ThreeMode Abstracts, Part H
With one can go to the index of
this part of the Abstracts, with
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parts (letters) of the Abstracts.
INDEX
Ha  Hb 
Hc  Hd 
He  Hf 
Hg  Hh 
Hi  Hj 
Hk  Hl 
Hm  Hn 
Ho  Hp 
Hq  Hr 
Hs  Ht 
Hu  Hv 
Hw  Hx 
Hy  Hz 


Haack, M. B., Eliasson, A. & Olsson, L. (2004).
Online cell mass monitoring of Saccharomyces cerevisiae cultivations by
multiwavelength fluorescence.
Journal of Biotechnology, 114, 199208.
The catalyst in bioprocesses, i.e. the cell mass, is one of the most
challenging and important variables to monitor in bioprocesses. In the present study,
cell mass in cultivations with Saccharomyces cerevisiae was monitored online with a
noninvasive in situ placed sensor measuring multiwavelength culture fluorescence.
The excitation wavelength ranged from 270 to 550 nm with 20 nm steps and the emission
wavelength range was from 310 to 590 nm also with 20 nm steps. The obtained spectra
were analysed chemometrically with the multiway technique, parallel factor analysis
(PARAFAC), resulting in a decomposition of the multivariate fluorescent landscape,
whereby underlying spectra of the individual intrinsic fluorophors present in the
cell mass were estimated. Furthermore, gravimetrically determined cell mass concentration
was used together with the fluorescence spectra for calibration and validation of
multivariate partial least squares (PLS) regression models. Both two and threeway
models were calculated, the models behaved similarly giving root mean square error of
prediction (RMSEPs) of 0.20 and 0.19 g l(1), respectively, when test set validation
was used. Based on this work, it is evident that online monitoring of culture
fluorescence can be used for estimation of the cell mass concentration during
cultivations.

Halstensen, M., & Esbensen, K. (2004).
New developments in acoustic chemometric prediction of particle sice distribution 
'the problem is the solution'.
Journal of Chemometrics, 14, 463481.
We present a new prototype acoustic chemometric approach for
prediction of powder particle size distributions, intended for inline implementation.
The standard basic solutions demand that calibration be carried out on representative,
'nonsegregated' reference powder samples. However, as practical powder flow with no
segregation is extremely difficult to achieve with the precision needed for calibration,
there will always be a significant uncertainty in the reference values relative to
what is actually measured. The problem is flow segregation. In order to solve this
problem, we have designed a completely new acoustic chemometric approach, which by
way of contrast forces the flowing powder mass to segregate as much as possible by
various mechanical means. The new approach measures the acoustic signals from an
integrated series of segregated, partsample characteristics. The calibration Xdata
matrix now becomes a threeway matrix, which demands a threeway calibration solution
to 'unscramble' the latent information in the maximally segregated powder sample.
Thus the problem is now, the solution. Our earlier forays into this matter, which were
based on twoway calibrations, have all been limited by a severe 'particle size ratio'
bracket outside which destructive selfdamping has effectively negated practical,
useful accuracy and precision. The new approach allows a much greater range of contrasting
particle sizes. Our firstgeneration results achieved by using threeway PLSR as
well as the standard twoway calibrations show that it is more precise than all earlier
attempts and can be used for manycomponent mixtures without extensive further modifications.
We also look at the feasibility of quantifying for prediction of inline particle size
distributions in an industrial environment.

Hammers, W.E., Janssen, R.H.A.M., Baars, A.G., & De Ligny, C.L. (1978).
Standardization and determination of the selectivity of octadecylsilylsilica in
highperformance liquid chromatography. Journal of Chromatography,
167, 273289.
Net retention volumes per gram of octadecylsilylsilica have been measured
for a large number of mono and disubstituted benzene derivatives, some monosubstituted
hexanes and cyclohexanes and a number of polycyclic aromatic compounds, using
nhexane, methylene chloride and a mixture of both solvents as the eluent
at 25° and 43.5°. The retention data are interpreted in terms of the
semiempirical adsorption model, developed by Snyder for bare adsorbents. The
effects of adsorbent deactivation temperature, solute and eluent localization,
change of the charge distribution in the solute molecule and adsorption mode of
the solute on retention and selectivity are discussed quantitatively.

Hammers, W.E., Spanjer, M.C., & De Ligny, C.L. (1979).
Selectivity of nucleosil 10 NH_{2} as an adsorbent in highperformance
liquid chromatography. Journal of Chromatography, 174, 291305.
Net retention volumes per gram of Nucleosil 10 NH_{2} have been measured
for a large number of mono and disubstituted benzene derivatives and of polycyclic
aromatic hydrocarbons, using nhexane, dichloromethane and a mixture of
both as eluents at 25°. The retention data are interpreted in terms of the semi
empirical adsorption model, developed by Snyder for bare adsorbents, using
octadecylsilylsilica as a reference adsorbent. The effects of the bound monomers
on adsorbent deactivation, solute and eluent localization, change of the charge
distribution in the solute molecule and adsorption mode of the solute are
evaluated and discussed in terms of donoracceptor interaction (including hydrogen
bonding).

Hanafi, M., & Lafosse, R. (2001).
Généralisations de la régression simple pour analyser
la dépendance de K ensembles de variables avec un K + 1ème.
Revue Statistique Appliquée, 49, 530.
By introducing a projector, the simultaneous dependency analysis considered
between a matrix and K matrices by Lafosse & Hanafi (1997) boils down
to an analysis between two matrices. Some simultaneous simple regressions then
lead to a calculus of the contributions to this dependency for every row of
each matrix. The simultaneous calculus of the regression coefficient now comes
from the solution of one optimization problem.

Hanke, B., Lohmöller, J.B., & Mandl, H. (1980).
Schülerbeurteilung
in der Grundschule: Ergebnisse der Augsburger Längsschnittuntersuchung
[Evaluation of
students at primary school: Results of the Augsburger longitudinal
study]. München,
FRG.: Oldenbourg Verlag.
In the Augsburg longitudinal study about 2500 primary school
children were tested for four years. Chapter 6 reports four
threemode studies based on correlation matrices (8 school
subjects; 6 occasions; 8 rating scales with teacher
judgements, 4 occasions; 8 primary mental abilities, 3
occasions; 8 sociometric tests, 3 occasions). The variable modes
are varimax rotated. Target rotations to orthogonal polynomials,
symmetric rotation of core matrices. Results are interpreted in
terms of stability, transformation, and continuity (see also
Lohmöller, 1982).

Hansen, P. W., Van Brakel, A. S., Garman, J., & Norgaard, L. (1999).
Detection of specific sugars in dairy process samples using multivariate curve
resolution.
Journal of Dairy Science, 82, 13511360.
Dairy process monitoring by application of
multivariate curve resolution using alternating
least squares is presented. Alternating least
squares was used for resolving Fourier transform
infrared spectral data from a dairy batch process
in which lactose is enzymatically hydrolyzed to
glucose and galactose. It was possible to extract
four compounds (fat, lactose, and two other sugar
components) from the spectral data obtained from
nine process runs. Subsequently, the pure spectra
obtained in this way were used to monitor the
content of these compounds in two new process
runs. In this way, alternating least squares made
it possible to follow the hydrolysis process by
Fourier transform infrared spectroscopy without
the need for reference analyses. When the results
were correlated to reference results for lactose,
the accuracy was similar to that obtained when a
partial least squares regression was performed on
the same data; lactose correlation was 0.980 when
alternating least squares was used and was 0.987
when partial least squares was used.

Harris, M.L., & Romberg, T.A. (1974).
An analysis of content and task dimensions of mathematics items designed
to measure level of concept attainment. Journal for Research in
Mathematics Education, 5, 7286.
Used factor analytic techniques to study content and task
dimensions of mathematics items, developed to measure concept
attainment, using a crossed design involving 30 concepts and 12
tasks. Conventional factor analyses were performed separately for
196 female 5th graders and 195 male 6th graders for concept and
task scores. Also, threemode factor analyses were performed. From
results of the conventional factor analyses, it is concluded that
all 30 of the concepts are measures of a single functional
relationship existing among the concepts and that all 12 tasks are
measures of a single underlying ability or latent trait. The
threemode results indicate that there are no important
concepttask interactions for idealized persons.

Harshman, R.A. (1970).
Foundations of the PARAFAC procedure: Models
and conditions for an "explanatory" multimodal factor analysis.
UCLA Working Papers in Phonetics, 16, 184.
Proposes the same model, CANDECOMP, as Carroll & Chang
(1970).

Harshman, R.A. (1972a).
Determination and proof of minimum
uniqueness conditions for PARAFAC1. UCLA Working Papers in
Phonetics,22, 111117.
A relatively simple proof that gives some
"minimal" data characteristics required for the PARAFAC
(PARAFAC1) solution to be unique. These requirements are
weaker than in Jennrich (in Harshman, 1970),
in that only two levels of Mode C (or B or A) are
necessary for uniqueness, provided that each factor changes
by a distinct percentage. Although less general than the
proof by Kruskal (1976) and Kruskal (1977), this proof shows
how uniqueness can break down "partially" (i.e., for some
factors but not others), which Kruskal's proof does not
cover. (see, also, Carroll &
Wish, 1974, and Carroll &
Arabie, 1980).

Harshman, R.A. (1972b).
PARAFAC2: Mathematical and technical notes.
UCLA Working Papers in Phonetics,
22, 3044.
A model for the analysis of scalar products which allows for
common oblique axis projections of the stimuli and individual
differences in weights or saliences (and thus is related to
INDSCAL and IDIOSCAL). The model is a special case of T2, but with
PARAFAClike uniqueness properties. [These properties are only
conjectured here (and are subsequently questioned in Carroll & Wish, 1974, and Carroll & Arabie, 1980) but are later
proven as a special case of PARATUCK2 (see Harshman & Lundy, 1996).].

