by a distance in Euclidean
space. A large distance corresponds to a small association; a small distance
corresponds to a large association. A more direct interpretation is that more
transitions occur between categories that are close together in a social space.
It is assumed that the same social structure (space) exists for the different
slices (cohorts/time points) of a table, but that the dimensions of this space
are weighted for the different slices, i.e., for each slice the dimensions are
stretched or squeezed. We will propose a model, discuss an algorithm to obtain
maximum likelihood estimates and apply the model to an empirical data set.

De Rooij, M., (2002).
Distance models for threeway tables and threeway association.
Journal of classification, 19, 161178.
In the present paper we study distance models for the analysis of threeway
contingency tables. Specifically, we will study threeway association under these
models measured by the second order odds ratio. Two kinds of distance models will
be studied: (a) Models for threeway tables where each way is treated on an equal
footing; (b) Models for multiple twoway tables, where one of the three ways has
a special importance. For the first kind of models, called triadic distance models,
we will show that there exists a natural conjugacy between the Exponentialp
similarity function, the Lptransform and the Minkowskip distance. For triadic
distance models defined by the Lptransform we will prove that they do not model
threeway association. Moreover, triadic distance models defined by the Lptransform
are restricted multiple dyadic distances, where each dyadic distance is defined
for a twoway margin of the threeway table. Distance models for threeway twomode
data, called threeway distance models, do succeed in modeling threeway association.

De Rooij, M., & Heiser, W.J. (2000).
Triadic distance models for the analysis of asymmetric threeway proximity data.
British Journal of Mathematical and Statistical Psychology, 53,
99119.
Triadic distance models can be used to analyse proximity data defined on triples
of objects. Threeway symmetry is a common assumption for triadic distance
models. In the present study threeway symmetry is not assumed. Triadic distance
models are presented for the analysis of asymmetric threeway proximity data
that result in a simultaneous representation of symmetry and asymmetry in a low
dimensional configuration. An iterative majorization algorithm is developed for
obtaining the coordinates and the representation of the asymmetry. The models
are illustrated by an example using longitudinal categorical data.

De Rooij, M., & Gower, J. C. (2004).
The geometry of triadic distances.
Journal of Classification, 20, 181220.
Triadic distances t defined as functions of the Euclidean (dyadic)
distances a(1), a(2), a(3) between three points are studied. Special attention is
paid to the contours of all points giving the same value of t when a(3) is kept constant.
These isocontours allow some general comments to be made about the suitability, or not,
for practical investigations of certain definitions of triadic distance. We are
especially interested in those definitions of triadic distance, designated as canonical,
that have optimal properties. An appendix gives some results we have found useful.

DeSarbo, W.S., & Carroll, J.D. (1985).
Threeway metric unfolding via alternating weighted least squares.
Psychometrika,50, 275300.
Threeway unfolding was developed to accommodate the analysis
of
twomode, threeway data (e.g., nonsymmetric proximities for
stimulus objects collected over time) and threemode, threeway
data (e.g., Ss rendering preference judgments for various
stimuli in different usage situations). The authors present a
revised objective function and new algorithm to prevent the
common type of degenerate solutions encountered in typical
unfolding analysis. The threeway unfolding model, weighted
objective function, and new algorithm are presented, and Monte
Carlo work investigating the effect of several data and model
factors on overall algorithm performance is described. Three
applications of the methodology are reported.

DeSarbo, W.S., Carroll, J.D., Clark, L.A., & Green, P.E.
(1984).
Synthesized clustering: A method for amalgamating alternative
clustering bases with differential weighting of variables.
Psychometrika, 49, 5778.
In the application of clustering methods to real world data sets, two
problems frequently
arise: (a) how can the various contributory variables in a specific
battery be weighted so as
to enhance some cluster structure that may be present, and (b) how can
various alternative
batteries be combined to produce a single clustering that "best"
incorporates each
contributory set. A new method is proposed (SYNCLUS,
SYNthesized
CLUStering) for dealing with these two problems.

DeSarbo, W.S., Carroll, J.D., Lehmann, D.R., &
O'Shaughnessy, J.
(1982).
Threeway multivariate conjoint analysis. Marketing Science,
1, 323350.
Threeway multivariate conjoint analysis is developed as an
extension of
traditional metric conjoint analysis allowing one to examine
several dependent
variables simultaneously, as well as individual differences in
response. Four nested
models are developed to examine the effects of experimental design,
the dependent
variables, and individual differences. An illustration concerning
the relationship
of product characteristics to the importance of various decision
making criteria for
industrial purchasing is provided. Finally, extensions of the
model(s) to other
marketing applications and nonmetric analyses are discussed.

