Three-Mode Abstracts, Part W
With one can go to the index of
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|Wa | Wb |
Wc | Wd |
We | Wf |
Wg | Wh |
Wi | Wj |
Wk | Wl |
Wm | Wn |
Wo | Wp |
Wq | Wr |
Ws | Wt |
Wu | Wv |
Ww | Wx |
Wy | Wz |
Wainer, H., Gruvaeus, G., & Blair, M. (1974).
TREBIG: A 360/75 FORTRAN program for three-mode factor analysis
designed for big data sets. Behavioral Research Methods and
Instrumentation, 6, 53- 54.
A computational outline of Tucker's (1966) Method II is des-
Wainer, H., Gruvaeus, G., & Zill, N., II. (1973a).
Senatorial decision making: I. Determination of structure.
Behavioral Science, 18, 7-19.
A T3 analysis (Tucker's (1966), Method II) of US Senate roll
call voting was performed (8 issues, 6 years, 132 senators).
The entries in the data matrix were the point-biserial
correlations of senator's votes on a particular issue in a
particular year with the popularity of the roll calls in that
set. Varimax rotation. Introduction of the mixed-modal
matrices (MMM), which give the loadings of the variables of
one mode on the factors of an other. These MMMs turned out be
useful in interpreting the Senator factors. These factors were
validated using indices that purport to measure various facets
on senatorial voting behavior.
Wainer, H., Zill, N., II, & Gruvaeus, G. (1973b).
Senatorial decision making: II. Prediciton. Behavioral
Science, 18, 20-26.
Not a three-mode paper, but uses the results of Wainer, Gruvaeus &
Walsh, J.A. (1964).
An IBM 709 program for factor analyzing three-mode matrices.
Educational and Psychogical Measurement,
Describes a computer program for Tucker's (1966) Method I
which needs relative large amounts of storage.
Walsh, J.A., & Walsh, R. (1976).
A revised Fortran program for three-mode factor analysis.
Educational & Psychological Measurement,
A revision of the Walsh (1964) program. Main improvements are
organizational with respect to the program itself.
Walter, J. (1976).
Komplexe taaksituaties en hartsnelheidsvariabiliteit in de
psychiatrie. Technical Report, Stichting Centrum St.-Bavo,
Noordwijkerhout, The Netherlands.
During 15 conditions of varying mental stress hart frequences
were measured in three ways from 67 members of the staff and
patients of a psychiatric institution. T2 (as implemented by
Kroonenberg & De Leeuw, 1980) was applied to the data of all
subjects together and to the data of the staff and those of
the patients separately.
Wang, J.H., & Hopke, P.K. (2001).
Equation-oriented system: an efficient programming approach to solve multilinear
and polynomial equations by the conjugate gradient algorithm.
Chemometrics and Intelligent Laboratory Systems, 55, 13-22.
The factor analysis problem can be conceptualized as an expansion of polynomial
equations that are solvable using least-squares methods. The equation-oriented
system (EOS) is introduced as a method for solving polynomial equations using
a preconditioned conjugate gradient (CG) algorithm for the normal equations.
EOS is a fast, easy to program, low computer memory requirement method
for accomplishing this task. EOS can be used to solve multilinear and PARAFAC
problems. The practical aspects of implementing EOS in MATLAB are discussed.
Wang, J. H., Hopke, P. K., Hancewicz, T. M., & Zhang, S. L. L. (2003).
Application of modified alternating least squares regression to spectroscopic
Analytica Chimica Acta, 476, 93-109.
Analysis of synthetically generated and real Raman imaging
data sets were used to show the significance of modified alternating least
squares (MALS) regression as a superior method of analysis compared with
several other well established mathematical algorithms. The performance of
MALS was compared with that of ordinary alternating least squares regression
(ALS) and fast non-negative least squares (FNNLS) regression in applications
of spectroscopic image analysis and self-modeling curve resolution (SMCR).
The MALS algorithm is shown to be superior in terms of computational speed,
stability, and component resolution ability in the analysis of both real
and synthetic data sets. Results of the analysis show that MALS is significantl
y faster than FNNLS and generally produces equivalent or superior results.
This work also shows that MALS is superior to ordinary ALS in all performance
aspects. A detailed description of the regression equations is given along
with a discussion of the application of MALS to the general spectroscopic
image analysis problem.
Wang, K., Begleiter, H., & Porjesz, B. (2000).
Trilinear Modeling of Event-Related Potentials.
Brain Topography, 12, 263-271.
This paper describes a method for estimating a set of spatial components (brain maps) and temporal components (waveforms) of brain potentials.
These components play the role of bases of a coordinate system, in the sense that the brain potentials of any subject can be represented as
superpositions of these components. The representation is unique given the spatial and temporal components, and this decomposition is particularly
appealing for comparing the brain potentials of different subjects (say alcoholics and controls). It can also be used for single trial modeling, clinical
classification of patients, and data filtering. The method is based on the topographic component model (TCM, Mocks 1988) which models brain potentials
in a trilinear form. We extend the TCM in two aspects. First, the diagonal amplitude matrix is replaced by a general loading matrix based on
some neurophysiological considerations. Secondly, the number of spatial components and the number of temporal components can be different. The
spatial components and temporal components are obtained respectively by performing singular value decomposition (SVD). This method is illustrated
with visual P3 data.
Wang, Y.D., Borgen, O.S., & Kowalski, B.R. (1993).
Comments on the residual bilinearization method.
Journal of Chemometrics, 7, 439-445.
Through theoretical analysis and computer
simulation, this short communication comments on
the residual bilinearization (RBL) method and
compares it with non-bilinear rank annihilation
(NBRA) for the treatment of second-order
calibration with non-bilinear data. It is found
that these two methods are mathematically
equivalent but have different noise propagation
properties. The second-order advantage, namely
quantitation in the presence of unknown
interferences, can be carried over to non-bilinear
data only if there exists a net analyte rank (NAR)
for the analyte of interest.
Wang, Y.D., Borgen, O.S., Kowalski, B.R., Gu, M., & Turecek, F.
Advances in second-order calibration.
Journal of Chemometrics, 7, 117-130.
Several multivariate methods are now available for
the calibration of second-order or hyphenated
instruments (e.g. GC/MS). When applied to bilinear
data, it has been shown that calibration can be
performed in the presence of unknown interferences -
a significant advantage over first-order
calibration. In this paper, non-bilinear rank
annihilation (NBRA), a method which has the
potential of handling, second-order non-bilinear
data, is studied through theoretical analysis and
computer simulation. It is found that the
second-order advantage can be carried over to
non-bilinear data if a property defined as net
analyte rank (NAR) holds for the analyte of
interest. The net analyte signal (NAS) is defined
accordingly for second-order calibration and the
analogy to and difference from lower-order
calibration are discussed. With NAS, some
analytical figures of merit such as signal-to
noise ratio, selectivity, sensitivity and limit of
determination can be calculated for second order
calibration. An application to MS/MS data is also
Wang, Y.D., & Kowalski, B.R. (1993).
Standardization of second-order instruments.
Analytical Chemistry, 65, 1174-1180.
A method is presented to standardize
two-dimensional responses (e.g., GC/MS, LC/UV)
measured on multiple instruments or on a single
instrument under different operational conditions.