Harshman, R.A. (1976).
PARAFAC: Methods of threeway
factor analysis and multidimensional scaling according to the
principle of proportional profiles. Unpublished doctoral
thesis, University of California. (Dissertation Abstracts
International, 37, 24782479).

Harshman, R.A. (1994a).
Substituting statistical for physical decomposition: Are there
applications for parallel factor analysis (PARAFAC) in non
destructive evaluation? In P.V. Malague (Ed.), Advances in
Signal Processing for Nondestructive Evaluation of Materials
(pp. 469483).
Dordrecht: Kluwer.
We describe the threeway factor analysis method PARAFAC
(PARAllel FACtor analysis) and its possible application to
Nondestructive Evaluation (NDE). Because standard analysis
methods usually seperate a signal into abstract, mathematically
convenient parts such as frequency bands, orthogonal variance
components, etc., irrelevant signals often remain mixed with
important ones. In contrast, Parallel Factor Analysis separates
mixtures into functionally distinct parts, i.e., parts showing
distinct patterns of variation in magnitude across varying
measurement conditions. It is used, for example, to decompose the
mixtures of curves generated by fluorescence spectroscopy of
complex samples into the individual spectra of the constituent
chemical compounds in the mixture; this is feasible because each
compound shows distinct patterns of variation in fluorescence
intensity across varying stimulus frequencies. In NDE, PARAFAC
could similarly separate the mixture of signals (or image
patches) from an object under test into those arising from each
causally/physically distinct component of interest in the object,
provided that there are several parallel test conditions, or
multiple time slices, where the signals from different components
of interest show distinct patterns of variation in magnitude
accross the conditions. Various normal and anomalous signals can
then be isolated onto distinct factors, allowing anomalous ones
to be identified and linked to their physical sources.

Harshman, R.A. (1999).
Use of angle bracket notation to simplify expression of multilinear
models. (Research Bulletin, no. 757). London, Canada: University of Western
Ontario, Department of Psychology.
To adapt matrix notation to three or higherway structures, the array structure
is often represented by considering only a twoway subpart, an arbitrary slice.
The description of a twoway structure for that slice is then understood to
generalize (with appropriate change of weights) to all slices and hence to the
array as a whole. In this report, a new approach to handling threeway structure
is proposed, called 'anglebracket notation'.

Harshman, R.A. (2000).
Generalization of matrix notation and algebra to nway arrays (Research
Bulletin, no. 758). London, Canada: University of Western Ontario, Department of
Psychology.
Matrix notation and the rules of matrix algebra are generalized to nway arrays.
The resulting language seems easy to use; all the capabilities of matrix
notation are retained and most appear to carry over naturally to the nway
context. For example, one can multiply a threeway array times a fourway array
to obtain a threeway product. Many of the language's key characteristics are
based on the rules of tensor notation and algebra. The most important example of
this is probably the incorporation of subscript/index related information into
both the names of array objects and the rules used to operate on them. Some
topics that emerge are relatively unexplored, such as inverses of nway arrays;
these might prove interesting for future theoretical study. It is hoped that
this language will facilitate expression of multilinear and quasimultilinear
models and exploration of new directions in nway research, after the critical
scrutiny of other researchers who will no doubt suggest useful improvements or
modifications. Thus, the language described here is offered as a working
draft.

Harshman, R.A. (2001).
An index to formalism that generalizes the capabilities of matrix notation and algebra
to nway arrays. Journal of Chemometrics, 15, 689714.
The capabilities of matrix notation and algebra are generalized to nway arrays.
The resulting language seems easy to use; all the capabilities of matrix notation are
retained and most carry over naturally to the nway context. For example, one can
multiply a threeway array times a fourway array to obtain a threeway product. Many
of the language's key characteristics are based on the rules of tensor notation and
algebra. The most important example of this is probably the incorporation of
subscript/indexrelated information into both the names of array objects and the
rules used to operate on them. Some topics that emerge are relatively unexplored,
such as inverses of nway arrays; these might prove interesting for future
theoretical study.

Harshman, R.A., & Berenbaum, S.A. (1981).
Basic concepts underlying the PARAFACCANDECOMP threeway factor
analysis model and its application to longitudinal data. In D.H. Eichorn,
J.A. Clausen, N. Haan, M.P. Honzik & P.H. Mussen
(Eds.), Present and past in middle life (pp. 435459). New York:
Academic Press.
This paper presents the basic concepts and assumptions underlying the
PARAFACCANDECOMP factor analysis model and consider possible benefits
and disadvantages of this approach to analyzing longitudinal data.

Harshman, R. A., & Hong, S. (2002).
'Stretch' vs. 'slice' methods for representing threeway structure via matrix
notation. Journal of Chemometrics, 16, 198205.
A threeway array must be represented in twoway form if its structure is to be
described and manipulated by means of matrix notation. Historically, two methods,
here called 'array stretching' and 'array slicing', have been used. More recently,
however, array slicing has often been overlooked, resulting in a loss of mathematical
flexibility. 'Stretching' involves matricizing (unfolding) the threeway array and
applying one's mathematical operations to the resulting twoway matrix; this results
in expressions that are often quite useful for parameter estimation but which are
relatively long and require practice to interpret properly. 'Slicing' involves
taking a representative twoway subarray and applying operations to it; this often
gives compact and easily understood expressions but requires the introduction of
extra matrix names and becomes awkward if the array is not 'slicewise regular'.
In this paper the advantages of each approach are demonstrated and compared by
applying them to a set of models from the Tucker and Parafac families. In addition,
we show how slicewise representation can be improved by using (i) angle brackets
to eliminate the need for extra diagonal matrices, and (ii) 'encapsulated summation'
notation to allow representation of array structure that is orderly but not slicewise
regular.

Harshman, R. A., Hong, S. J. & Lundy M. E.(2003).
Shifted factor analysis  Part I: Models and properties.
Journal of Chemometrics, 17, 363378.
The factor model is modified to deal with the problem of factor shifts. This problem
arises with sequential data (e.g. time series, spectra, digitized images) if the
profiles of the latent factors shift position up or down the sequence of measurements:
such shifts disturb multilinearity and so standard factor/component models no longer
apply. To deal with this, we modify the model(s) to include explicit mathematical
representation of any factor shifts present in a data set; in this way the model can
both adjust for the shifts and describe/recover their patterns. Shifted factor
versions of both two and three (or higher)way factor models are developed. The
results of applying them to synthetic data support the theoretical argument that
these models have stronger uniqueness properties; they can provide unique solutions
in both twoway and threeway cases where equivalent nonshifted versions are
underidentified. For uniqueness to hold, however, the factors must shift independently;
two or more factors that show the same pattern of shifts will not be uniquely resolved
if not already uniquely determined. Another important restriction is that the models,
in their current form, do not work well when the shifts are accompanied by substantial
changes in factor profile shape. Threeway factor models such as Parafac, and shifted
factor models such as described here, may be just two of many ways that factor analysis
can incorporate additional information to make the parameters identifiable.
Copyright (C) 2003 John Wiley Sons, Ltd.

Harshman, R.A., Ladefoged, P., & Goldstein, L. (1977).
Factor analysis of tongue shapes. Journal of the Acoustical
Society of America, 62, 693707.
A new analytic procedure PARAFAC has been applied to the
description of the shape of the tongue in English vowels. The
procedure models the data in terms of a unique set of possibly
explanatory factors. It solves in parallel for factors in several
data sets, simultaneously describing the differences among data
sets in terms of different relative involvement of these common
factors. Tracings were made of xrays taken during the
pronunciation of 10 English vowels by five speakers. The position
of the tongue in these 50 vowels were quantized in terms of 13
superimposed grid lines. PARAFAC analysis shows that the data can
be described in terms of two factors. One factor generates a
forward movement of the root of the tongue accompanied by an
upward movement of the front of the tongue. The second factor
generates an upward and backward movement of the tongue.
Movements from front to back vowels involve decreasing amounts of
factor one. Movements from high to low vowels involve decreasing
amounts of factor two. Different speakers use the two factors to
different degrees which may be associated with their individual
anatomy. The correlation between the observed data and that
predicted by the model is greater than 0.96.

Harshman, R. A., & Lundy, M. E. (1984a).
The PARAFAC model for threeway factor analysis and
multidimensional scaling. In H. G. Law, C. W. Snyder Jr, J. A.
Hattie, & R. P. McDonald (Eds.), Research methods for
multimode data analysis (pp. 122215). New York: Praeger.
This is a comprehensive discussion of the different forms of the PARAFAC(CANDECOMP)
threeway factor analysis model, its "uniqueness" properties, and its relationship with other
two and threeway factor analysis models. First, the PARAFAC1 model for raw score or profile
data ("direct fit") is derived as a generalization of the twoway factor model, issues of
scaling and interpretation of the factor loading matrices are discussed (pp. 128139;
192203), and "system" vs. "object" variation as they relate to the model are examined (pp.
125133). Next, the PARAFAC1 model for covariances ("indirect fit") is derived, first from
the raw score model and then from more general assumptions. The first derivation shows
PARAFAC1 to be a special case of PARAFAC2 (pp. 1367). Indirect and direct fitting are
compared and the advantages and disadvantages of the orthogonality assumption required by the
indirect fit model are discussed (pp. 1378), along with why correlations are inappropriate
(p. 141), and whether the principal components model differs appreciably from the common
factors model in the threeway indirect fit context (pp. 1413). Finally, the relationship
between factor analysis (PARAFAC) and metric MDS (INDSCAL, IDIOSCAL) is examined (pp. 1447).
The next major section in the chapter deals with the uniqueness properties of the PARAFAC
model (pp. 147169). "Uniqueness" or "intrinsic axes" means that given certain assumptions,
the solution determined from the data by PARAFAC has no alternative, equalfitting form
(i.e., any other rotation would reduce its fit to the data). Why this is important (pp.
147150; 1639) and the minimum conditions for uniqueness (pp. 1612) are explained. The
value of empirically confirming a PARAFAC solution by splithalf, bootstrapping, and/or
jackknifing procedures is also discussed.
The final section compares PARAFAC with other models, most notably Tucker's T3 (pp. 169182),
Corballis' threeway model (pp. 1845), and Sands and Young's ALSCOMP (pp. 188190). PARAFAC1
is described as a special case of the T3 model and vice versa, and a diagram on p. 175 shows
how Carroll transforms a T3 representation into the corresponding PARAFAC one (two other
methods of embedding T3 in PARAFAC are also discussed on pp. 176178 and pp. 2037). A family
of related models for threeway profile data, arranged from most general to most restricted,
is presented on p. 184. PARAFAC3 is listed between T3 and PARAFAC1 and is discussed on pp.
1856. PARAFAC2 and DEDICOM, not in the table, are also discussed in relation to PARAFAC3 and
T3 (p. 187).
Full text