DeSarbo, W.S., & Harshman, R.A. (1985).
Celebritybrand congruence analysis. Journal of Current Issues &
Research in Advertising, 1, 1752.
This paper proposes a method for uncovering the perceptualcognitive overtones
of product and possible commercial spokesmen, and then examines their
relationships so as to establish a basis for "optimizing" potentially desirable
source effects. As a demonstration of this method, the PARAFAC threeway factor
analysis procedure is applied to individuals' associative judgements (measured
on a set of semantic differential scales) concerning twelve automobile makes and
twelve celebrities (commercial spokesmen).

DeSarbo, W.S., Libby, R., & Jedidi, K. (1994).
CATSCALE: A stochastic multidimensional scaling methodology for
the spatial analysis of sorting data and the study of stimulus
categorization. Computational Statistics & Data
Analysis, 18, 165184.
Sorting tasks have provided researchers with valuable
alternatives to traditional
pairedcomparison similarity judgments. They are particularly
wellsuited to studies
involving large stimulus sets where exhaustive pairedcomparison
judgments become
infeasible, especially in psychological studies investigating
stimulus
categorization. This paper presents a new stochastic
multidimensional scaling
procedure called CATSCALE for the analysis of threeway sorting
data (as typicaly
collected in categorization studies). We briefly present a
review of the role of
sorting tasks, especially in categorization studies, as well as
a description of
several traditional modes of analysis. The CATSCALE model and
maximum likelihood
based estimation procedure are described. An application of
CATSCALE is presented
with respect to a behavioral accounting study examining
auditors' categorization
processes with respect to various types of errors found in
typical financial
statements.

De Sena, M. M., Poppi, R. J., Frighetto, R. T. S., & Valarini, P. J. (2000).
Evaluation of the use of chemometric methods in soil analysis.
Quimica Nova, 23, 547556.
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 Networks.

De Soete, G., & Carroll, J.D. (1988).
Optimal weighting for onemode and twomode ultrametric tree
representations of threeway threemode data. In M.G.H. Jansen
&
W.H. van Schuur (Eds.), The many faces of multivariate
analysis.
Vol. I. Groningen: RION.
Two different approaches are proposed for representing a threeway
threemode array by a single ultrametric tree structure. In the
first
approach, the elements corresponding to the levels of one mode
(say,
the first) are represented by the terminal nodes of a onemode
ultrametric tree. Dissimilarities between the levels of that mode
are
computed from the data, weighting the levels of the other two
modes.
These weights are estimated such that the resulting dissimilarities
satisfy the ultrametric inequality as well as possible. In the
second approach, the objects of two modes (say, the first two) are
jointly represented by the terminal nodes of a twomode (or two
class)
ultrametric tree, From the data, a rectangular proximity matrix is
calculated weighting the levels of the third way optimally.

De Soete, G., & Carroll, J.D. (1989).
Ultrametric tree representations of threeway threemode data.
In R. Coppi & S. Bolasco (Eds.), Multiway data analysis
(pp. 415426). Amsterdam: Elsevier.
Three different procedures are developed for representing threeway
threemode data by one or
more ultrametric trees. In the first approach, the levels of one mode
(say, the first) are
represented by the terminal nodes of an ultrametric tree, using
proximities that are computed
from the complete data array weighting the levels of the second and third
ways optimally. In
the second approach, the levels of two modes (say, the first two) are
jointly represented by
the terminal nodes of a twoclass ultrametric tree. The data are first
optimally aggregated
over the third way. Finally, in the third approach, the first two modes
are represented for
each level of the third mode by a twoclass ultrametric tree subject to
the constraint that
all trees have the same topology.

De Soete, G., & Carroll, J.D. (1996).
Tree and other network models for representing proximity data. In
P. Arabie, L.J. Hubert, & G. De Soete (Eds.), Clustering
and
Classification (pp. 157197). River Edge, NJ: World Scientific
Publishing.
In this paper tree and other network models for analyzing different
kinds of proximity data are discussed. In the section on threeway
data techniques for both one, two and three different modes are
considered.

