Multiway methods in agriculture
- Multiway methods in chemistry
Barry Wise, Eigenvector Research, Inc., Wenatchee, WA, USA.
Rasmus Bro, Department of Food Science, University of Copenhagen, Denmark
The interesting impact of psychometrics in analytical chemistry will be described using
calibration as an example. Calibration is the task of quantifying the amount of analytes in a
sample and is an everyday task in analytical chemistry. The multiway methods developed in
psychometrics, however, have provided completely new and revolutionary tools for solving this
task. Multiway methods have also be applied to monitoring of batch chemical processes, which
are sensibly modeled by three-way methods were the modes are variables, batch time and batch
number. In monitoring applications, models are developed on good batches, then new batches
are compared with the models.
- Advances in signal processing and numerical computation
Lieven De Lathauwer, Electrical Engineering Department, Katholieke Universiteit Leuven, Belgium
In the past decades, tremendous progress has been made in the theory and application of
multiway methods. We give a short survey of developments in the understanding of basic
algebraic aspects and in the numerical computation of tensor decompositions. We focus on
applications in signal processing, paying special attention to techniques for signal
separation and factor analysis
- Iterative and closed form solutions for simplicity in T3 and multiway/multiset models
Jos ten Berge, Heymans Institute for Psychological Research, University of Groningen.
Henk Kiers,Heymans Institute for Psychological Research, University of Groningen
Marieke Timmerman, Heymans Institute for Psychological Research, University of Groningen
The transformational indeterminacy of Tucker3 solutions has given rise to the study of
transformations to simplicity of the component matrices and the core array. Early experiences
with Simplimax have shown that extreme simplicity (a vast majority of zero's) in the core can
be attained in a number of cases. This led to the search for closed-form solutions for the
transformations involved. Ten Berge will present an overview of such transformations.
In the first extensive study on Tucker models, Pieter Kroonenberg (1984) carefully and quite
quite extensively addressed the issues of algorithms and their quality, as well as
possibilities for rotation (or more generally transformation) of the solutions. His seminal
work has led to a host of further developments on algorithms and techniques for rotation to
Kiers will present an overview of a selection of such developments. Three-way models and
multi-set models have been fruitfully illustrated using multisubject, multivariate
longitudinal data. When facing such data in empirical practice, selecting a proper model can
be rather cumbersome. The appearance of the data offers little direction, because multi-set
data can be disguised as multiway data and vice versa.
Timmerman will present an overview of multiway and multiset models and discuss how to track
a suitable modeling approach in empirical practice.
- Multiway methods in psychology
Iven Van Mechelen, Faculty of Psychology and Education, Katholieke Universiteit Leuven, Belgium
Eva Ceulemans, Faculty of Psychology and Education, Katholieke Universiteit Leuven, Belgium
We illustrate the use of three-way methods in psychology with a brief outline of four
applications: (1) a PARAFAC analysis of real-valued three-way three-mode (family by scale by
judgment condition) data on behaviors of parents towards their children (and vice versa) from
developmental psychology (Kroonenberg, Harshman & Murakami, 2009), (2) a Boolean PARAFAC
(INDCLAS) analysis of binary three-way three-mode (person by frustrating situation by hostile
behavior) data from personality psychology (Vansteelandt & Van Mechelen, 1998), (3) a
constrained linked-mode three-mode/two-mode partitioning (CLASSI) analysis of a binary
three-way three-mode (person by situation by appraisal) data block coupled with a binary
two-way two-mode (person by situation) data block on experienced anger from the psychology of
emotions (Ceulemans, Kuppens, & Van Mechelen, 2012), and (4) an INDSCAL analysis of
real-valued three-way two-mode (person by affective state by affective state) data on
correlations between affective states across voxels (with regard to neural activity) from
neuropsychology (Baucom et al., 2012). For each application, we briefly summarize the
research context and research question, the type of data, the type of model, and the gist of
the modeling output. We conclude with a short discussion of threats and opportunities for the
application of three-way methods in psychology.
Multiway analysis in metabolomics
Kaye Basford, School of Land and Food Sciences, University of Queensland, Australia
Having introduced Pieter Kroonenberg to genotype × environment × attribute data from plant
breeding trials more than twenty-five years ago, I reflect on his contribution to three-way
three-mode analytical methods in agriculture. Not only has Pieter provided theoretical
developments, he has analysed and interpreted data from plant improvement programs on cotton,
maize, groundnut, common bean, adzuki bean and wheat. In this address, I comment on some
common themes and my perception of how the focus has changed over time. I conclude with
extracts from a paper which aimed to develop a detailed understanding of the heritable
variation in the wheat genome and to directly translate this knowledge into gains in wheat
breeding. This was achieved via a Wheat Phenome Atlas (a collection of diagrammatic
representations of chromosome regions that affect trait inheritance) and three-way principal
component analysis of the genotype marker-trait association profiles.
Multiway data analysis in Japan
Age Smilde, Swammerdam Institute for Life Sciences and Amsterdam Medical Center, University of Amsterdam
Department of Food Science and Faculty of Health & Medical Sciences, University of Copenhagen, Denmark.
Metabolomics is the new kid on the block in functional genomics and relies heavily on
advanced instrumental techniques such as GC-MS, NMR and LC-MS. It can be used to probe
metabolism in cellular organisms, to analyze metabolites in body-fluid samples, plant
extracts and food to name a few examples. The purpose of these measurements is dictated by
the biological question underlying the study. Multiway analysis has proven to be a very
useful tool in several stages of analyzing metabolomics data. An overview of these
applications will be given and some examples will be worked out in more detail.
Borrowing strength from multiway thinking by attacking two-way problems with multiway methods
Takashi Murakami, Department of Sociology, Chukyo University, Nagoya, Japan
Hisao Miyano, National Center for University Entrance Examinations, Tokyo, Japan
There were some potential demands for methods of multiway data analysis in 70's and 80's
of the previous century in Japan. Models such as TUCKER3, PARAFAC, and INDSCAL were
appreciated with considerable enthusiasm by groups of research workers, and a lot of
application works were done in several laboratories. We will demonstrate some of them with
Some researchers have made a few innovations in the methodology of multiway data analysis,
for example, improvements of the algorithms, proposals of ways of transformations of output
to facilitate interpretations. Also in the context of multidimensional scaling, a couple of
the scaling methods for analysing asymmetric similarity data have been developed. We will
explain some of them briefly.
Finally, we will introduce some unique works for multiway categorical data analysis in Japan.
Although they were not known well even in Japan, and have not yet been in practical use, they
seem to give some useful intuitions of complex interactions in a higher order cross
Prof. Pieter Kroonenberg has visited and stayed in Japan many times, and has been interested
in most of works that we will demonstrate in this presentation. He has been interacting with
many Japanese psychometricians in a positive way, collaborating with some of them.
Willem Heiser, Mathematical Institute, Leiden University
Jacqueline Meulman, Mathematical Institute, Leiden University
Multiway data analysis has been a source of inspiration for us not only because it
obviously is valuable for the analysis of multiway data, but even more so because multiway
thinking can be a fruitful strategy for solving certain problems in two-way data analysis. We
give some examples of this strategy from our own work, which is often concerned with multiple
dissimilarity- or attribute relations among individuals or between categories and
individuals. In an attempt to predict what lies ahead for multiway data analysis, we will
point out some recent work in the areas of relational learning and preference learning that
is becoming increasingly important, for example, in social network modeling, the semantic
web, and comorbidity networks of psychiatric symptoms. Here we see the borrowing strength
strategy in action for the prediction of links between individuals and categories, with new
alternatives of well-known three-way models.