Harshman, R. A., & Lundy, M. E. (1984b).
Data preprocessing and the extended PARAFAC model. In H. G. Law,
C. W. Snyder Jr, J. A. Hattie, & R. P. McDonald (Eds.),
Research methods for multimode data analysis (pp. 216284).
New York: Praeger.
The data preprocessing discussed here is restricted to additive adjustments (centering) and
multiplicative adjustments (rescaling or normalization) that may be applied to threeway
profile data, for example, before direct fitting of the PARAFAC model. It does not include
conversion of profile data to covariances or crossproducts, nor does it include conversion of
proximity data to scalar products. Eight reasons for preprocessing are given, the most
important of which is "to make the data appropriate for the PARAFAC model" (p. 218), which is
accomplished by centering. It is shown algebraically that "fiber"centering and
"slab"reweighting are the only appropriate ways to preprocess data for the trilinear PARAFAC
model (see p. 231 for a diagram of fibers and slabs). Also shown is the effect the proper
preprocessing has on the original factor loadings (e.g., centering Mode A of the data centers
the Mode A factors; rescaling Mode B similarly reweights the rows of the Mode B factor
matrix). Practical guidelines for deciding how to preprocess data are given on pp. 257259.
Preprocessing is also discussed from the perspective of extending the PARAFAC model to more
general data (instead of making the data appropriate for a restricted model, as above). In
this context, "degenerate" solutions and their possible causes are described. Degenerate
solutions are characterized by two or more factors whose loadings are highly correlated across
all three modes, with a negative tripleproduct. Appropriate centering can sometimes correct
this problem, but not always. Other times an orthogonally constrained PARAFAC procedure can
block the high correlations and yield an interpretable solution (alternatively,
zerocorrelation constraints can be used, e.g., if the solution requires positive loadings).
In these instances, it seems that while more general Tuckertype structure is present in the
data, the constraints allow a subset of Tucker variations to be meaningfully expressed via
orthogonal/uncorrelated PARAFAC factors.
Full text

Harshman, R.A., & Lundy, M.E. (1994).
PARAFAC: Parallel factor analysis. Computational Statistics
& Data Analysis, 18, 3972.
We review the method of Parallel Factor Analysis, which
simultaneously fits multiple twoway arrays or 'slices' of a
threeway array in terms of a common set of factors with
differing relative weights in each 'slice'. Mathematically, it
is a straightforward generalization of the bilinear model of
factor (or component) analysis (x_{ij} =
Sigma_{r}^{R} =
_{1}a_{ir}b_{jr}) to a trilinear
model (x_{ijk} =
Sigma_{r}^{R} =
Sigma_{r}a_{ir}b_{jr}c_{kr}).
Despite this simplicity, it has an important property not
possessed by the twoway model: if the latent factors show
adequately distinct patterns of threeway variation, the model
is fully identified; the orientation of factors is uniquely
determined by minimizing residual error, eliminating the need of
a separate 'rotation' phase of analysis. The model can be used
several ways. It can be directly fit to a threeway array
of observations with (possibly incomplete) factorial structure,
or it can be indirectly fit to the original observations
by fitting a set of covariance matrices computed from the
observations, with each matrix corresponding to a twoway subset
of the data. Even more generally, one can simultaneously analyze
covariance matrices computed from different samples, perhaps
corresponding to different treatment groups, different kinds of
cases, data from different studies, etc. To demonstrate the
method we analyze data from an experiment on right vs. left
cerebral hemispheric control of the hands during various tasks.
The factors found appear to correspond to the causal influences
manipulated in the experiment, revealing their patterns of
influence in all three ways of the data. Several generalizations
of the parallel factor analysis model are currently under
development, including ones that combine parallel factors with
Tuckerlike factor 'interactions'. Of key importance is the need
to increase the method's robustness against nonstationary factor
structures and qualitative (nonproportional) factor
change.

Harshman, R.A., & Lundy, M.E. (1996).
Uniqueness proof for a family of models sharing features of
Tucker's threemode factor analysis and PARAFACCANDECOMP.
Psychometrika, 61, 133154.
Some existing threeway factor analysis and MDS models incorporate
Cattell's "Principle of
Parallel Proportional Profiles". These models can  with appropriate data
 empirically
determine a unique best fitting axis orientation without the need for a
separate factor
rotation stage, but they have not been general enough to deal with what
Tucker has called
"interactions" among dimensions. This article presents a proof of unique
axis orientation for
a considerably more general parallel profiles model which incorporates
interacting
dimensions. The model, X_{k} = A
^{A}D_{k}
H ^{B}D_{k} B', does not assume
symmetry in the data or
in the interactions among factors. A second proof is presented for the
symmetrically weighted
case (i.e., where ^{A}D_{k} =
^{B}D_{k}). The
generality of these models allows one to impose successive restrictions
to obtain several
useful special cases, including PARAFAC2 and threeway DEDICOM.

Hart, S. J., & Jiji, R. D. (2002).
Light emitting diode excitation emission matrix fluorescence spectroscopy.
Analyst, 127, 16931699.
An excitation emission matrix (EEM) fluorescence instrument has been
developed using a linear array of light emitting diodes ( LED). The wavelengths covered
extend from the upper UV through the visible spectrum: 370640 nm. Using an LED array to
excite fluorescence emission at multiple excitation wavelengths is a lowcost alternative
to an expensive high power lamp and imaging spectrograph. The LEDEEM system is a
departure from other EEM spectroscopy systems in that LEDs often have broad excitation
ranges which may overlap with neighboring channels. The LED array can be considered a
hybrid between a spectroscopic and sensor system, as the broad LED excitation range
produces a partially selective optical measurement. The instrument has been tested and
characterized using fluorescent dyes: limits of detection (LOD) for 9,10bis(phenylethynyl)
anthracene and rhodamine B were in the mid partspertrillion range; detection limits for
the other compounds were in the low partsperbillion range (< 5 ppb). The LEDEEMs were
analyzed using parallel factor analysis ( PARAFAC), which allowed the mathematical
resolution of the individual contributions of the mono and dianion fluorescein tautomers
a priori. Correct identification and quantitation of six fluorescent dyes in two to six
component mixtures ( concentrations between 12.5 and 500 ppb) has been achieved with root
mean squared errors of prediction (RMSEP) of less than 4.0 ppb for all components.

Hartley, R. I. (1997).
Lines and points in three views and the trifocal tensor.
International Journal of Computer Vision, 22, 125140.
This paper discusses the basic role of the trifocal tensor in scene
reconstruction from three views. This 3 x 3 x 3 tensor plays a role in the analysis of
scenes from three views analogous to the role played by the fundamental matrix in the
two view case. In particular, the trifocal tensor may be computed by a linear algorithm
from a set of 13 line correspondences in three views. It is further shown in this paper,
that the trifocal tensor is essentially identical to a set of coefficients introduced by
Shashua to effect point transfer in the three view case. This observation means that the
13 line algorithm may be extended to allow for the computation of the trifocal tensor
given any mixture of sufficiently many line and point correspondences. From the trifocal
tensor the camera matrices of the images may be computed, and the scene may be
reconstructed. For unrelated uncalibrated cameras, this reconstruction will be unique up
to projectivity. Thus, projective reconstruction of a set of lines and points may be
carried out linearly from three views.

Hartmann, W. (1986).
Canonical decomposition with linear equality and inequality constraints
on parameters. In W. Gaul & M. Schader (Eds.), Classification
as a tool of research (pp. 191199). Amsterdam: Elsevier.
A numerical method is developed for the restricted canonical
decomposition with which the single components of the parameter
matrices can be subjected not only to linear equality but also
linear inequality constraints. By this method especially
boundary and/or order constraints can be handled very
effectively. With simple modifications the technique can be
used also for the minimizing of related models.

Harvey, D., & Greenway, P. (1982).
How parent attitudes and emotional reactions affect their
handicapped child's selfconcept. Psychological Medicine,
12, 357370.
The parents of 24 physically handicapped children were grouped
according to their responses to a Primary Mood Factors grid and
comparisons were made with their children's responses to a
selfconcept scale. It was found that parents who were close
together in their primary mood reactions had handicapped children
who were more positive in selfesteem than those dyads who were
divided in their primary mood reaction.

Hasegawa, K., Arakawa, M., & Funatsu, K. (1999).
3DQSAR study of insecticidal neonicotinoid compounds based on
3way partial least squares model. Chemometrics and Intelligent
Laboratory Systems, 47, 3340.
A choice of an active conformer and the corresponding alignment
rule is an important problem for determining the success of
3DQSAR study. For flexible molecules, this problem is the most
difficult one and construction of the method with appropriate
chemometric tools has been required. Recently,
Bro
has proposed a trilinear PLS algorithm as the
trilinear extension of standard bilinear PLS in the field of
analytical chemistry. This method seems to be suitable
to the 3DQSAR problem but only few attempts have so far been
made at the subject. The object of this study is to investigate
the ability of Bro's method for solving the
conformer/alignment problem in 3DQSAR study. The
structureactivity data of insecticidal neonicotinoid compounds
were used as a test example. The 3way arrays were constructed
from eight sample vectors and eight electrostatic similarity
matrices derived from eight combinations of conformers and
alignment rules. The correlation between the 3way arrays and the
insecticidal activity vector was investigated by the 3way PLS
method. A model with three significant components was
obtained, and from its PLS loading the best combination of
conformer and alignment rule could be selected.