This second-order standardization method proceeds
by calculating two banded diagonal transformation
matrices, using the responses of a common standard
sample, to simultaneously correct for the response
channel shift and intensity variations in both
dimensions or orders. Different from first-order
standardization, these two transformation matrices
must be estimated from a set of simultaneous
nonlinear equations via the Gauss-Newton method.
The effects of noise and transformation matrix
bandwidth on the standardization performance are
studied through computer simulation. When tested
with experimental LC/UV data, the proposed
standardization method can reduce the variation
between two runs from 0.15-0.20 to 0.025-0.03 AU.
From both the computer simulation and experimental
data study, it is found that the design of the
standard sample is critical for the parameter
estimation and response standardization.
Wansbeek, T., & Buyze, J. (1981).
Multi-dimensional matrices and multiplicative interdependence
in regression analysis. (Research Report, BPA no. 13593-81-M1),
Voorburg, The Netherlands: Department for Statistical Methods.
A model for multiplicative interdependence in regression is introduced, and
interpreted as a way to describe the relation between two multi-dimensional
matrices. For several versions of this model, least-squared estimation and
identification is considered.
Wansbeek, T., & Verhees, J. (1989).
Models for multidimensional matrices in econometrics and
psychometrics. In R. Coppi & S. Bolasco (Eds.), Multiway
data analysis (pp. 543-552). Amsterdam: Elsevier.
The potential of notation and calculus introduced by
Kapteyn, Neudecker and Wansbeek (1986) is
used to formulate a number of models for multidimensional matrices, and to
analyse estimation of their parameters.
Wansbeek, T., & Verhees, J. (1990).
The algebra of multimode factor analysis. Linear Algebra and
its Applications, 127, 631-639.
Extending the work of Bentler and Lee, the multimode factor-analysis model is
introduced. First-order conditions are given for maximum-likelihood, weighted
least-squares, and unweighted least-squares estimation, using the calculus for
handling multidimensional matrices due to Kapteyn, Neudecker, and Wansbeek.
Also, the asymptotic distribution of the various estimators is
Warmerdam, M. (1990).
Affectieve reakties op reclame [Affective reactions to advertising]
. Master's Thesis. Department of Psychology, Leiden University.
Respondents; procedure; stimulusmaterial; questionnaire.
Three-mode principal components analysis; PROFIT-analyses; reliability
Scores; relationships between affetive reactions, advertising and
respondents: Three-way analysis; relationships between affective reactions,
advertising and communication effects: PROFIT-analyses; scale-constructions; the
predictive validity of the affective reaction profile.
Conclusions and discussion
Wasserman, S., & Iacobucci, D. (1991).
Statistical modeling of one-mode and 2-mode networks - Simultaneous analysis of graphs and bipartite graphs.
Britisch Journal of Mathematical & Statistical Psychology, 44, 13-43.
A bipartite graph, in which the nodes (or actors in a social network) are partitioned into two
sets, can be studied using recent statistical models for dyadic interactions. These models, which are longlinear
for the probabilities of dyadic choices or interactions, allow not only arcs or relationships to exist between
the sets but also within the sets. Thus, the methods described here are applicable not only to bipartite graphs,
consisting of arcs existing between nodes in different sets, but also to directed graphs that are defined within
the two sets of nodes. Data on both types of graphs can be analysed simultaneously.
A bipartite graph has an adjacency matrix (or sociomatrix) with two 'modes'. The set of nodes in the row mode
differs from the set of nodes in the column mode. For example, in marketing, one could study the dyadic relations
in a 'buyers-by-sellers' network. Generally, the relations observed in a one-mode network, which has a square
sociomatrix (row mode = column mode) are bidirectional-the actors indexing the columns may also 'relate to' the
actors indexing the rows. The relations observed in a two-mode network are generally unidirectional-the row
actors relate to or choose the column actors, but the column actors do not relate to the row actors. Referring
to our example, a buyer might pay a seller for some item, but a seller would not pay a buyer.
Statistical models for the separate analysis of these one-mode and two-mode matrices are extended in this paper
to the simultaneous analysis of both types of networks. A superordinate one-mode sociomatrix is created in which
the rows and columns consist of all actors (that is, all buyers and sellers). This larger matrix contains both
the one-mode matrices and the two-mode matrices. Multivariate analysis of unidirectional and bidirectional
relations in social networks and complex directed graphs becomes possible with this simultaneous consideration
of both types of matrices.
Watkins, D., & Hattie, J. (1985).
A longitudinal study of the approaches to learning of Australian
tertiary students. Human Learning, 4, 127-141.
A longitudinal study of 540 college students using the Approaches to Studying
Inventory provided little evidence that students' approaches to learning became
deeper during the course of their tertiary studies. This is despite many of the
most disillusioned of the original sample having withdrawn from their studies or
not responding to the follow-up survey. Contrary to predictions, the changes
that did occur were independent of the faculty and the age of the students. An
improved method of conducting a three mode factor analysis (McDonald, 1984) was
used to compare the factor analytic models over time. In this study covariances
were used with the means unconstrained over time and the residual covariance
matrices patterned with every submatrix diagonal, to allow for stable specific
components (See McDonald,
1984, for details).
Weesie, J., & Van Houwelingen, H. (1983).
GEPCAM users' manual: Generalized principal components
analysis with missing values. (Technical report), Utrecht: University
of Utrecht, Institute of Mathematical Statistics.
This very important report is the only full exposition of GEPCAM (Generalised
PCA with Missing values). An alternating least squares algorithm is described in
which not only the component matrices but also the slices of the core array are
estimated via regression. The standard approach in regression, using a binary
weight matrix is used to handle missing data. It contains the first explicit
statement about the three-way orthogonality of the core array. A possible
extension to robust regression is mentioned. The program described is no longer
available in that form, however. For an adapted version please contact the
three-mode company. Published applications include Spanjer, et al.; De Ligny, e.a.
Wei, W.Z., Zhu, W.H., & Yao, S.Z. (1992).
Application of ridge trace analysis in direct
Talanta, 39, 1629-1636.**
The use of ridge trace analysis for multivariate
calibration problems is described. Application is
made to the simultaneous quantitative
determination of components for several
pharmaceutical systems with unknown sample UV
spectra by the direct calibration technique. The
results indicate that with the help of ridge trace
analysis and ridge regression, the parameter k can
be selected to obtain estimation of the
colinearity of a system based on the stability of
relative concentration as a function of k. Much
information about the system to be analyzed can be
obtained, such as whether there is colinearity
among the variables, which measurement wavelength
range is suitable for performing quantitative
analysis, which components cannot be measured and
which components can only be measured as a sum,
and whether the quantitative model is correct.
Weinberg, S. L., & Menil, V. C. (1993).
The recovery of structure in linear and ordinal data - indscal versus alscal.
Multivariate Behavioral Research, 28, 215-233.
The ability of three-way INDSCAL and ALSCAL to recover true
structure in proximity data is examined in a Monte Carlo study using data
based on two-dimensional configurations. Extending earlier work in this area,
data were simulated to vary on four factors: number of subjects (15 and 30),
number of stimuli (12 and 20), amount of error (0.10 and 0.70), and type of
monotonic transformation (linear, square, logarithmic, general cubic, and
rank order). Recovery was measured using two indicators, corresponding to
the two sets of parameters estimated by these techniques: recovery of true
stimulus dimensions, and recovery of true subject weights. In this study,
INDSCAL outperformed metric and nonmetric versions of ALSCAL under all
conditions. Implications for practice and future research are discussed.