De Soete, G., Carroll, J.D., & Chaturvedi, A.D. (1993).
A modified CANDECOMP method for fitting the extended INDSCAL
model. Journal of Classification, 10, 7591.
A modified CANDECOMP algorithm is presented for fitting the metric
version of the Extended INDSCAL model to threeway proximity data. The
Extended INDSCAL model assumes, in addition to the common dimensions, a
unique dimension for each object. The modified CANDECOMP algorithm fits
the Extended INDSCAL model in a dimensionwise fashion and ensures that
the subject weights for the common and the unique dimensions are non
negative. A Monte Carlo study is reported to illustrate that the method is
fairly intensive to the choice of the initial parameter estimates. A second Monte Carlo
study shows that the method is able to recover an underlying Extended INDSCAL
structure if present in the data. Finally, the method is applied for
illustrative purposes to some empirical data on pain relievers. In the final section, some other
possible uses of the new method are discussed.

Devaux, M. F., Courcoux, P., Vigneau, E., & Novales, B. (1998).
Generalised Canonical Correlation Analysis for the interpretation of fluorescence spectral data.
Analusis, 26, 310316.
The paper reports an application of Generalised Canonical Correlation Analysis to
fluorescence spectral data. Emission fluorescence spectra can be recorded for several excitation
wavelengths and can be presented as 3way data tables. The objectives of the data treatment are to
describe and compare the samples by taking into account all the emission spectra, and to reveal
characteristic excitation and emission wavelengths. Generalised Canonical Correlation Analysis has
been tested on fluorescence emission spectra acquired for binary mixtures of raw materials in the
food domain. The application of the method within the context of spectral data is presented.

Di Ciaccio, A., & Bove, G. (1987).
A factorial method for the analysis of threeway data in tensor
spaces.
In the Fifth International Symposium on Data Analysis and
Informatics,
2, 137145.
A threemode data matrix X can be decomposed in three
different ways according to each of its modes and several relevant matrices can be
defined following the three scheme of decomposition. These matrices are
represented as tensors, according to the definition, in RKxRK or in RJxRJ or else
in RIxRI and their properties and relationships are investigated. Useful
graphical representations of these tensors are proposed to support standard results of other
threeway methods. An application to the LanguedocRoussillon data is
presented.

Dien, J. (1998).
Adressing Misallocation of Variance in Principal Components Analysis of EventRelated
Potentials. Brain Topography, 11 (pp. 4355).
Interpretation of evoked response potentials is complicated by the extensive superposition of multiple electrical events.
The most common approach to disentangling these features is principal components analysis (PCA). Critics have demonstrated a number of caveats that complicate
interpretation, notably misallocation of variance and latency jitter. This paper describes some further caveats to PCA as well as using simulations to
evaluate three potential methods for addressing them: parallel analysis, oblique rotations, and spatial PCA. An improved simulation model is
introduced for examining these issues. It is concluded that PCA is an essential statistical tool for eventrelated potential analysis, but only if applied
appropriately.

Diewok, J., De Juan, A., Tauler, R., & Lendl, B. (2002).
Quantitation of mixtures of diprotic organic acids by FTIR flow titrations
and multivariate curve resolution.
Applied Spectroscopy, 56, 4050.
The combination of FTIR flow titrations and secondorder calibration methods is
assessed for the first time as a potential method for quantifying mixtures of organic acids.
FTIR spectral information is richer and more specific than that provided by other spectrometric
techniques. Also, the flow titration of the sample allows the use of secondorder data analysis
methods, such as multivariate curve resolution, which can quantify multianalyte systems using
pure analyte standards in the presence of unknown interferents. Problems linked to FTIR flows
titrations, such as the impossibility of using buffer substances and the presence of major
baseline contributions in the measurements due to changes in the water structureless absorption,
have been overcome through the design of an adapted experimental setup and the use of second
derivative spectra. Malic and/or tartaric acid are the model substances chosen to be quantified
in the presence or absence of interferents. Both substances are diprotic acids with similar pK(a)
values and, therefore, similar pHdependent evolution. Samples with one or both acids with their
related standards in the presence or absence of an inert interferent (sugar) are successfully
resolved and quantified for a wide range of [analyte] : [interferent] ratios with no need for pH
control in the process. These results suggest this methodology as an optimal and robust
alternative for routine analysis.