Hasegawa, K., Arakawa, M., & Funatsu, K. (2000).
Rational choice of bioactive conformations through use of
conformation analysis and 3way partial least squares modeling
Chemometrics and Intelligent Laboratory Systems, 50, 253261.
Comparative molecular field analysis (CoMFA) has become widely
used in threedimensional (3D) QSAR studies. Although CoMFA has
been of general use, there are some critical problems in the
proper application. A major problem of CoMFA, including most
other 3D QSAR methodologies, is that the results are dependent
on the chosen bioactive conformations and the corresponding
alignment rules of molecules. Recently, we have proposed a novel
method with a 3way PLS formulation for solving the
conformation/alignment problem in 3D QSAR studies (Hasegawa, Arakawa, & Funatsu,
1999).
The purpose of the present study is to demonstrate the general
utility of our approach by applying to a real CoMFA data set.
The data set of ProteinTyrosine Kinase (PTK) inhibitors was
used as a test sample. The possible 3D conformations of all
molecules were generated by conformational analysis and they
were characterized by field variables of CoMFA. To each unique
conformation of the most active compound, one samplevariable
sheet comprising of the most similar conformations was defined.
The 3way arrays for 3way PLS analysis were created by
collecting all samplevariable sheets. From the regression
coefficient values of the 3way PLS model, conformations largely
contributing to inhibitory activity were selected and the
resulting final CoMFA model could give the reasonable 3D
coefficient contour maps.

Hasegawa, K., Arakawa, M., & Funatsu, K. (2003a).
Simultaneous determination of bioactive conformations and alignment rules by
multiway PLS modeling.
Computational Biology and Chemistry, 27, 211216.
In this study, we propose a new threedimensional quantitative
structureactivity relationship (3DQSAR) method for selecting bioactive conformations
and alignment rule simultaneously. The possible conformations of all molecules are
generated by conformational analysis and they are superimposed on template conformer with
possible alignment rules. The field variables are calculated as 3D descriptor of
structures. Fourway partial leastsquares (PLS) analysis is applied, and the
conformations and alignment rule largely contributing to biological activity are
selected. In order to demonstrate this method, the data set of benzodiazepine
derivatives, antagonists of (CCKB), was used as a test sample. As a result, appropriate
conformers and alignment rule were selected and significant PLS model was obtained. The
resulting final model could give the reasonable 3D coefficient contour maps. Moreover,
external prediction was carried out by use of external data sample and its prediction
was proved to be high enough.

Hasegawa, K., Matsuoka, S., Arakawa, M., & Funatsu, K. (2003b).
Multiway PLS modeling of structureactivity data by incorporating electrostatic
and lipophilic potentials on molecular surface.
Computational Biology and Chemistry, 27, 381386.
We devised and elaborated a surfacebased threedimensionalquantitative
structureactivity relationship (3DQSAR) method, which had been proposed in the previous
study. This approach can be applied to more general case where both the electrostatic and
lipophilic potentials on molecular surface simultaneously change. The 3D coordinates of
all sampling points on molecular surface are projected into a 2D map by Kohonen neural
network (KNN). Each node in the map is coded by the associated molecular electrostatic
potential (MEP) or molecular lipophilic potential (MLP) values. The electrostatic and
lipophilic KNN maps are generated for each compound and the fourway array is constructed
by collecting two KNN maps of all samples. The correlation between fourway array and
biological activity is examined by fourway partial leastsquares (PLS). For validation,
the structureactivity data of estrogen receptor antagonists was investigated.
The fourway PLS model gave the high statistics at calibration and validation stages.
The coefficients of the fourway PLS model backprojected on molecular surface had a
reasonable 3D distribution and it was nicely consistent with active site of the estrogen
receptor which was recently made clear by Xray crystallography.

Hayashi, C. (1981).
Distance or generalized variance. Classification Automatique et
Perception par Ordinateur, 129141.
The various criteria or measures are discussed and used for clustering,
pattern
recognition and representation of goodness of fit or discrimination in
data analysis
[2,6,8,10]. In the present paper, some discussions of the topic of the
title will be
given.

Hayashi, C. (1982).
An algorithm for the solution of PARAFAC model and analysis of
the data by the international rice adaptation experiments.
Bulletin of the Biometric Society of Japan, 3,
7791.
PARAFAC is a three mode factor analytic method developed by R.A.
Harshman and is useful for
data analysis. However, the computer program of PARAFAC developed by
Harshman seems to
require great skill to understand how to handle it and to select the
optimal solution
through many steps. Here a new foolproof algorithm is presented that
does not require any
skill, with an application to the data of the international rice
adaptation
experiments.

Hayashi, C. (1985).
Recent theoretical and methodological developments in
multidimensional scaling and its related methods in Japan.
Behaviormetrika, 18, 6779.
This is a review paper. The term multidimensional scaling (MDS)
is used in two senses. One is a narrow sense, a technical term
which is divided into metric MDS and nonmetric MDS. The other is
a wider sense and has many variations in multidimensional data
analysis. In this review, MDS in a narrow sense and its closely
related methods, which are a part of MDS in a wider sense, are
taken into consideration. And Japanese works are introduced.

Hayashi, C. (1989).
Multiway data matrices and method of quantification of
qualitative data as a strategy of data analysis. In R. Coppi &
S. Bolasco (Eds.), Multiway data analysis (pp. 131142).
Amsterdam: Elsevier.
In the present paper, the analysis of multiway data matrices is
discussed in the light of a
method of quantification of qualitative data. The following three topics
will be discussed.
1. Multiway frequency data matrix; 2. Threeway data matrix of
dissimilarity indices among
three elements; 3. Generalization of the method of quantification of
response pattern
(correspondence analysis) to a threeway matrix.

Hayashi, C. & Hayashi, F. (1982).
A new algorithm to solve PARAFACmodel. Behaviormetrika,
11, 4960.
PARAFAC is a threemode factor analytic method developed by R.A.
Harshman and is useful for data analysis. The fundamental idea
says: x(ijk) ~ Sum{a(is)b(js)c(ks) where x(ijk) is given by
measurement for i=1,...,I, j=1,...,J, k=1,...,K;
a(is), b(js), and c(ks) are unknown.

Hayashi, F., Yamaoka, K., & Terao, H. (1982).
A comparative study between two algorithms of PARAFAC model (in
Japanese). Japanese Journal of Behaviormetrics, 1,
4762.
In utilizing the PARAFAC model, when Dr. Harshman's program was
used, there seems to be too many steps involved in leading to the
optimum solution. In order to avoid such complexities and
difficulties, Dr. Hayashi has suggested that a different, more
fool proof method be used. A comparison was made between these
two methods using data about the physical constitution of
children. The results showed that these two methods yielded two
different solutions. Yet the solution from Dr. Hayashi's mathod
was found to be much more understandable than from Dr. Harshman's
method.

Heimdal, H., Bro, R., Larsen, L.M., & Poll, L. (1997).
Prediction of polyphenol oxidase activity in model solutions
containing various combinations of chlorogenic
acid,()epicatechnin, O_{2}, CO_{2}, temperature, and pH
by multiway data analysis.
Journal of Agricultural and Food Chemistry,45, 23992406
Controlled and modified packing of lettuce is simulated in model
solutions containing various chemicals under various conditions
and enzymatic browning is measured. Results were analysed by
multiway data analysis. A very descriptive fivecomponent
multiplicative Parafac model was obtained. Moreover it was
shown that it is possible to predict polyphenol oxidase activity
even though the samples are of very different constitutions.

Heiser, W.J. (1989).
The cityblock model for threeway multidimensional scaling. In R. Coppi
& S. Bolasco (Eds.), Multiway data analysis (pp. 395404).
Amsterdam: Elsevier.
The cityblock representation of threeway proximity data, with
diagonal dimension weights, is studied for four reasons: (1) since it
is the model of choice in certain domains, (2) because it naturally
enjoys a unique axes property, (3) a large class of cityblock
(dis)similarity coefficients exists, and (4) there are some algorithmic
problems to solve. A convergent algorithm based on iterative
majorization and alternating least squares is presented, and a number
of special applications with Gower's (1971) general coefficient of
similarity are discussed.

Heiser, W. J., & Bennani, M. (1997).
Triadic distance models: Axiomatization and least squares representation.
Journal of Mathematical Psychology,41, 189206.
Distance models for threeway proximity data, which consist of
numerical values assigned to triples of objects that indicate
their joint (lack of) homogeneity or resemblance. require a
generalization of the usual distance concept defined on pairs
of objects. An axiomatic framework is given for characterizing
triadic dissimilarity, triadic similarity, and triadic
distance, where the term triadic implies that each element of
the triple is treated on an equal footing. Two kinds of
distance models are studied in detail: the Minkowskip or Mp
model, which is based upon dyadic components and includes the
perimeter model as an important special case, and several
models based on presenceabsence variables. They are shown to
satisfy the tetrahedral inequality, a condition that is
characteristic for the present axiomatization. Two
monotonically convergent algorithms are described that find
weighted least squares representations of threeway proximity
data under the Euclidean M1 model and the Euclidean M2 model.
To enable a scalefree evaluation of the quality of the fit, an
additive decomposition of the sum of squares of the
dissimilarities is derived. As illustrated in one of the
examples, distance analysis of threeway, threemode tables is
possible by a suitable manipulation of the least squares
weights.