Wentzell, P. D., & Lohnes, M. T. (1999).
Maximum likelihood principal component analysis with correlated measurement errors:
theoretical and practical considerations.
Chemometrics and Intelligent Laboratory Systems, 45, 65-85.
Procedures to compensate for correlated measurement errors in multivariate data analysis are
described. These procedures are based on the method of maximum likelihood principal component analysis (MLPCA),
previously described in the literature. MLPCA is a decomposition method similar to conventional PCA, but it takes
into account measurement uncertainty in the decomposition process, placing less emphasis on measurements with large
variance. Although the original MLPCA algorithm can accommodate correlated measurement errors, two drawbacks have
limited its practical utility in these cases: (1) an inability to handle rank deficient error covariance matrices,
and (2) demanding memory and computational requirements. This paper describes two simplifications to the original
algorithm that apply when errors are correlated only within the rows of a data matrix and when all of these row
covariance matrices are equal. Simulated and experimental data for three-component mixtures are used to test the
new methods. It was found that inclusion of error covariance information via MLPCA always gave results which were
at least as good and normally better than PCA when the true error covariance matrix was available. However, when
the error covariance matrix is estimated from replicates, the relative performance depends on the quality of the
estimate and the degree of correlation. For experimental data consisting of mixtures of cobalt, chromium and nickel
ions, maximum likelihood principal components regression showed an improvement of up to 50% in the cross-validation
error when error covariance information was included.
Wentzell, P. D. Nair, S. S., & Guy, R. D. (2001).
Three-way analysis of fluorescence spectra of polycyclic aromatic hydrocarbons
with quenching by nitromethane.
Analytical Chemistry, 73, 1408-1415.
The application of trilinear decomposition (TLD) to the analysis of
fluorescence excitation-emission matrices of mixtures of polycyclic aromatic hydrocarbons
(PAHs) is described. The variables constituting the third-order tenser are excitation
wavelength, emission wavelength, and concentration of a fluorescence quencher
(nitromethane), The addition of a quencher to PAH mixtures selectively reduces the
fluorescence intensity of mixture components according to the Stern-Volmer equation.
TLD allows the three-way matrix to be decomposed to give unique solutions for the
excitation spectrum, emission spectrum, and quenching pro files for each component.
The availability of spectra and calculated Stern-Volmer constants can aid in the
identification of unknown components. Preprocessing of the data to correct for
Rayleigh/Raman scatter and primary absorption by the quencher is necessary. Both
three-component (anthracene, pyrene, l-methylpyrene) and four-component (fluoranthene,
anthracene, pyrene, 2,3-benzofluorene) synthetic mixtures are successfully resolved by
TLD using quencher concentrations up to 100 mM, Results are compared using both
alternating least-squares and direct trilinear decomposition algorithms. The
reproducibility of extracted Stern-Volmer constants is determined from replicate
experiments. To illustrate the application of TLD to a real sample, a chromatographic
cut from the analysis of a light gas oil sample was used. Analysis of the TLD extracted
spectra and quenching constants suggests the presence of three classes of polycyclic
aromatic hydrocarbons consistent with data from a second dimension of chromatography
and mass spectrometry.
Westerhuis, J.A., Kourti, T. & MacGregor, J.F. (1999).
Comparing alternative approaches for multivariate
statistical analysis of batch process data.
Journal of Chemometrics, 13, 397-413.
Batch process data can be arranged in a three-way
matrix (batch × variable × time). This paper
provides a critical discussion of various aspects
of the treatment of these multiway data. First,
several methods that have been proposed for
decomposing three-way data matrices are discussed
in the context of batch process data analysis and
monitoring. These methods are multiway principal
component analysis (MPCA)-also called
Tucker1-parallel factor analysis (PARAFAC) and
Tucker3. Secondly, different ways of unfolding,
mean centering and scaling the three-way matrix
are compared and discussed with respect to their
effects on the analysis of batch data. Finally,
the role of the time variable in batch process
data is considered and methods suggested to
predict the per cent completion of batch runs
with unequal duration are discussed.
Westerhuis, J. A., Gurden, S. P., & Smilde, A. K. (2000a).
Standardized Q-statistic for improved sensitivity in the monitoring of residuals in MSPC.
Journal of Chemometrics, 14, 335-349.
This paper presents the standardized Q-statistic for monitoring residuals
of latent variable models in multivariate statistical process control (MSPC). Before the
summation of the squared residuals, they are scaled according to their expected variation
obtained from normal operating conditions (NOC) data. Data from a simulated batch process
and from an industrial batch process are used to show that this scaling improves the
sensitivity of the Q-statistic considerably. The standardized Q-statistic is introduced
for the off-line monitoring of batch processes, but it can also be used for the monitoring
of continuous processes as well as for the on-line monitoring of batch processes.
Westerhuis, J. A., Gurden, S. P., & Smilde, A. K. (2000b).
Generalized contribution plots in multivariate statistical process monitoring.
Chemometrics and Intelligent Laboratory Systems, 51, 95-114.
This paper discusses contribution plots for both
the D-statistic and the Q-statistic in
multivariate statistical process control of batch
processes. Contributions of process variables to
the D-statistic are generalized to any type of
latent variable model with or without
orthogonality constraints. The calculation of
contributions to the Q-statistic is discussed.
Control limits for both types of contributions
are introduced to show the relative importance of
a contribution compared to the contributions of
the corresponding process variables in the
batches obtained under normal operating
conditions. The contributions are introduced for
off-line monitoring of batch processes, but can
easily be extended to on-line monitoring and to
continuous processes, as is shown in this paper.
Whitman, D. A., Seasholtz, M. B., Christian, G. D., Ruzicka, J., &
Kowalski, B. R. (1991).
Double-injection flow-injection analysis using multivariate calibration for
Analytical Chemistry, 63, 775-781.
A flow injection analysis (FIA) system is
presented in which the reagent and sample are
simultaneously injected for multicomponent
analysis. A simple eight-port valve is described
to perform the double injection. The method is
illustrated by the determination of nickel and
iron in a model plating bath solution. First-order
calibration methods including classical least
squares (CLS), principal components regression
(PCR), and partial least squares (PLS) are used to
analyze the complex time profiles that this method
provides. This study shows that very moderate
sampling rates and small calibration data sets can
be used with multivariate calibration techniques.
Whitman, B.Y. (1980).
The relationship of client personality variables and worker skill
variables in the production of client behavioral self-disclosure
in the therapeutic interview. Dissertation Abstracts
International, 41, 1779.
The Tucker model was used to analyze self-disclosure measures of trained workers
and comparable students. Only the measure space was deemed of interest. No
further details in abstract.
Wiberg, K., Andersson, M., Hagman, A., & Jacobsson, S. P. (2003).
Use of control sample for estimation of prediction error in multivariate determination
of lidocaine solutions with non-column chromatographic diode array UV spectroscopy.
Journal of Pharmaceutical and Biomedical Analysis, 33, 859-869.