Diewok, J., De Juan, A., Maeder, M., Tauler, R., & Lendl, B. (2003).
Application of a combination of hard and soft modeling for equilibrium systems to
the quantitative analysis of pHmodulated mixture samples.
Analytical Chemistry, 75, 641647.
pH modulation of aqueous mixture samples combined with FTIR detection
and a powerful secondorder resolution method is proposed for both resolution and
quantitation of acid analytes in the presence of similarly behaving interferences. The
proposed method allows for the analyte determination in mixtures using a single standard
sample per analyte. Due to the very similar pK(a) values of the investigated analytes and
interferences, the highly correlated concentration profiles of these compounds cannot be
successfully resolved with pure softmodeling secondorder approaches. The inclusion of a
hardmodeling constraint based on the acidbase equilibrium model in the softmodeling
curve resolution method has allowed for the unambiguous resolution of the analyte
profiles and, as a consequence, for the correct quantitation of this compound in the
mixture sample. A detailed discussion of the combined hardsoftmodeling approach as well
as the analytical problem and the quantitation results is given. Also, strategies to
overcome problems associated with variation in pK(a) values between different samples are
addressed. Due to the flexible implementation of the hardmodel equilibrium constraint
in the multivariate curve resolutionalternating least squares method, this approach is
expected to be useful also for analysis of other complex mixed equilibriumbased chemical
systems.

Dijksterhuis, G.B., & Gower, J.C (1991/2)
The interpretation of generalized Procrustes analysis and allied
methods. Food Quality and Preference,
3, 6787.
Various issues surrounding the use and interpretation of
Generalised Procrustes Analysis and related methods are
discussed. Included are considerations that have to be made
before starting an analysis, how to handle different
dimensionalities of data, when to consider fitting scaling
factors and when not to, and the distinction between the number
of dimensions that are needed to give an adequate fit and the
need for graphical representation. The distinction between signal
and noise plays an important part in explaining how different
methods are suitable for exploring different aspects of the data,
rather than being viewed as competing models with the same
objectives. Explanations are largely set in a geometric context;
a common Analysis of Variance framework allows all methods to be
considered in a unified way and suggests some new ways in which
these kinds of data may be analysed. The whole is illustrated by
example analyses.

Dillon, W.R., Frederick, D.G., & Tangpanichdee, V.
(1985).
Decision issues in building perceptual product spaces with
multiattribute rating data. Journal of Consumer Research,
12, 4763.
This paper considers decisions that face consumer researchers as they
implement a perceptual
product space analysis based on multiattribute rating data. Decisions
that affect the
structure of the derived perceptual product space solution can be grouped
into six major
categories relating to issues of (1) data input, (2) mode, (3)
preprocessing transformation,
(4) choice/preference modeling, (5) technique, and (6) solution. The
major difficulties of
each decision area are provided whenever possible.

Disner, S.F. (2001).
Evaluation of vowel normalization procedures. Journal of the Accoustical Society
of America, 67, 253261.
Vowel normalization procedures are commonly evaluated on the basis of how
effectively they separate the vowels of a single test data set into distinct
groups corresponding to the phonetic categories of that language. A quantifiable
method of evaluation is proposed here, based on how much of he overall variance
is removed from the data. This evaluation method is applied to the vowels
of six different Germanic languages which have been normalized according to
four different procedures. It is shown that no one normalization procedure
is the most effective for all languages. Furthermore, some of the most successful
of these normalizations introduce procedural artifacts into the data, and
as a result the relative quality of vowels across languages or dialects is
altered. In such cases, it is shown that comparisons of the normalized vowels
of one language with the (separately) normalized vowels of another language
are not valid if the vowel systems are different. Some reasons for the appearance
of the procedural artifacts are discussed.

Do, T., & McIntyre, N. S. (1999a).
Pressure effects on aluminium oxidation kinetics using Xray photoelectron spectroscopy
and parallel factor analysis.
Surface Science, 440, 438450.
The effects of water vapour pressure on oxidation kinetics of aluminium have been
studied using Xray photoelectron spectroscopy (XPS) and threeway parallel factor analysis (PARAFAC).
While the first technique is a powerful experimental tool for surface oxidation studies, the PARAFAC
technique is a sophisticated analytical tool for analysing XPS data. The XPS Al(2p) and O(1s) core
level have been used to follow the oxide film growth on clean surfaces at room temperature as a
function of oxidation time (ranging from 1 to 60 min) and pressure of water vapour (ranging from 2.0
x 10(6) to 6.5 x 10(4) Pa). The growth of thin oxide films on aluminium surfaces has been found to
follow the CabreraMott inverse logarithmic law in all pressure ranges studied. The pressure effects
have shown that the defect formation reaction at the oxide film/gas interface is the rate determining
process in the aluminium oxidation. The pressure dependence of oxidation kinetics can be explained on
the basis of metal vacancies in the defect structure of thin aluminium oxide films.