Henrion, G., Henrion R., Bacsó J., & Uzonyi I. (1990).
Ausgewählte Methoden der Korrelationsanalyse am Beispiel der
Spurenelementrelationen im menschlichen Körper
[Selected methods of correlationanalysis for the
example of traceelement relations in humanbody].
Zeitschrift für Chemie, 30, 204211.**
Selected methods from uni and multivariate analysis of correlation are
discussed and applied to a 3dimensional data array of the objectvariable
occasion type. The data resulted from trace element determinations (by xray
fluorescence analysis in human tissues. Special attention is devoted to
3way principal component analysis, partial least squares, linear characteristics
and the nonparametric rank correlation coefficient by Kendall. It is shown
that the correlations between interior human tissues (brain, liver, kidney)
are strongly governed by a specific set of toxic trace elements (As, Se, Hg,
Pb, Ni). However the relations between tissues and hair, which are of special
interest in medicine, turn out to be rather weak. This results in an
unsatisfactory prediction of toxic elements in tissues by those in hair.

Henrion, G., Nass,
D.,
Michael, G., & Henrion, R. (1995).
Multivariate 3way data analysis of amino acid patterns of lakes.
Fresenius' Journal of Analytical Chemistry, 352,
431436.
Time dependent patterns of amino acid concentrations have been
studied by HPLC for different lakes of the Berlin area. Data
analysis has been performed by conventional principal component
analysis as well as by its more recent Nway extension. It turns
out that lakes mainly differ by their general amino acid
production as a function of time and season. Apart from this, in
a single case there occurs a specific pattern which might be
related to an exterior influence. This pattern, although clearly
detected, has not been stable over time. Measurements are
reproducible with respect to time (comparison of two succeeding
years) and to position (comparison of isolated parts of a
lake).

Henrion, R. (1993).
Body diagonalization of core matrices in threeway principal
components analysis: Theoretical bounds and simulation. Journal
of Chemometrics, 7, 477494.
In contrast with conventional PCA, a direct superposition and
joint interpretation of loading plots is not possible in
threeway PCA, since there may be data variance which is
described by unequal components of different modes. The
contributions to variance of all possible combinations of
components are described in the core matrix. Body
diagonalization, which is achieved by appropriate rotation of
component matrices, is an essential tool for simplifying the
core matrix structure. The maximum degree of body diagonality
which may be obtained from such transformations is analysed from
both the mathematical and simulation viewpoints. It is shown
that, at least in the average case, high degrees can be
expected, which makes the procedure reasonable for many
practical applications. Furthermore, simulation as well as
theoretical derivation show that the success of body diagonality
depends on the socalled polarity of the core array. The
methodology is illustrated by a threeway data example from
environmental chemistry.

Henrion,
R. (1994).
Nway principal component analysis:
Theory, algorithms and applications. Chemometrics and
Intelligent Laboratory Systems, 25, 123.
Due to sophisticated experimental designs and to modern
instrumental constellations the investigation of
Ndimensional (or Nway or Nmode) data
arrays is attracting more and more attention. Threedimensional
arrays may be generated by collecting data tables with a fixed
set of objects and variables under different experimental
conditions, at different sampling times, etc. Stacking all the
tables along varying conditions provides a cubic arrangement of
data. Accordingly the three index sets or modes spanning a
threeway array are called objects, variables and conditions. In
many situations of practical relevance even higherdimensional
arrays have to be considered. Among numerous extensions of
multivariate methods to the threeway case the generalization of
principal component analysis (PCA) has central importance. There
are several simplified approaches of threeway PCA by reduction
to conventional PCA. One of them is unfolding of the data array
by combining two modes to a single one. Such procedure seems
reasonable in some specific situations like multivariate image
analysis, but in general combined modes do not meet the aim of
data reduction. A more advanced way of unfolding which yields
separate component matrices for each mode is the Tucker 1 method.
Some theoretically based models of reduction to twoway PCA
impose some specific structure on the array. A proper model of
threeway PCA was first formulated by Tucker (socalled Tucker3
model among other proposals). Unfortunately the Tucker 1 method
is not optimal in the least squares sense of this model.
Kroonenberg and De Leeuw demonstrated that the optimal solution
of Tucker's model obeys an interdependent system of eigenvector
problems and they proposed an iterative scheme (alternating least
squares algorithm) for solving it. With appropriate notation
Tucker's model as well as the solution algorithm are easily
generalized to the Nway case (N > 3). There are
some specific aspects of threeway PCA, suc as complicated ways
of data scaling or interpretation and
simplestructuretransformation of a socalled core matrix, which
make it more difficult to understand than classical PCA. An
example from water chemistry serves as an illustration.
Additionally, there is an application section demonstrating
several rules of interpretation of loading plots with examples
taken from environmental chemistry, analysis of complex round
robin tests and contamination analysis in tungsten wire
production.

Henrion,
R. (1994).
Simultaneous simplification of loading and core matrices
in Nway PCA: application to chemometric data arrays Fresenius Journal
of Analytical Chemistry, 361, 1522.
In the Tucker3 model of Nway principal components analysis (NPCA), a socalled
core matrix describes the possible interactions between components from different
modes. For an easy interpretation of solutions, it is necessary to have as few
interactions as possible (in conventional PCA of data tables, such interactions
can always be avoided). This goal may be realized by various approaches of core
matrix transformations. At the same time, it is desirable to have simple component
(or loading) matrices. Usually, the simplicity of the core conflicts to a certain
degree with the simplicity of the components. The paper demonstrates how the
conditional optimization of both goals can be used to find a compromise. For the
purpose of illustration, the procedure is first applied to a small threeway data
array from heavy metal analysis of tissues in different samples of game. Later,
a data array of bigger size from a threeway interlaboratory study is considered.

Henrion, R. (2000).
On global, local and stationary solutions in threeway data analysis.
Journal of Chemometrics, 14, 261274.
The issue of global and local solutions to optimization problems is of much
interest in the context of threeway analysis, in particular when dealing with
the PARAFAC and Tucker3 models or core transformations within the latter. For
clarity of statements, it is useful to consider the most simple yet reasonable
situation, namely onecomponent PARAFAC decomposition or, closely related,
maximization of the leading squared core entry in Tucker3. In the paper,
necessary and sufficient conditions for global solutions are derived.
Furthermore, it is shown that, in general, the usual cyclic coordinate
optimization scheme of threeway methods does not converge towards a local
minimum (or maximum) even if the iterates yield global solutions in each co
ordinate direction. Finally, an example for a proper local minimum in one
component PARAFAC is given.

Henrion, R. & Andersson, C.A. (1999).
A new criterion for simplestructure
transformations of core arrays in Nway principal
components analysis.
Chemometrics and Intelligent Laboratory Systems, 47, 189
204.
Among the possible (orthogonal) transformations
of core arrays in Nway principal components
analysis (PCA), the conventional approach of body
diagonalization turns out not to provide the
simplest structure (in the sense of minimizing
the number of significant entries). As an
alternative, the maximization of the
varianceofsquared core entries is proposed.
Both criteria are equivalent in a twoway
constellation but may differ markedly for N
greater than or equal to 3. Actually, using the
variance criterion may provide more insight into
the rank structure of the given data, and it is
also easily applied to general rectangular core
arrays. In order to clarify the relation between
body diagonality and varianceofsquares, we
prove the following main result of the paper: If
some cubic Nway core array can be transformed to
exact body diagonality, then the same
transformation yields maximum varianceofsquared
entries. This result implies the equivalence in
the twoway case mentioned above. A solution
algorithm is formulated and illustrated with a
small numerical example. The application to data
examples from environmental chemistry and
chromatographic analysis is briefly discussed.

Henrion, R., Henrion, G., Böhme, M. & Behrendt, H.
(1997).
Threeway principal components analysis for fluorescence spectroscopic
classification of algae species.
Fresenius' Journal of Analytical Chemistry, 357,
522526.
In this paper it is illustrated how threeway prinicpal components
analysis as the appropriate generalisation of conventional
prinicpal components analysis may serve as a powerful method for
clasisifcation of algae species using the excitationemission
matrices from fluorescence spectroscopy from different species.

Henrion, R., Henrion, G., Heininger, P., & Steppuhn, G. (1991).
Statistical analysis of complex round robin tests.
Acta Hydrochimica et Hydrobiologica, 19, 603614.
Different possibilities for the evaluation of
complex round robin tests are presented. The
advantages of Threeway over classical principal
components analysis when applied to Threeway data
arrays are discussed. The method allows extreme
data reduction without essential loss of
information. This is useful first of all for a
graphically oriented evaluation of laboratories.
The results of 4 round robin tests (8
laboratories, 5 parallel estimations, 4 trace
element concentrations) for the analysis of heavy
metals in waters (synthetic solutions with known
concentrations) serve as an example. Special
attention is paid to the recognition of different
kinds of errors (random and systematic errors or
unstable working).

Henrion, R., Henrion, G., & Onuoha, G.C. (1992).
Multiway principal componentsanalysis of a
complex data array resulting from physicochemical
characterization of naturalwaters.
Chemometrics and Intelligent Laboratory Systems, 16, 87
94.**
Multiway principal components analysis (MPCA) is
an efficient tool for reducing higher dimensional
data arrays. Using the Kroonenberg algorithm:
which originally was developed for
threedimensional data arrays but may be
generalized to arbitrary dimensions in a
straightforward manner: MPCA is applied to a
complex example from the chemistry of waters. The
data originated from the measurements of fifteen
physicochemical parameters (variables) at ten
different locations (objects) within some specific
area of the Niger delta. These measurements were
consistently recorded 22 times (occasions) in the
course of a year. MPCA allows the detection of
spatial and temporal factors of influence and the
classification of the parameters considered
according to these factors.