The aim of this study was to investigate the ability of a control sample, of
known content and identity, to diagnose and correct errors in the predictions when the same
multivariate calibration model was used for analysis of new samples over time. A calibration
set consisting of 16 samples with a known content of lidocaine was analysed and two external
test sets, A and B, were used for the validation. Test set A contained 15 samples with
different concentrations of lidocaine and test set B contained three samples with different
lidocaine content, which were analysed six times in order to obtain a measure of
repeatability. The multivariate calibration was done with PLS regression on UV spectra
collected between 245 and 290 nm. A representative UV spectrum was exported from the
collected DAD files by two methods, average spectrum over the whole file and average
spectrum over the sample plug. Test set A was analysed further on another three occasions
together with a control sample. The results showed that the control sample could be used to
give a diagnosis and estimate of the prediction error. Moreover, the measured prediction
error of the control sample could also be used to correct the predictions, thereby reducing
the prediction error. Finally, some practical considerations regarding use of the proposed
DAD method with a control sample are presented. The procedure suggested could lead to an
efficient analytical approach where the same calibration model could be used over time
without recalibration, which may be attractive in industrial quality control or screening
analysis in pharmaceutical research.
Wiberg, K., Andersson, M., Hagman, A., & Jacobsson, S. P. (2004a).
Peak purity determination with principal component analysis of high-performance liquid
chromatography-diode array detection data.
Journal of Chromatography A, 1029, 13-20.
A method is proposed for the determination of chromatographic peak purity by
means of principal component analysis (PCA) of high-performance liquid chromatography with
diode array detection (HPLC-DAD) data. The method is exemplified with analysis of binary
mixtures of lidocaine and prilocaine with different levels of separation. Lidocaine and
prilocaine have very similar spectra and the chromatograms used had substantial peak overlap.
The samples analysed contained a constant amount of lidocaine and a minor amount of
prilocaine (0.02-2conc.%) and hence the focus was on determining the purity of the lidocaine
peak in the presence of much smaller levels of prilocaine. The peak purity determination was
made by examination of relative observation residuals, scores and loadings from the PCA
decomposition of DAD data over a chromatographic peak. As a reference method, the functions
for peak purity analysis in the chromatographic data system used (Chromeleon) were applied.
The PCA method showed good results at the same level as the detection limit of baseline-
separated prilocaine, outperforming the methods in Chromeleon by a factor of ten. There is
a discussion of the interpretation of the result, with some comparisons with evolving factor
analysis (EFA). The main advantage of the PCA method for determination of peak purity over
methods like EFA lies in its simplicity, short time of calculation and ease of use.
Wiberg, K., & Jacobsson, S. P. (2004b).
Parallel factor analysis of HPLC-DAD data for binary mixtures of lidocaine and
prilocaine with different levels of chromatographic seperation.
Analytica Chimica Acta, 514, 203-209.
A set of 17 samples containing a constant amount of lidocaine (667 muM) and
a decreasing amount of prilocaine (667-0.3 muM) was analysed by LC-DAD at three different
levels of separation, followed by parallel factor analysis (PARAFAC) of the data obtained.
In Case 1 no column was connected, the chromatographic resolution (R-s) therefore being
zero, while Cases 2 and 3 had partly separated peaks (R-s = 0.7 and 1.0). The results
showed that in Case 1, analysed without any separation, the PARAFAC decomposition with a
model consisting of two components gave a good estimate of the spectral and concentration
profiles of the two compounds. In Cases 2 and 3, the use of PARAFAC models with two
components resolved the underlying chromatographic, spectral and concentration profiles.
The loadings related to the concentration profile of prilocaine were used for regression
and prediction of the prilocaine content. The results showed that prediction of prilocaine
content was possible with satisfactory prediction (RMSEP & 0.01). This study shows that
PARAFAC is a powerful technique for resolving partly separated peaks into their pure
chromatographic, spectral and concentration profiles, even with completely overlapping
spectra and the absence or very low levels of separation.
Wicker, F.W. (1966).
A scaling study of synesthetic thinking. ETS Res. Bull.
RB-66-25); doctoral thesis, Princeton, New Jersey, 1966.
(Dissertation Abstracts International,
27 (6-B), 2173).
Two types of multivariate procedure - based, respectively, on similarity
and semantic judgments - were used in the attempt to map intersensory
associations between colors and tones. With both procedures it was possible to
investigate individual differences as well as group trends. For both procedures
stable associations were found for the group as a whole. The two methods agreed
considerably in the types of intersensory analogy indicated. Individual
differences were great, but the attempt to relate these differences to other
attributes of individuals met with little success. In particular, people who
reported synesthetic imagery did not differ systematically in their judgments
from those who did not. Two types of alignment were concluded to underlie the
intersensory relationships obtained. Bright colors were aligned with high
pitched tones, and loud tones were aligned with colors which contrasted sharply
with a gray background.
Wickremasinghe, W. N., & Johnson, D. E. (2002)
Testing subhypotheses and estimating sigma(2) in the nonreplicated three-way
multiplicative interaction model Communication in Statistics-simulation and Computation,
Standard statistical techniques do not provide methods for analyzing data from
nonreplicated factorial experiments. Such experiments occur for several reasons.
Many experimenters may prefer conducting experiments having a large number of factor
levels with no replications than conducting experiments with a few factor levels
with replications particularly in pilot studies. Such experiments may allow one to
identify factor combinations to be used in follow-up experiments. Another possibility
is when the experimenter thinks that an experiment is replicated when in fact it is
not. This occurs when a naive researcher believes that sub-samples are replicates when
in reality they are not. Nonreplicated two-way experiments have been extensively
studied. This paper discusses the analysis of nonreplicated three-way experiments.
In particular, estimation of sigma(2) is discussed and a test is derived for testing
whether three-factor interaction is absent in sub-areas of three-way data using a
nonreplicated three-way multiplicative interaction model with a single multiplicative
term. Approximate null distribution of the derived test statistic is studied using
Monte Carlo studies and results are illustrated through an example.
Widen, B., Andersson, S., Rao, G. Y., & Widen, M. (2002)
Population divergence of genetic (co)variance matrices in a subdivided plant species, Brassica cretica.
Journal of Evolutionary Biology, 15, 961-970.
The present study of Brassica cretica had two objectives. First, we compared estimates of
population structure (Q(st)) for seven phenotypic characters with the corresponding measures for allozyme
markers (F-st) to evaluate the supposition that genetic drift is a major determinant of the evolutionary
history of this species. Secondly, we compared the genetic (co) variance (G) matrices of five populations
to examine whether a long history of population isolation is associated with large, consistent differences
in the genetic (co) variance structure. Differences between estimates of Fst and Qst were too small to be
declared significant, indicating that stochastic processes have played a major role in the structuring of
quantitative variation in this species. Comparison of populations using the common principal component (CPC)
method rejected the hypothesis that the G matrices differed by a simple constant of proportionality: most of
the variation involved principal component structure rather than the eigenvalues. However, there was strong
evidence for proportionality in comparisons using the method of percentage reduction in mean-square error (MSE),
at least when characters with unusually high (co) variance estimates were included in the analyses. Although
the CPC and MSE methods provide different, but complementary, views of G matrix variation, we urge caution in
the use of proportionality as an indicator of whether genetic drift is responsible for divergence in the G matrix.
Wicker, F.W. (1968).
Mapping the intersensory regions of perceptual space. American
Journal of Psychology, 81, 178-188.
Presents a summary of a T3 analysis (25 semantic scales, 26
tones and colours, 59 subjects) which attempted to map inter-
sensory associations between colour vision and the perception
of tones on the basis of similarity and semantic judgements.