Do, T., & McIntyre, N. S. (1999b).
Application of parallel factor analysis and Xray photoelectron spectroscopy to
the initial stages in oxidation of aluminium.
Surface Science, 435, 136141.
The threeway parallel factor analysis (PARAFAC)
has been used to decompose a set of XPS (Xray
photoelectron spectroscopy) spectra which result
during the oxidation of aluminium surfaces by
water vapour. Al(2p) and O(1s) corelevel
photoelectron lines have been used to follow
oxide film growth on clean aluminium surfaces as
a function of exposure time and pressure of water
vapour. The PARAFAC solution provides new
information on elemental processes in the very
initial stages of oxidation kinetics, showing new
components in the XPS spectrum, as well as their
evolution through the range of time and pressure
variables. Reaction of H2O vapour with aluminium
results in attenuation of the metallic peak,
binding energy (BE) at 72.87 +/ 0.05 eV, and
increase of the oxidic peak, BE at 75.80 +/ 0.05
eV. An additional factor is identified, which
suggests the formation of an interface metal
hydride, with BE at 72.4(4) eV, as well as a
concomitant oxide peak at 75.4(3) eV, At
pressures above 1.3 x 10(5) Pa this factor is
diminished; this is presumably due to the
increase in recombination of atomic hydrogen.

Do, T., McIntyre, N.S., Harshman, R.A., Lundy, M.E., & Splinter, S.J.
(1999c).
Application of parallel factor analysis and xray photoelectron spectroscopy to
the initial stages in oxidation of aluminium  I. The Al 2p photoelectron line.
Surface and Interface Analysis, 27, 618628.
Threeway parallel factor analysis (PARAFAC) has
been used to decompose a set of xray
photoelectron spectroscopy (XPS) spectra that
result during the oxidation of aluminium
surfaces. The Al 2p corelevel photoelectron
lines have been used to follow oxide film growth
on clean aluminium surfaces as a function of
exposure time and pressure of water vapour. In
this paper, a fine peak structure of the XPS Al
2p spectrum has been extracted using PARAFAC. The
PARAFAC solution provides new information on
elemental processes in the very initial stages of
oxidation kinetics, showing new components in the
XPS spectrum as well as their evolution through a
range of time and pressure variables.

Donchin, E., Gerbrandt, L.A., Leifer, L. & Tucker, L.
(1972).
Is the
contingent negative variation contingent on a motor response?
Psychophysiology, 9, 178188.
T3 on evoked potential data (7 subjects, 4 conditions, 125
time segments). Results are only partially presented.

Dong, D., & McAvoy, T.J. (1996).
Batch tracking via nonlinear principal component
analysis.
AIChE Journal, 42, 21992208.
Batch processes are very important to the chemical
and manufacturing industries. Techniques for
monitoring these batch processes to ensure their
safe operation and to produce consistently
highquality products are needed. Nomikos and
MacGregor (1994) presented a multiway principal
component analysis (MPCA) approach for monitoring
batch processes, and test results show that the
method is simple, powerful, and effective. MPCA,
however, is a linear method, and most batch
processes are nonlinear. Although data treatment
techniques can remove some nonlinearity from the
data, nonlinearity is still a problem when using
mpca for monitoring. In this article a nonlinear
principal component analysis (NLPCA) method (Dong
and McAvoy, 1993) is used for batch process
monitoring. Results show that this method is
excellent for this problem. Another interesting
extension of this approach involves multistage
batch process monitoring which is illustrated
through a detailed simulation study.

Drava, G., Leardi, R., Portesani, A., & Sales, E. (1996).
Application of chemometrics to the production of friction materials: Analysis
of previous data and search of new formulations.
Chemometrics and Intelligent Laboratory Systems, 32, 245255.
A friction material is a composite containing up to 18 different
components which can be chosen among a large number of possible raw materials having
different characteristics, like graphite, sulphides, metals, fibers, rubbers, resins
and fillers. The requested form is obtained by moulding at controlled pressure and
temperature. In order to prepare new formulations having good performances, the
problem is to choose the best raw materials and to mix them in the optimal proportions.
Since the quality of a formulation is not expressed by a single value, but several
responses have to be taken into account at the same time (friction coefficient,
comfort, wear, etc.), the analysis of the data obtained from different formulations
is quite difficult. In this study an approach to the analysis of this kind of data is
presented, in order to evaluate different products on the basis of a small number of
'quality indicators'. The techniques of experimental design are successfully applied
in order to investigate the effect of process variables on the performances of the
product and to perform a screening of the raw materials for new optimal formulations.