Henshaw, J.M., Burgess, L.W., Booksh, K.S., & Kowalski, B.R.
(1994).
Multicomponent determination of chlorinated
hydrocarbons using a reactionbased chemical
sensor .1. Multivariate calibration of fujiwara
reactionproducts.
Analytical Chemistry, 66, 33283336.**
Multicomponent analysis for 1,1,1trichloroethane,
trichloroethylene, and chloroform is demonstrated
by partial least squares modeling of absorbance
data collected from the Fujiwara reaction of these
analytes over time. Optimal calibration times are
determined for each analyte dependent upon its
reaction rate. This is the simplest example of
trying to use the selectivity gained from a second
data dimension or order. Problems associated with
firstorder calibration are demonstrated when
interferences unaccounted for in the calibration
model are present. Determination of
1,1,1trichloroethane in the presence of the other
two species is also demonstrated using the
generalized rank annihilation method and trilinear
decomposition for secondorder calibration. a
subsequent paper describes an approach using
multivariate curve resolution to extract the
analytical information from the spectral and
temporal profiles of analytes in the Fujiwara
reaction.

Hentschel, U. & Klintman, H. (1974).
A 28variable semantic
differential. I. On the factorial identification of content.
Psychological Research Bulletin, 14.
T3 was used to assess the structure of semantic differential
data of 4 concepts (primarily selfdescription) scored on 28
bipolar scales by 209 subjects who did, however, not all
score all concepts. Therefore, only very partial results could
be obtained.

HernandezArteseros, J. A., Beltran, J. L., Compano, R., & Prat, M. D. (2002).
Fastscanning fluorescence spectroscopy as a detection system in liquid chromatography
or confirmatory analysis of flumequine and oxolinic acid.
Journal of Chromatography A, 942, 275281.
Oxolinic acid and flumequine were analysed by reversedphase liquid chromatography
after extraction from the sample matrix with dichloromethane and partitioning with NaOH. The
detection system consisted of a fastscanning fluorescence detector, which provides the full
spectra of the eluting peaks and can thus be used to confirm the identity of analytes.
Determination was performed by partial least squares (PLS) and threeway PLS over the
threedimensional data, i.e. fluorescence intensity versus retention time and excitation
wavelength. In both cases, similar results, with prediction errors around 4%, were obtained.
The method was successfully applied to the analysis of salmon, pork and chicken muscle spiked
up to 300 ng g(1).

Herrero, A., Zamponi, S., Marassi, R., Conti, P., Ortiz, M. C. & Sarabia, L. A.
(2002).
Determination of the capability of detection of a hyphenated method: application
to spectroelectrochemistry.Chemometrics en Intelligent Laboratory Systems,
61, 6374.
A procedure to evaluate the capability of detection of a secondorder analytical
technique to determine an analyte in presence of an interferent has been proposed
taking into account alpha and beta errors in a similar way as ISO norms indicate
for the univariate analytical methods. The potentiality of spectroelectrochemistry
as a quantitative threeway technique of analysis has been analysed. Trilinearity
of spectroelectrochemical data has been studied since it is a necessary condition
to apply the trilinear decomposition (TLD) method. As an example, the voltabsorptometric
determination of otolidine in presence of high concentration of ferrocyanide was
chosen to test the applicability of the proposed method. In the same way, the
capability of discrimination has been determined. In addition, a secondorder
standard addition method (SOSAM) has been applied to calculate the concentration
of the analyte of interest in the presence of this interferent, avoiding the need
to previously identify and determine the quantity of the interferent. (C) 2002
Elsevier Science B.V. All rights reserved.

Herrmann, W.M., Röhmel, J., Streitberg, B., & Willmann, J. (1983).
Example for applying the COMSTAT multimodal factor analysis algorithm to EEG data
to describe variance sources. Neuropsychobiology, 10, 164172.
An example is given for the application of the COMSTAT algorithm for multimodal
factor analysis to EEG power spectra data. The COMSTAT algorithm enlarges Tucker's
threemode factor analysis to a multimodal one, and improves his algorithm by a least
squares solution. The EEG power spectral data from 65 healthy subjects with an occipital
rythm between 8 and 12 Hz were taken. For demonstration purposes we selected three
modes, which have been used by other authors: mode 1: 29 frequency classes, ln of
relative power, in delta f = 1.0Hz steps between 1 and 30 Hz; mode 2: 16 segments,
40 s each, during the two situational vigilance conditions reaction time (RT) and
resting (RS), and mode 3: 65 persons. The frequency mode could be described
sufficiently by five factors. The factorloading profiles were similar to those
described earlier in independent data. Thus, in the threemode model we obtained
results comparable to those of two models. On the basis of these data, we formulate
the hypothesis that in EEG data from subjects with occipital alphaEEG and for the
occipital lead, the most important Pvariance sources are the alpha power, the dominant
alpha frequency, and variance due to dynamic changes which can be caused by a shift
in vigilance or a dissociative shift in vigilance. The aim of applying our model in
EEG data is to describe variance sources in a multidimensional space. The ultimate
goal, however, is to arrive at procedures which allow us to keep more natural sources
of variance in our models, and not to exclude these variance sources by rigorous
selection of subjects.

Hiden, H. G., Willis, M. J., Tham, M. T., & Montague, G. A. (1999).
Nonlinear principal components analysis using genetic programming.
Computers & Chemical Engineering, 23, 413425.
Principal components analysis (PCA) is a standard statistical
technique, which is frequently employed in the analysis of large highly correlated
data sets. As it stands, PCA is a linear technique which can limit its relevance
to the nonlinear systems frequently encountered in the chemical process industries.
Several attempts to extend linear PCA to cover nonlinear data sets have been made,
and will be briefly reviewed in this paper. We propose a symbolically oriented
technique for nonlinear PCA, which is based on the genetic programming (GP)
paradigm. Its applicability will be demonstrated using two simple nonlinear
systems and data collected from an industrial distillation column.

Hildebrandt, L., & Klapper, D. (1994).
The analysis of threeway threemode data: A program based on
GAUSS. In F. Faulbaum (Ed.), Advances in Statistical Software, 4.
(pp.
527534). Stuttgart  Jena  New York: Gustav Fischer.
Four different methods are commonly proposed for the exploratory analysis
of threeway
threemode data (TUCKALS3, TUCKALS2, CANDECOMP/PARAFAC, PFCORE).
Available computer
programs are in general stand alone versions and do not permit an
interactive stepwise
analysis of the data. The program TREMODA (ThRee MOde Data Analysis),
written in GAUSS,
allows to combine the four methods and can handle large data sets on a
PC. The output is
available with a high performance graphics. After a short presentation of
the methodological
and mathematical background of these methods the application of TREMODA
to a problem of
consumer research is shown.

Hildebrandt, L., & Klapper, D. (2001).
The analysis of price competition between corporate brands. International Journal
of Research in Marketing, 18, 139159.
The methodology developed in this paper provides a means to analyze price
competition between corporate brands. Corporate brands are considered to be
produced and marketed by the same company. We establish price competition
from an array of crossprice elasticities across time, which provides the
necessary information to uncover the competitive interaction effects between
corporate brands. The crossprice elasticities across time form a threemode
threeway array. The Constrained TUCKALS3approach is developed and introduced
for the analysis of the complex array of crosselasticities. The approach
takes explicitly a priori information about the competitive reaction or pattern
of the marketing activities in a competitive market into account. This new
methodology will enable brand management to gain further and deeper insight
into the competitive interaction effects in the market. The Constrained
TUCKALS3model parameters provide the basis to investigate cannibalistic effects
between corporate brands and thus helps to improve the marketingmix,
especially the price management of these brands. Furthermore, the results
of the Constrained TUCKALS3approach can serve to determine idealized market
share estimates for certain a priori defined competitive conditions. The
applicability and the methodological advantages of this approach will be shown by an
empirical study on the price competition between two corporate brands. The
reported results provide managerial useful information for the development and
improvement of marketingmixstrategies of these corporate brands.

Hindmarch, P., Kavianpour, K., & Brereton, R.G. (1997).
Evaluation of parallel factor analysis for the
resolution of kinetic data by diodearray
highperformance liquid chromatography.
Analyst, 122, 871877.
The Parafac algorithm for factor analysis of three
or higher way datasets is summarised. A series of
simulations of kinetic profiles of twoway
diodearray HPLC data is described. A threephase
reaction system of reactant, intermediate and
product is used to illustrate the method, each
closely eluting and with similar spectra based on
experimental HPLC with diodearray detection of
chlorophyll degradation products. A kinetic
parameter is varied to change the relative
concentration of the intermediate in each series
of simulations. Several indices of quality of
reconstruction are introduced. It is concluded
that the number of factors used to model the data
is crucial to the quality of reconstruction. A
good approach is first to use fewer factors than
are expected, then increasing the number until
each elution profile shows a single maximum.

Hirschberg, N. (1980).
Individual differences in social judgment:
A
multivariate approach. In M. Fishbein (Ed.), Progress in
social psychology. Hillsdale, NJ: Erlbaum.
Contains an overview of multivariate methods to assess
individual differences, like MDS, pointofview analysis,
INDSCAL, T3, and preference analyses. One of the examples is a
detailed summary of Wiggins & Blackburn (1976).

Hoffman, E.L. & Tucker, L.R. (1964).
Threeway factor
analysis of a
multitraitmultimethod matrix. (Technical Report), Urbana: University
of Illinois,
Department of Psychology, and the Office of Naval Research.
H & T reanalyse a multitraitmultimethod (MM) matrix (with
communalities in the diagonal) of Fiske by using the T3 model.
Some special formulas were derived to obtain the method and
the trait correlation matrices and the core matrix as the
individual scores were not available. The factors of the
trait, method, and MM correlation matrices and the core
matrix were interpreted, and compared with Fiske's
results.