Details reported in Wicker (1966).
Wicker, F.W., Thorelli, I.M., Barron, III, W.L., & Ponder, M.R.
Relationships among affective and cognitive factors in humor.
Journal of Research in Personality, 15,
In a study to assess the relationships between various factors
in humor, 2 lists of 37 jokes were scored on 14 scales by 125
students. Tucker's methods were employed, and just the scale
spaces were compared.
Wienke, D., Van den Broek, & Buydens, L. (1995).
Identification of plastics among nonplastics in mixes wase by remote-sensing near-infrared spectroscopy.
2. Multivariate image rank analysis for rapid classification.
Analytical Chemistry, 67, 3760-3766..
Macroscopic samples of household waste were experimentally characterized by a sequence of images,
taken in four distinct wavelength regions by NIRIS. The obtained three-dimensional stack of images serves as
individual fingerprint for each sample, A rapid data compression, followed by an abstract factor rotation of
this stack into a spectroscopically meaningful intermediate four-element vector by a method called multivariate
image rank analysis (MIRA), finally provided a single number. This number serves as decision limit for
detection of plastics among nonplastic waste. The MIRA results are independent of sample size and sample
position within the camera image. They are sensitive to only the type of sample material, MIRA was also found
to be robust against image errors such as shadow or slight sample replacements between measurements.
Wienke, D., Van den Broek, W., Melssen, W., Buydens, L., Feldhoff, R., HuthFehre, T., Kantim, T.,
Winter, F., & Cammann, K. (1996).
Near-infrared imaging spectroscopy (NIRIS) and image rank analysis for remote identification of plastics
in mixed waste.
Fresenius Journal of Analytical Chemistry, 354, 823-828.
An infrared camera with focal plane InSb array detector has been applied to the characterization
of macroscopic samples of household waste over distances up to two meters. Per waste sample (singelized), a
sequence of images was taken at six optical wavelength ranges in the near infrared region (1100 nm - 2500 nm).
The obtained three-dimensional data stack served as individual fingerprint per sample. An abstract factor
rotation of this stack of six images into a spectroscopical meaningful intermediate six-element vector by
Multivariate Image Rank Analysis (MIRA) finally provided a decision limit for the discrimination of plastics
and nonplastics. A correct classification of better than 80% has been reached. The experimental NIRIS set-up
has been automated so far to allow an on-line identification of a real world waste sample within a few seconds.
Wiggins, N., & Blackburn, M.C. (1976).
Implicit theories of personality: an individual differences approach.
Multivariate Behavioral Research,
Twenty ratees were described on 20 bipolar personality trait
adjectives by 51 raters in an own-control design. Both close
friends and complete strangers were judged to assess possible
individual differences in personality perception. T3 was
applied and the rater dimensions were rotated using binorma
oblique rotation, the ratee and trait dimensions by varimax.
The resulting dimensions were correlated with a host of other
variables. Two subject factors were interpreted using the core
Wiggins, N., & Fishbein, M. (1969).
Dimensions of semantic space: A problem of individual differences.
In J.R. Snider & C.E. Osgood (Eds.), The semantic
differential technique: A book of readings (pp. 183-193).
Chicago: Aldine Press.
Despite the general findings of intra- and inter-cultural comparability of
semantic dimensions and their extension into the personality realm, a few
exceptions to the usual lack of individual differences in meaning structure have
been noted. The major purpose of this paper is to point out that individual
differences in semantic structure do indeed exist. The authors are arguing the
question of whether there is a single universal set of indicants for this
underlying framework within or across given population groupings. The
dimensionality of the subject space was investigated with the Tucker & Messick (1963) procedure.
Wilkinson, C., Schipper, M., & Leguijt, T. (2000).
Weighted analysis for missing values in generalized procrustes analysis.
Food Quality and Preverence, 11, 85-90.
Generalized Procrustes Analysis (GPA), a popular tool in
sensory science, is generally carried out on panelist data matrices averaged
over replicates. This paper addresses the problem of missing values arising
when panelists miss sessions. Because this does not necessarily result in missing
values in the final averaged data matrices, a weighted analysis is proposed with
weights set proportional to the number of replicates for each panelist product
combination. In a simulation study the weighted analysis gives a better match of
the rotated panelist matrices (a lower loss) than the unweighted analysis although
the resulting average configuration is not significantly closer to the true
configuration. The weighted analysis is a straightforward extension to GPA for
dealing with missing sessions and offers an improved basis on which to evaluate
Williams, R. P., Swinkels, D. A. J., & Maeder, M. (1992).
Identification and application of a prognostic vector for use in multivarate calibration.
Chemometrics and Intelligent Laboratory Systems, 15, 185-193.
Examination of the mathematical structures of
principal components regression and partial
least-squares regression has led to the
identification of a prognostic vector for both
techniques that contains information about the
contribution of each feature in a sample spectrum
to the quality of the sample. The properties and
use of the prognostic vector are demonstrated by a
practical application involving the estimation of
electrolytic manganese dioxide battery activity
from X-ray diffraction patterns. Results from the
study suggest that the prognostic vectors derived
from both PCR and PLS are similar, and provide
information that can ultimately be used to improve
Williams, W.T., & Stephenson, W. (1973).
The analysis of three-dimensional data (sites × species ×
in marine ecology. Journal of Experimental Marine Biological
Ecology, 11, 207-227.
A new numerical model is defined for the partition of three-dimensional data; it
is based on the analysis of variance, and is shown to be equivalent to an
unstandardized Euclidean distance preceded by a specified form of
standardization. The resulting quantity can be used as a dissimilarity measure
for classification; it will serve to define a two-way table and provides a
simple and elegant method for data-reduction requiring only a single subjective
decision. The concept of 'mean variance per comparison' is introduced, and it is
shown that such mean variances can be used to assess the relative importance of
the three dimensions; two important symmetry properties of mean variance are
established. The model is applied to a small real-life problem of 15 sites
× 56 species × 8 seasons, and is shown to produce ecologically
Wilson, B.E., Sanchez, E., & Kowalski, B.R. (1989).
An improved algorithm for the generalized rank annihilation method.
Journal of Chemometrics, 3, 493-498.
An improved algorithm for the generalized rank annihilation
method (GRAM) is presented. GRAM is a method for multicomponent
calibration using two- dimensional instruments, such as GC-MS. In
this paper an orthonormal base is first computed and used to
project the calibration and unkown sample response matrices into
a lower-dimensional subspace. The resulting generalized
eigenproblem is then solved using the QZ algorithm. The result of
these improvements is that GRAM is computationally more stable,
particularly in the case where the calibration sample contains
chemical constituents not present in the unknown sample and the
unknown contains constituents not present in the calibration (the
most general case).
Windig, W., Antalek, B., Robbins, M.J., Zumbulyadis, N., & Heckler, C.E.
Applications of the direct exponential curve resolution algorithm (DECRA) to
solid state nuclear magnetic resonance and mid-infrared spectra. Journal of
Chemometrics, 14, 213-227.
DECRA (direct exponential curve resolution algorithm) is a fast multivariate
method used to resolve spectral data with concentration profiles that are linear
combinations of exponential functions. DECRA has been previously applied to a
wide variety of spectroscopies. Results are presented in this paper for two new
application areas: solid state nuclear magnetic resonance spectra of polymorphic
crystal mixtures and mid-infrared spectroscopy of chemical reactions.