Dueñas Cueva, J.M., Rossi, A.V., & Poppi, R.J. (2001).
Modeling kinetic spectrophotometric data of aminophenol isomers by PARAFAC2.
Chemometrics and Intelligent Laboratory Systems, 55, 125132.
This paper describes an applicaion of PARAFAC2 in the modeling of
kineticspectophotometric data. The data were obtained by spectrophotometric
monitoring of the reaction between aminophenol isomers and NaNO_{2}
in acid solution. The data set of various samples produces a
threeway data array. This reaction has the property that isomers in different
proportions produce different kinetic profiles. Due to this property, PARAFAC2
is suitable to model the system because it does not assume parallel proportional
kinetic profiles. The results with PARAFAC2 were satisfactory, it being possible
to recover the spectral and kinetic profiles, as well as the initial isomer
concentrations with good accuracy.

Dunn, T.R., & Harshman, R.A. (1982).
A multidimensional scaling model for the sizeweight illusion.
Psychometrika, 47, 2545.
The kinds of individual differences in perceptions permitted by the weighted
euclidean model for multidimensional scaling (e.g., INDSCAL) are much more
restricted than those allowed by Tucker's Threemode Multidimensional Scaling
(TMMDS) model or Carroll's Idiosyncratic Scaling (IDIOSCAL) model. Although, in
some situations the more general models would seem desirable, investigators have
been reluctant to use them because they are subject to transformational indeterminacies
which complicate interpretation. This article shows how these indeterminacies
can be removed by constructing specific models of the phenomenon under investigation.
The data were also analysed using INDSCAL, however, INDSCAL cannot represent
individual differences in the strength of the illusion.

Dunn, W.J., Hopfinger, A.J., Catana, C., & Duraiswami, C.
(1996).
Solution of the conformation and alignment tensors for the
binding of trimethoprim and its analogs to dihydrofolate
reductase: 3Dquantitative structureactivity relationship study
using molecular shape analysis, 3way partial least squares
regression, and 3way factor analysis. Journal of Medicinal
Chemistry, 39, 48254832.
Molecular recognition is the basis of rational drug design.
However, the process by which a ligand recognizes and binds its
receptor is complex. A general treatment for solving for the
receptorbound geometry (conformation and alignment) of a series
of ligands is presented. A 20 (inhibitor structors) by 10
(compounds or ligands) by 4 (alignments) data array (included in
the paper) with molecular shapes as measured by common overlap
steric volume was available for analysis, as well as an inhibitor
concentration as criterion variable. A PLS 3way decomposition
was applied to the complete data (see also Lohmöller &
Wold,
1980) and a threemode PCA (Tucker, 1966) to the threeway array
using software developed by the authors. Random permutations of
the criterion variable were used to validate the PLS solution.

Durell, S.R., Lee, C.H., Ross, R.T., & Gross, E.L. (1990).
Factor analysis of the nearultraviolet absorption spectrum of
plastocyanin using bilinear, trilinear, and quadrilinear models.
Archives of Biochemistry and Biophysics, 278, 148160.
Factor analysis was used to resolve the spectral component in the nearuv
absorption spectrum of plastocyanin. The data set was absorption as a function
of four variables: wavelength, species of plastocyanin, oxidation state of the
copper center, and environmental pH. The data were fit with the traditional
bilinear model as well as with trilinear and quadrilinear models. Trilinear and
quadrilinear models have the advantage that they uniquely define the components,
avoiding the indeterminacy of bilinear models. Bilinear analysis using the
absorption spectra of tyrosine and copper metallothionein as targets resulted in a
twocomponent solution which was nearly identical to that obtained using trilinear and
quadrilinear models, for which no targets are required. The twocomponent models
separate the absorption into tyrosine and copper center components. The absorption of
tyrosine is found to be pH dependent in reduced plastocyanin, and the absorption
magnitude of the reduced copper center is the same in the four different plastocyanin
species. Further resolution is provided by a threecomponent quadrilinear model.
The results indicate that there are at least two different electronic transitions
which cause the absorption of the reduced copper center and that one of them
couples to a tyrosine residue which is pH dependent. Correlation of the results with
previous studies indicates that it is Tyr 83 which is the perturbed residue. The
separation of the absorption of the copper center and Tyr 83 provides spectroscopic
probes for the conformations of the north pole and east face reaction sites on
the plastocyanin protein.