Hogden, J., Lofqvist, A., Gracco, V., Zlokarnik, I., & Rubin,
P., & Saltzman, E. (1996).
Accurate recovery of articulator positions from
acoustics: New conclusions based on human data.
Journal of the Acoustical Society of America, 4, 4.**
Vocal tract models are often used to study the
problem of mapping from the acoustic transfer
function to the vocal tract area function (inverse
mapping). Unfortunately, results based on vocal
tract models are strongly affected by the
assumptions underlying the models. In this study,
the mapping from acoustics (digitized speech
samples) to articulation (measurements of the
positions of receiver coils placed on the tongue,
jaw, and lips) is examined using human data from a
single speaker: Simultaneous acoustic and
articulator measurements made for voweltovowel
transitions, /g/ closures, and transitions into
and out of /g/ closures. Articulator positions
were measured using an emma system to track coils
placed on the lips, jaw, and tongue. Using these
data, lookup tables were created that allow
articulator positions to be estimated from
acoustic signals. On a data set not used for
making lookup tables, correlations between
estimated and actual coil positions of around 94%
and rootmeansquared errors around 2 mm are
common for coils on the tongue. An error source
evaluation shows that estimating articulator
positions from quantized acoustics gives
rootmeansquared errors that are typically less
than 1 mm greater than the errors that would be
obtained from quantizing the articulator positions
themselves. This study agrees with and extends
previous studies of human data by showing that for
the data studied, speech acoustics can be used to
accurately recover articulator positions. (c) 1996
acoustical society of america.

Hohn, M.E. (1979).
Principal components analysis of threeway
tables.
Journal of the International Association of Mathematical
Geology, 11, 611626.
A concise, straight forward description of T3 based on Tucker
(1966). Illustrated with geological data: 4 localities of
sample collection from the Early Jurassic scales of the Paris
Basin, 3 fractions of the organic extracts and 6 organic
elements or elemental ratio's. Data standardized by elements.
Varimax rotation for all components. Neat solutions. Uses a
'classical' score matrices based on combinationmodes for
interpretation.

Hohn, M.E. & Friberg, L.M. (1979).
A generalized principal
components
model in petrology. Lithos, 12, 317324.
An exposition of T3 is presented and its usefulness in
petrology is explained. The method is illustrated with 4
samples of Machas charnockites of which 9 cations and 1 ratio
were determined from 3 minerals. The data were standardized
per sample; factor scores on combinationmode components were
used. A second example comprises a set of data from the
Spuhler Peale Formation in Montana (9 cations, 4 minerals and
3 samples).

Holmes, S. (1989).
Using the bootstrap and the RV coefficient in the multivariate context.
In E. Diday (Ed.), Data analysis, learning symbolic and numeric
knowledge (pp. 119131). New York: Nova Science.
When bootstrapping in the multivariate context several difficulties arise, one of
these is the need to find an appropriate vector space where the different bootstraps
can be studied. One solution to this problem is provided through the analysis of
a cube of data as in Conjoint Analysis. This method uses the concepts of characteristic
operators and their inner product which will be defined in the first part of this
paper. Another possibility is to bootstrap a unidimensional statistic, namely the
RV coefficient, this provides a way of choosing the number of components to be
retained in PCA, without the indecision of graphical procedures and the distributional
assumptions in the usual parametric procedures.

Hong, S., & Harshman, R.A. (2000).
Shifted factor analysis, Part II: Algorithms and applications.
Unpublished manuscript, University of Western Ontario Psychology Department,
London, Canada.
The authors previously proposed a family of models that overcome the problem of
factor position shift in sequential data and used the information provided by
the shifts to make all the model parameters identifiable. Now they consider
methods of parameter estimation, and study some properties of the algorithms and
their underlying models using both errorfree and fallible position shifted
data. The Alternating Least Squares (ALS) approach is not fully suitable for
estimation because factor position shifts destroy multilinearity of the latent
structure. Therefore, and alternative "quasiALS" approach is developed, and
some of its practical and theoretical problems are dealt with. QuasiALS
algorithms for the twoway, threeway, and nway cases are described in detail.
A fourway chromatographic dataset previously analyzed by Bro et al. is
reanalyzed, and (two or) three out of four factors are recovered. The reason for
the incomplete success may be factor shape changes combined with the lack of
distinct shift patterns for two of the factors. SFA is compared with Parafac2
from both theoretical and practical points of view.

Hong, S., & Harshman, R. A. (2003a).
Shifted factor analysis, Part II: Algorithms.
Journal of Chemometrics, 17, 379388.
We previously proposed a family of models that deal with the problem of factor position shift in
sequential data. We conjectured that the added information provided by fitting the shifts would
make the model parameters identifiable, even for twoway data. We now derive methods of
parameter estimation and give the results of experiments with synthetic data. The alternating least
squares (ALS) approach is not fully suitable for estimation, because factor position shifts destroy the
multilinearity of the latent structure. Therefore an alternative ‘quasiALS’ approach is developed,
some of its practical and theoretical properties are dealt with and several versions of the quasiALS
algorithm are described in detail. These procedures are quite computationintensive, but analysis of
synthetic data demonstrates that the algorithms can recover shifting latent factor structure and, in the
situations tested, are robust against high error levels. The results of these experiments also provide
strong empirical support for our conjecture that the twoway shifted factor model has unique
solutions in at least some circumstances.

Hong, S., & Harshman, R. A. (2003b).
Shifted factor analysis  Part III: Nway generalization and application
Journal of Chemometrics, 17, 389399.
The 'quasiALS' algorithm for shifted factor estimation is generalized to threeway
and nway models. We consider the case in which mode A is the only shifted sequential
mode, mode B determines shifts, and modes above B simply reweight the factors.
The algorithm is studied using errorfree and fallible synthetic data. In addition,
a fourway chromatographic data set previously analyzed by Bro et al. (J. Chemometrics
1999; 13: 295309) is reanalyzed and (two or) three out of four factors are recovered.
The reason for the incomplete success may be factor shape changes combined with the
lack of distinct shift patterns for two of the factors. The shifted factor model
is compared with Parafac2 from both theoretical and practical points of view.

HongPing, X., JianHui, J. GuoLi, S., & RuQin, Y. (2002).
Estimation of the chemical rank for the threeway data: a principal norm vector orthogonal projection approach.
Computers & Chemesty, 26, 183190.
A new approach for estimating the chemical rank of the threeway array called the principal norm
vector orthogonal projection method has been proposed. The method is based on the fact that the chemical rank of
the threeway data array is equal to one of the column space of the unfolded matrix along the spectral or
chromatographic mode. A vector with maximum Frobenius norm is selected among all the column vectors of the
unfolded matrix as the principal norm vector (PNV). A transformation is conducted for the column vectors with an
orthogonal projection matrix formulated by PNV. The mathematical rank of the column space of the residual matrix
thus obtained should decrease by one. Such orthogonal projection is carried out repeatedly till the contribution
of chemical species to the signal data is all deleted. At this time the decrease of the mathematical rank would
equal that of the chemical rank, and the remaining residual subspace would entirely be due to the noise
contribution. The chemical rank can be estimated easily by using an Ftest. The method has been used successfully
to the simulated HPLCDAD type threeway data array and two real excitationemission fluorescence data sets of
amino acid mixtures and dye mixtures. The simulation with added relatively high level noise shows that the method
is robust in resisting the heteroscedastic noise. The proposed algorithm is simple and easy to program with quite
light computational burden.

Hoole, P. (1999).
On the lingual organization of the German vowel system. Journal of the
Acoustical Society of America, 106, 10201032.
A hybrid PARAFAC and principalcomponent model of tongue configuration in vowel
production is presented, using a corpus of German vowels in multiple consonant
contexts (fleshpoint data for seven speakers at two speech rates from
electromagnetic articulography). The PARAFAC approach is attractive for
explicitly separating speakerindependent and speakerdependent effects within a
parsimonious linear model. However, it proved impossible to derive a PARAFAC
solution of the complete dataset (estimated to require three factors) due to
complexities introduced by the consonant contexts. Accordingly, the final model
was derived in two stages. First, a twofactor PARAFAC model was extracted. This
succeeded; the result was treated as the basic vowel model. Second, the PARAFAC
model error was subjected to a separate principalcomponent analysis for each
subject. This revealed a further articulatory component mainly involving tongue
blade activity associated with the flanking consonants. However, the subject
specific details of the mapping from raw fleshpoint coordinates to this
component were too complex to be consistent with the PARAFAC framework. The
final model explained over 90% of the variance and gave a succinct and
physiologically plausible articulatory representation of the German vowel space.

Hopke, P.K., Paatero, P., Jia, H., Ross, R.T., & Harshman, R.A.
(1998).
Threeway (PARAFAC) factor analysis: examination
and comparison of alternative computational
methods as applied to illconditioned data.
Chemometrics and Intelligent Laboratory Systems, 43, 25
42.
Four different approaches to solving the
trilinear threeway factor analysis problem are
compared, and their performance with 'difficult'
(i.e., illconditioned) data is tested. These
approaches ape represented by four different
computer programs: one using a simple alternating
least squares (ALS) algorithm with only minimal
extrapolation (HLPARAFAC), one in which the ALS
is supplemented by a sophisticated extrapolation
to speed convergence (TPALS), one using a
nonlinear curve fitting method (PMF3), and one
using a noniterative closedform approximation
(DTDMR). The options provided by these programs
(e.g., with regard to missing values, weighted
least squares, nonnegativity and other
constraints) are compared, criteria for choosing
synthesized test data and a method for
synthesizing exponential test data are described.
A numerical index is introduced to characterize
the illconditioning of nway arrays (n > 2). Two
well characterized synthetic data sets serve as
'difficult' (illconditioned) test data.
Intercomparisons among HLPARAFAC, TPALS, DTDMR
and PMF3 were implemented with these test data.
Consequently, their limitations and strengths are
determined, in addition, these trilinear analysis
approaches are applied to a difficult set of
illconditioned real data: a set of fluorescence
spectroscopy measurements that characterize the
steadystate fluorescence of an amino acid in
aqueous solution. When converged, the results
produced by the three leastsquares techniques
(but not DTDMR) agree. However, there are large
differences in convergence speed when these
difficult problems are solved: TPALS is faster
than PARAFAC by a factor of ten, and PMF3 is
faster than TPALS, again by a factor of ten. The
program DTDMR is the fastest, bur it only solves
half of the problems.