Furthermore, the paper will show the effect of the way the data set is split,
which is a part of the algorithm, on the results.
Windig, W., Antalek, B., Sorriero, L.J., Bijlsma, S., Louwerse, D.J., &
Smilde, A.K. (1999a).
Applications and new developments of the direct exponential curve resolution
algorithm (DECRA). Examples of spectra and magnetic resonance images. Journal
of Chemometrics, 13, 95-110.
Recently, a new multivariate analysis tool was
developed to resolve mixture data sets, where the
contributions ('concentrations') have an
exponential profile. The new approach is called
DECRA (direct exponential curve resolution
algorithm). DECRA is based on the generalized
rank annihilation method (GRAM). Examples will be
given of resolving nuclear magnetic resonance
spectra resulting from a diffusion experiment,
spectra in the ultraviolet/visible region of a
reaction and magnetic resonance images of the
Windig, W., & Antalek, B. (1999b).
Resolving nuclear magnetic resonance data of complex mixtures by three-way
methods: Examples of chemical solutions and the human brain.
Chemometrics and Intelligent Laboratory Systems, 46, 207-219.
Despite the use of hyphenated and/or
high-resolution instruments in analytical
spectroscopy, the resulting spectral data often
represent mixtures of several components. When no
reference data in the form of reference spectra
or concentration profiles are available,
self-modeling mixture analysis techniques can be
utilized to obtain the spectra of the pure
components and their concentration profiles,
There are many different algorithms to resolve
mixture spectra, and the mathematical procedures
involved are not always simple. This paper will
discuss some of the aspects and problems of
self-modeling mixture analysis, with the focus on
the three-way method and without going into the
mathematical details. Practical examples will be
shown of methods applied to nuclear magnetic
resonance data. The techniques discussed can also
be applied to magnetic resonance images and an
example will be shown of the human brain.
Windig, W., Hornak, J. P., & Antalek, B. (1998).
Multivariate image analysis of magnetic resonance images with the direct exponential curve resolution
algorithm (DECRA) - Part 1: Algorithm and model study.
Journal of Magnetic Resonance, 132, 298-306.
Antalek and Windig recently presented a fast method to resolve a series of NMR mixture spectra,
where the contribution of the components varies with a decaying exponential [B. Antalek and W. Windig, J. Am.
Chem. Sec. 118, 10,331-10,332 (1996); W. Windig and B. Antalek, Chemom. Intell. Lab. Syst. 37, 241-254(1997)].
The method was called DECRA (direct exponential curve resolution algorithm). In this paper DECRA will be
applied to two series of magnetic resonance images. The signal of one series is based upon T-2 relaxation, and
the other is based upon T-1 relaxation. In order to evaluate the technique, the magnetic resonance images of a
phantom where used. A transformation is introduced to enable the application of DECRA to a T-1 series of
magnetic resonance images. A separate paper in this issue will describe the application of the techniques to
magnetic resonance images of the human brain.
Winsberg, S., & Carroll, J.D. (1989).
A quasi-nonmetric method for multidimensional scaling of multiway
data via a restricted case of an extended INDSCAL model.
In R. Coppi & S. Bolasco (Eds.) Multiway data analysis,
(pp. 405-414). Amsterdam: North Holland.
An extended three-way Euclidean Multidimensional Scaling (MDS) model which
assumes both common and specific dimensions is described and contrasted with the
"standard" (three-way) INDSCAL MDS model. In this extended INDSCAL model the
N stimuli (or objects) are assumed to be characterized not only by
coordinates on P common dimensions, but in addition each stimulus is
assumed to have a dimension (or dimensions) specific to it alone. A numerical
procedure alternating a modified Newton-Raphson algorithm with one for fitting
an optimal spline (or linear function) is used to obtain maximum likelihood
estimates of the parameters. AIC and/or BIC statistics can be used to test
hypotheses about the number of common dimensions, and/or the existence of
specific (in addition to the P common) dimensions, and/or the necessity
for individual weights for the dimensions, and/or the necessity for nonlinear
transformations. Thus a wide variety of models can be compared statistically.
This approach is illustrated with applications to both artificial data and data
on judged similarity of adjectives relating to emotions as well as other real
Winsberg, S.L., & De Soete, G. (1993b).
A latent class approach to fitting the weighted Euclidean model,
CLASCAL. Psychometrika, 58,
A weighted Euclidean distance model for analyzing three-way
proximity data is proposed that incorporates a latent class
approach. In this latent class weighted Euclidean model, the
contribution to the distance function between two stimuli is per
dimension weighted identically by all subjects in the same latent
class. This model removes the rotational invariance of the
classical multidimensional scaling model retaining
psychologically meaningful dimensions, and drasticlly reduces the
number of parameters in the traditional INDSCAL model. The
probability density function for the data of a subject is posited
to be a finite mixture of spherical multivariate normal
densities. The maximum likelihood function is optimized by means
of an EM algorithm; a modified Fisher scoring method is used to
update the parameters in the M-step. A model selection strategy
is proposed and illustrated on both real and artificial data.
Wise, B.M., & Gallagher, N.B. (1996).
The process chemometrics approach to process
monitoring and fault detection.
Journal of Process Control, 6, 329-348.
Chemometrics, the application of mathematical and
statistical methods to the analysis of chemical
data, is finding ever widening applications in the
chemical process environment. This article reviews
the chemometrics approach to chemical process
monitoring and fault detection. These approaches
rely on the formation of a
mathematical/statistical model that is based on
historical process data. New process data can then
be compared with models of normal operation in
order to detect a change in the system. Typical
modelling approaches rely on principal components
analysis, partial least squares and a variety of
other chemometric methods. Applications where the
ordered nature of the data is taken into account
explicitly are also beginning to see use. This
article reviews the state-of-the-art of process
chemometrics and current trends in research and
Wise, B. M., Gallagher, N. B., Bulter, S. W., White, D. D., & Barna, G. G. (1999).
A comparison of principal component analysis, multiway principal component analysis, trilinear
decomposition and parallel factor analysis for fault detection in a semiconductor ETCH process.
Journal of Chemometrics, 13, 379-396.
Multivariate statistical process control (MSPC) tools have been developed for monitoring a Lam 9600 TCP metal
etcher at Texas Instruments. These tools are used to determine if the etch process is operating normally or if a
system fault has occurred. Application of these methods is complicated because the etch process data exhibit a
large amount of normal systematic variation. Variations due to faults of process concern can be relatively minor
in comparison. The Lam 9600 used in this study is equipped with several sensor systems including engineering
variables (e.g. pressure, gas flow rates and power), spatially resolved optical emission spectroscopy (OES) of the
plasma and a radio-frequency monitoring (RFM) system to monitor the power and phase relationships of the
plasma generator. A variety of analysis methods and data preprocessing techniques have been tested for their
sensitivity to specific system faults. These methods have been applied to data from each of the sensor systems
separately and in combination. The performance of the methods on a set of benchmark fault detection problems is
presented and the strengths and weaknesses of the methods are discussed, along with the relative advantages of
each of the sensor systems.
Wise, B. M., Gallagher, N. B., & Martin, E. B. (2001).
Application of PARAFAC2 to fault detection and diagnosis in semiconductor etch.