D'Urso, P. (2004).
Fuzzy Cmeans clustering models for multivariate timevarying data: Different approaches.
International Journal of Uncertainty Fuzziness and Knowledgebases Systems,
12, 287326.
The classification of multivariate timevarying data finds application
in several fields, such as economics, finance, marketing research, psychometrics,
bioinformatics, medicine, signal processing, pattern recognition, etc. In this paper,
by considering an exploratory formalization, we propose different unsupervised clustering
models for multivariate data time arrays (objects x quantitative variables x times).
These models can be classified in two different approaches: the cross sectional and the
longitudinal approach. In the first case, after the objects, observed at each time, have
been classified, comparison among the classifications made in different time instants
will be done. In the second approach, we cluster the time trajectories of the objects;
then, we obtain only one classification by comparing the instantaneous and evolutive
features of the trajectories of the objects. In particular, in this work, the second
approach is analyzed in detail, with reference to the socalled single and double step
procedures. Geometric, correlative, instantaneous, evolutive and trend characteristics
of the multivariate time arrays are taken into account in the different proposed
clustering models. Furthermore, the fuzzy approach, that is particularly suitable in
the dynamic classification, problem, has been considered. Extensions of a clustervalidity
criterion for the proposed fuzzy dynamic clustering models are also suggested. A
socioeconomic example concludes the paper.

D'Urso, P. & Vichi, M. (1998).
Dissimilarities between trajectories of a threeway longitudinal data
set.
In A. Rizzi, M. Vichi, & H.H. Bock (Eds.) Advances in data
science and classification (pp. 585592). Berlin: Springer.
Methods are presented to evaluate dissimilarities between trajectories in a
threeway longitudinal data (sets of multiple time series). The dissimilarity
between trajectories is defined as a conic combination of the dissimilarities between
trends, velocities and acccelerations of pairs of trajectories. The coefficients of the
linear combinations are estimated maximising its variance. As an example trajectories of
Italian regions are classiified by their employment dynamics.

D'Urso, P., & Giordani, P. (2004).
A least squares approach to principal component analysis for interval valued data.
Chemometrics and Intelligent Laboratory Systems, 70, 179192.
Principal Component Analysis (PCA) is a wellknown technique, the aim of
which is to synthesize huge amounts of numerical data by means of a low number of
unobserved variables, called components. In this paper, an extension of PCA to deal
with interval valued data is proposed. The method, called Midpoint Radius Principal
Component Analysis (MRPCA), recovers the underlying structure of interval valued data
by using both the midpoints (or centers) and the radii (a measure of the interval width)
information. In order to analyze how MRPCA works, the results of a simulation study and
two applications on chemical data are proposed.

Dyson, R., Maeder, M., Neuhold, Y. M. & Puxty, G. (2003).
Analyses of threeway data from equilibrium and kinetic investigations
Analytica Chimica Acta, 490, 99108.
In kinetic or equilibrium investigations it is common to measure twoway
multiwavelength data, e.g. absorption spectra as a function of time or reagent
addition. Often it is advantageous to acquire experimental data at various initial
conditions or even on different instruments. A collection of these measurements
can be arranged in threedimensional arrays, which can be analysed as a whole
under the assumption of a superimposed function, e.g. a kinetic model, and/or
common properties of the subsets, such as molar absorptivity. As we show on selected
formation equilibria (Zn2+/phen) and kinetic studies (Cu2+/cyclam) from our own
research, an appropriate combination of multivariate data can lead to an improved
analysis of the investigated systems. Crown Copyright (C) 2003 Published by
Elsevier B.V. All rights reserved.
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Pedagogiek 
Centre for Child and
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ThreeMode bibliography

P.M. Kroonenberg
Education and Child Studies, Leiden University
Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
Tel. *31715273446/5273434 (secr.); fax *31715273945
Email:
kroonenb@fsw.leidenuniv.nl
First version : 12/02/1997;