Hopke, P. K. (2003).
The evolution of chemometrics.
Analytica Chimica Acta, 500, 365377.
mathematical methods to chemical problems to permit maximal collection
and extraction of useful information. The development of advanced chemical instruments
and processes has led to a need for advanced methods to design experiments, calibrate
instruments, and analyze the resulting data. For many years, there was the prevailing
view that if one needed fancy data analyses, then the experiment was not planned correctly,
but now it is recognized that most systems are multivariate in nature and univariate
approaches are unlikely to result in optimum solutions. At the same time, instruments
have evolved in complexity, computational capability has similarly advanced so that it
has been possible to develop and employ increasing complex and computationally intensive
methods. In this paper, the development of chemometrics as a subfield of chemistry and
particularly analytical chemistry will be presented with a view of the current
stateoftheart and the prospects for the future will be presented.

Houle, D., Mezey, J., & Galpern, P. (2002).
Interpretation of the results of common principal components analyses.
Evolution, 56, 433440.
Common principal components (CPC) analysis is a new tool for the comparison of phenotypic and genetic
variancecovariance matrices. CPC was developed as a method of data summarization, but frequently biologists would
like to use the method to detect analogous patterns of trait correlation in multiple populations or species. To investigate
the properties of CPC, we simulated data that reflect a set of causal factors. The CPC method performs as expected
from a statistical point of view, but often gives results that are contrary to biological intuition. In general, CPC tends
to underestimate the degree of structure that matrices share. Differences of trait variances and covariances due to a
difference in a single causal factor in two otherwise identically structured datasets often cause CPC to declare the
two datasets unrelated. Conversely, CPC could identify datasets as having the same structure when causal factors are
different. Reordering of vectors before analysis can aid in the detection of patterns. We urge caution in the biological
interpretation of CPC analysis results.

Huang, J., Wium, H., Qvist, K. B., & Esbensen, K. H. (2003a).
Multiway methods in image analsisrelationships and applications.
Chemometrics and Intelligent Laboratory Systems, 66, 141158.
This paper gives an overview of multiway methods in image analysis, termed Nway image analysis. Both weak and strong
multiway methods are applied in order to decompose and characterize image data, and obtain insight into their abilities to
capture and model the interpretable data structure. Multivariate Image Analysis (MIA) is a typical example based on weak
multiway methods like unfoldPCA/PLS. Strong multiway methods such as PARAFAC, Tucker3, NPLS are also introduced
and applied to image analysis in this work. Which method to use is problemdependent. Through macroscopic satellite images,
virtual fluorescence images and microscopic functional property image examples, the performance of each alternative method is
presented, as well as comparisons between weak and strong multiway models. It is demonstrated that efficient handling of
multiple images requires a clear a priori overview of the relationship between problem formulation and data array configuration.
Appropriate preprocessing techniques, such as 2D FFT and Wavelet transform, may also be needed in order to transform and
configure some special types of image data to forms specifically suited for multiway modeling. Application I shows the
possibility for application of strong multiway methods on multispectral images, otherwise conventionally analyzed by MIA.
By contrast, application II attempts to investigate the feasibility of applying MIA models on typical threeway data, normally
handled by the strong multiway methods and provides a new perspective of dealing with fluorescence spectra as images. In
application III, attempts have been made to predict rheological parameters from microscopic cheese images by multiway
methods. The present didactic exposition allows to draw some tentative first conclusions as to the dominant relationships
between strong and weak multiway data decompositions, their pros and cons and their relative merits.

Huang, J. R., Li, T. H., Chen, K., & Qi, Y. P. (2003b).
A preprocessing method applied in multidimension data  NOSC.
Chemical Journal of Chinese UniversitiesChinese, 24, 10091012.
Orthogonal signal correction (OSC) is a novel spectral preprocessing
method, which is based on the orthogonal projection. This preprocessing way removes from
the spectral vector or matrix(X) only the part that definitely is unrelated to Yvector
or Ymatrix. Due to the merits of OSC, much interesting is: focus on it, and several
modified algorithms have been presented to improve it. In this paper, we present a
modified multidimension method, named NOSC, which is applied in preprocessing
threedimension data. The threedimension data is the measurement of a drug mixture by
HPLCDAD, in which there are three components, that are enoxacin, norfloxacin, and
ciprofloxacin. Compared with, those only processed by NPLS, the multidimension data
preprocessed by NOSC have an optimal analytic result, and the covariance sauqre root is
0.33, 0.21 and 0.16 for enoxacin, norfloxacin, and ciprofloxacin respectively. NOSC was
recommended for processing multidimension data with NPLS, PRFA and GRAFA, etc..

Hubert, L., & Arabie, P. (1995).
Iteratieve projectiion strategies for the leastsquares fitting of tree structures
to proximity data.
British Journal of Mathematical & Statistical Psychology, 48, 281317.
A least squares optimization strategy is first reviewed and
applied to the task of fitting a given collection of symmetric
proximity values defined between the objects from one set by a
collection of reconstructed proximity values, satisfying a
fixed set of constraints, generated from some specified graph
theoretic structure, such as an ultrametric or an additive
tree, selected for representing the objects. Our method uses
iterative projection on to closed convex sets defined by the
collection of given constraints characterizing the structural
representation specified, and in contrast to least squares
optimization methods that impose such constraints through the
use of penalty functions, avoids the use of the latter, as well
as the implementation of any gradientbased optimization
technique. Secondly, just as various penaltyfunction/gradient
based optimization techniques have been turned into heuristic
search strategies for such particular structures of interest as
ultrametrics or additive trees, the use of iterative projection
is suggested as a general heuristic search strategy for
locating the best structural representations to impose in the
first place, where the collection of constraints used may vary
over the course of the optimization process. Our evaluation of
the expected results uses several data sets previously analysed
in the literature. Finally, several other applications of
iterative projection as a heuristic optimization technique are
discussed, including the consideration of data beyond that of a
single symmetric proximity matrix (for example, extensions to
twomode proximity matrices, i.e. between two distinct object
sets, and to threeway proximity matrices either symmetric or
not), and to representations based on sums of matrices where
each is constrained separately to conform to some desired
representational structure.

Hunt, L. A., & Basford, K. E. (1999).
Fitting a mixture model to threemode threeway data with categorical and continuous variables.
Journal of Classification, 16, 283296.
The mixture likelihood approach to clustering is most often used with twomode twoway
data to cluster one of the modes (e.g., the entities) into homogeneous groups on the basis of the other
mode (e.g., the attributes). In this case, the attributes can either be continuous or categorical. When
the data set consists of a threemode threeway array (e.g., attributes measured on entities in different
situations), an analogous procedure is needed to enable the clustering of the entities (i.e., one of the
modes) on the basis of both of the other modes simultaneously (i.e., the attributes measured in different
situations). In this paper, it is shown that the finite mixture approach to clustering can be extended
to analyze threemode threeway data where some of the attributes are continuous and some are categorical.
The methodology is illustrated by clustering the genotypes in a threeway soybean data set where various
attributes were measured on genotypes grown in several environments.

Hunt, L.A., & Basford, K.E. (2001).
Fitting a mixture model to threemode threeway data with missing information.
Journal of Classification, 18, 209226.
When the data consist of certain attributes measured on the same set of items
in different situations, they would be described as a threemode threeway array.
A mixture likelihood approach can be implemented to cluster the items (i.e.,
one of the modes) on the basis of both of the other modes simultaneously
(i.e, the attributes measured in different situations). In this paper, it
is shown that this approach can be extended to handle threemode threeway
arrays where some of the data values are missing at random in the sense of
Little and Rubin (1987). The methodology is illustrated by clustering the
genotypes in a threeway soybean data set where various attributes were measured
on genotypes grown in several environments.

Huo, R., Wehrens, R., Van Duynhoven, J., & Buydens, L. M. C. (2003).
Assessment of techniques for DOSY NMR data processing.
Analytica Chimica Acta, 490, 231251.
Diffusionordered spectroscopy (DOSY) NMR is based on a pulsefield
gradient spinecho NMR experiment, in which components experience diffusion. Consequently,
the signal of each component decays with different diffusion rates as the gradient
strength increases, constructing a bilinear NMR data set of a mixture. By calculating the
diffusion coefficient for each component, it is possible to obtain a twodimensional NMR
spectrum: one dimension is for the conventional chemical shift and the other for the
diffusion coefficient. The most interesting point is that this twodimensional NMR allows
noninvasive "chromatography" to obtain the pure spectrum for each component, providing a
possible alternative for LCNMR that is more expensive and timeconsuming. Potential
applications of DOSY NMR include identification of the components and impurities in
complex mixtures, such as body fluids, or reaction mixtures, and technical or commercial
products, e.g. comprising polymers or surfactants.
Data processing is the most important step to interpret DOSY NMR. Single channel methods
and multivariate methods have been proposed for the data processing but all of them have
difficulties when applied to realworld cases. The big challenge appears when dealing
with more complex samples, e.g. components with small differences in diffusion
coefficients, or severely overlapping in the chemical shift dimension. Two single channel
methods, including SPLMOD and continuous diffusion coefficient (CONTIN), and two
multivariate methods, called direct exponential curve resolution algorithm (DECRA) and
multivariate curve resolution (MCR), are critically evaluated by simulated and real DOSY
data sets. The assessments in this paper indicate the possible improvement of the DOSY
data processing by applying iterative principal component analysis (IPCA) followed by
MCRalternating least square (MCRALS).
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P.M. Kroonenberg
Education and Child Studies, Leiden University
Wassenaarseweg 52, 2333 AK Leiden, The Netherlands
Tel. *31715273446/5273434 (secr.); fax *31715273945
Email:
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First version : 12/02/1997;