Journal of Chemometrics, 15, 285-298.
Monitoring and fault detection of batch chemical processes are complicated by stretching of the time axis,
resulting in batches of different length. This paper offers an approach to the unequal time axis problem using the
parallel factor analysis 2 (PARAFAC2) model. Unlike PARAFAC, the PARAFAC2 model does not assume
parallel proportional profiles, but only that the matrix of profiles preserves its ‘inner product structure’ from
sample to sample. PARAFAC2 also allows each matrix in the multiway array to have a different number of rows.
It has previously been demonstrated how the PARAFAC2 model can be used to model chromatographic data
with retention time shifts. Fault detection and, to a lesser extent, diagnosis in a semiconductor etch process are
considered in this paper. It is demonstrated that PARAFAC2 can effectively model batch process data from
semiconductor manufacture with unequal dimension in one of the orders, such as the unequal batch length
problem. It is shown that the PARAFAC2 model has approximately the same sensitivity to faults as other
competing methods, including principal component analysis (PCA), unfold PCA (often referred to as multiway
PCA), trilinear decomposition (TLD) and conventional PARAFAC. The advantage of PARAFAC2 is that it is
easier to apply than MPCA, TLD and PARAFAC, because unequal batch lengths can be handled directly rather
than through preprocessing methods. It also provides additional diagnostic information: the recovered batch
profiles. It is likely, however, that it is less sensitive to faults than conventional PARAFAC.
Wish, M., & Carroll, J.D. (1972).
Multi-dimensional scaling with differential weighting of
dimensions. In F.R. Hodson, D.G. Kendall & P. Tautu,
Mathematics in the Archeological and Historical Sciences
(pp. 150-167). Edinburgh: Edinburgh University Press.
Recently a new method was developed by Carroll and Chang (1970) based on a model
that related structures from different sources in a strong way, yet also permits
large differences among them. This method has been implemented in a computer
program called INDSCAL (for INdividual Differences SCALing). In this chapter,
the authors illustrate INDSCAL by applying it to data from three studies of
human perception. In the first and third illustrations they re-analyze data from
earlier experiments dealing respectively with 'psychological distances' among
colours and with confusions among acoustically degraded English consonants. The
data analyzed in the second example are from a recent study of individual
differences in perception of rhythm and accent in English speech (Wish 1969).
The authors conclude the paper with a discussion of potential applications of
INDSCAL in archeology.
Wish, M., & Carroll, J.D. (1982).
Multidimensional scaling and its applications. Handbook of
Statistics, 2, 317-345.
This review chapter gives an overview of both two-way (such as MDScal, KYST) and
three-way MDS (such as INDSCAL, IDIOSCAL, PARAFAC and CANDELINC) up to 1982. The
techniques are illustrated with the Rothkopf Morse-data, the societal-problems
data and Wish' perception-of-nations data.
Witzke, D.B. (1975).
Determining developmental changes in Holtzman inkblot technique
factors using three-mode factor analysis. Unpublished doctoral
thesis, University of Texas, Austin. ( Disserta
tion Abstracts International, 1975, 36 (5-A),
Wold, S., Geladi, P., Esbensen, K., & Öhman, J. (1987).
Multi-way principal components and PLS-analysis. Journal of
Chemometrics, 1, 41-56.
The Lohmöller-Wold decomposition of multi-way (three-way, four-way,
etc.)data arrays is combined with the non-linear partial least squares (NIPALS)
algorithms to provide multi-way solutions of principal components analysis (PCA)
and partial least squares modelling in latent variables (PLS). The decomposition
of a multi-way array is developed as the product of a score vector and a loading
array, where the score vectors have the same properties as those of ordinary
two-way PCA and PLS. In image analysis, the array would instead be decomposed as
the product of a loading vector and an image score matrix. The resulting methods
are equivalent to the method of unfolding a multi-way array to a two-way matrix
followed by ordinary PCA or PLS analysis. This automatically proves the
eigenvector and least squares properties of the multi-way PCA and PLS methods.
The methodology is presented; the algorithms are outlined and illustrated with a
small chemical example.
Wold, J. P., & Kvaal, K. (2000).
Mapping lipid oxidation in chicken meat by multispectral imaging of autofluorescence.
Applied Spectroscopy, 54, 900-909.
Multispectral imaging of autofluorescence was carried out to investigate the feasibility of
mapping the degree of lipid oxidation in ground chicken meat. Meat samples from both breast and thighs were
collected from 32 chickens, ground and freeze-stored for different time intervals. Sixteen samples were imaged
at the time, making up two sets of multispectral images, A and B. Lipid oxidation was measured by a method
using 2-thiobarbituric acid reactive substances (TBARS), and samples were in the range 0.15-3.23. Principal
component analysis was performed on image set A, and variation in score images of the two first components
corresponded well with lipid oxidation reference values. The multivariate image regression model based on image
set A was tested on set B. Pixel-wise prediction gave large individual errors, but averaging predicted values
within samples improved accuracy and resulted in a correlation of 0.98. Increasing the amount of spatial
variation (number of pixel vectors) in the regression models led to more robust models with lower prediction
errors. The technique has potential for nondestructive investigation of distribution and kinetics of lipid
oxidation in food.
Wold, J. P., Westad, F., & Heia, K. (2001).
Detection of parasites in cod fillets by using SIMCA classification in multispectral images in the
visible and NIR region.
Applied Spectroscopy, 55, 1025-1034.
The presence of parasitic nematodes in fillets of commercially important fish species has been
a serious quality problem for the fishing industry for several decades. Various approaches have been tried to
develop an efficient method to detect the parasites, but so far the only reasonable solution is manual
inspection and trimming of each fish fillet on a candling table. In this study we have investigated how
multispectral imaging in combination with SIMCA classification can be used for automatic detection of parasites.
The results indicate that the spectral characteristics of nematodes differ sufficiently from those of fish
flesh to allow one to obtain fairly good classifications. The method is able to detect parasites at depths down
to about 6 mm into the fish muscle. The method shows promising results, but further studies are required to
verify feasibility for the fish industry.
Wong, R. S. K. (2001).
Multidimensional association models - A multilinear approach.
Sociological Methods & Research, 30, 197-240.
This article develops several multidimensional multilinear
association models for sociologists and other social science researchers
to analyze the relationship between categorical variables in multiway
cross-classification tables. The proposed multilinear approach not only
provides satisfactory fit by conventional standards in the illustrative
examples but also offers better understanding of the complex relationship
between variables. This study highlights the relationship between two
alternative decompositions in the multilinear framework-the
PARAFAC/CANDECOMP and the Tucker 3-mode methods to decompose log-linear
parameters-as well as the relationship between the multilinear approach
and the log-multiplicative association models developed by Goodman and
others. In addition, the author discusses empirical strategies to
determine whether some or all cross-dimensional and other identifying
restrictions can be relaxed in certain restricted models and to account
for the proper degrees of freedom for these models.
Workman, J. (2002).
The state of mulivariate thinking for scientists in industry: 1980-2000.
Chemometrics and Intelligent Laboratory Systems, 60, 13-32.
Chemometrics has enjoyed tremendous success in the areas related to
calibration of spectrometers and spectroscopy-based measurements. These chemometric-based
spectrometers have been widely applied for process monitoring and quality assurance.
However, chemometrics has the potential to revolutionize the, very intellectual roots of
problem solving. Are there barriers to a more rapid proliferation of chemometric-based
thinking, particularly in industry? What are the potential effects of chemometrics technology
and the New Network Economy (NNE) working in concert? Who will be the winners in the race for
faster, better, cheaper systems and products? These questions are reviewed in terms of the
principles of the NNE and in the promise of chemometrics for industry. What then is the
state of multivariate thinking in industry? Several powerful principles are derived from an
evaluation of the NNE and chemometrics which could allow chemometrics to proliferate much more
rapidly as a key general problem-solving tool.
Wu, H. L., Shibukawa, M., & Oguma, K. (1997a).
Second-order calibration based on alternating trilinear decomposition: A comparison
with the traditional PARAFAC algorithm.
Analytical Sciences, 13, 53-58.
Quantitative analysis of p-chlorotoluene in the presence of o-
chlorotoluene as an interferent was attempted by using HPLC
with diode array detection and second-order calibration
methods. An emphasis was placed on a further comparison between
two methods, i.e., the traditional parallel factor analysis
(PARAFAC) and the alternating trilinear decomposition (ATLD)
methods. The following conclusions have been confirmed for the
calibration examples tested. PARAFAC does not always converge
to chemical meaningful solutions and its convergence rate is
slow for the. This seems to be owing to the deficiency of a
real trilinear sense in PARAFAC. The convergence rate of the
ATLD algorithm is extremely fast. The ATLD-based calibration
not only retains the advantage of second-order calibration but
can give satisfactory concentration predictions.
Wu, H.L., Feng, Y.Q., Shibukawa, M., & Oguma, K. (1997b).
Alternative algorithm for simultaneous
determinations of components poorly resolved by
liquid chromatography with multiwavelength
Analytical Sciences, 13, 99-108.
This paper describes an alternative algorithm for
a simultaneous multicomponent analysis with
three-mode three-dimensional array data generated
by liquid chromatography with diode array
detection (LC-DAD). Mainly based on a combination
of two-step Moore-Penrose pseudoinverse
computations based on a truncated singular value
decomposition (TSVD) and one-step direct bilinear
decomposition. It is modeled with a series of pure
or mixed reference samples and then used to
analyze several unknown samples. The algorithm was
evaluated by Monte-Carlo simulations of two
synthetic LC-DAD data sets with different noise
levels, and applied to the simultaneous
determination of chlorobenzene and toluene by
means of HPLC with a photodiode array detector.
The obtained results show that the proposed
algorithm is suitable for simultaneous
determinations of several components, of which the
chromatographic and absorption heavily overlap
each other, provided that their three-dimensional
data have trilinear properties.
Wu, H. L., Shibukawa, M., & Oguma, K. (1998).
An alternating trilinear decomposition algorithm with application to calibration
of HPLC-DAD for simultaneous determination of overlapped chlorinated aromatic hydrocarbons.
Journal of Chemometrics, 12, 1-26.
In this paper an alternating trilinear decomposition (ATLD) algorithm
that is an improvement of the traditional PARAFAC algorithm without any constraints is
described as an alternative algorithm for decomposition of three-way data arrays. It is
based on an alternating least squares principle and an improved iterative procedure that,
in a real trilinear sense, uses the Moore-Penrose generalized inverse with singular value
decomposition. Its performance is compared with that of the traditional PARAFAC algorithm
by a series of Monte Carlo simulations with different noise levels. It was found that the
ATLD algorithm has a capability to converge faster than the traditional PARAFAC algorithm.
The ATLD-based second-order calibration retains the second-order advantage that calibration
in the presence of unknown interferents can be performed to provide satisfactory concentration
estimates. Both algorithms have been used for simultaneous determination of overlapped
chlorinated aromatic hydrocarbons measured by means of a high-performance liquid chromatograph
with a diode array detector.
Wu, H. L., Yu, R. Q., & Oguma, K. (2001).
Trilinear component analysis in modern analytical chemistry.
Analytical Sciences, 17, i483-i486.
The purpose of this paper is to present an overview of the recent developments in three-mode three-way trilinear
component analysis with its applications in modern analytical chemistry. Emphasis is placed on the relatively new triadic
algorithms that provide new ways to decompose the three-way data arrays from HPLC/DAD or two-dimensional
excitation-emission fluorescence spectra, the rank estimation of three-way data as well as the uniqueness of the
presentations. It has been shown that the combination of three-way data analysis methods with fluorescence
spectroscopy or HPLC/DAD is a practical way to uniquely estimate the spectra and concentration of the analyte(s) of
interest in the presence of the unknown interferents.
Wu, H. L., Yu, R. Q., Shibukawa, M., & Oguma, K. (2000).
Second-order standard addition method based on alternating trilinear decomposition.
Analytical Sciences, 16, 217-220.
In this study, a second-order standard addition
method based on alternating trilinear
decomposition (ATLD-SOSAM) was developed. It was
applied to second-order HPLC-DAD data and
compared to methods employing direct trilinear
decomposition (DTLD) and PARAFAC. The results
show that ATLD-SOSAM is slightly superior to both
DTLD-SOSAM and PARAFAC-SOSAM.
Wu, W, Guo, Q., Jouan-Rimbaud, D., & Massart, D. L. (1999).
Using contrasts as data pretreatment method in pattern recognition of multivariate data.
Chemometrics and Intelligent Laboratory Systems, 45, 39-53.
A contrast method originally proposed by Spiegelman [C.H. Spiegelman, Calibration: a look at the mix
of theory, methods and experimental data, presented at Compana ’95, Wuerzburg, Germany.] is modified to pretreat
multivariate data for classification. Three NIR data sets and one pollution data set are used as examples. Our
results show that the contrast method greatly improves the ratios of between- to within-class variance. It is more
powerful than offset correction, SNV, first- and second-derivative methods in the cases studied. This conclusion
does not depend on the type of classifier used. Regularised discriminant analysis (RDA) and partial least squares
(PLS2) with univariate feature selection based on Fisher’s ratio were applied here. There is a risk that chance
correlations occur after the contrast pretreatment. The chance correlation decreases after first eliminating
un-informative variables using the modified Uninformative Variable Elimination (UVE)-PLS method.
Wu, W., Guo, Q., Massart, D.L., Boucon, C. & De Jong, S. (2003).
Structure preserving feature selection in PARAFAC using a genetic algorithm and
Chemometrics and Intelligent Laboratory Systems, 65, 83-95.
In this paper, a method is proposed to select subsets of variables in parallel
factor analysis (PARAFAC), such that information in the complete multi-way data
set is preserved as much as possible. The information retained is measured by means
of the percentage of consensus in Procrustes analysis. The best N-way subset is
obtained by applying a genetic algorithm (GA) to optimize the consensus between
the subset and the complete N-way data set in order to prevent exhaustive searching.
The method was applied to two industrial data sets: a three-way sensory data set
and a four-way gas chromatography (GC) data set. The results showed that the proposed
method successfully identified structure-bearing variables in both data sets and
that it led to better subsets of variables than feature selection based on loadings.
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Department of Educational
The Three-Mode Company |
Faculty of Social and Behavioural Sciences, Leiden University
The Three-Mode Company, Leiden, The Netherlands
E-mail: kroonenb at fsw.leidenuniv.nl
First version : 12/02/1997;