Statistical and Knowledge Supported Visualization of Multivariate data
Author
Editor
- Åström Kalle
- Persson Lars-Erik
- Silvestrov Sergei D.
Summary, in English
In the present work we have selected a collection of statistical and mathematical tools useful for the exploration of multivariate data and we present them in a form that is meant to be particularly accessible to a classically trained mathematician.
We give self contained and streamlined introductions to principal component analysis, multidimensional scaling and statistical hypothesis testing. Within the presented mathematical framework we then propose a general exploratory methodology for the investigation of real world high dimensional datasets that builds on statistical and knowledge supported visualizations.
We exemplify the proposed methodology by applying it to several different genomewide DNA-microarray datasets. The exploratory methodology should be seen as an embryo that can be expanded and developed in many directions. As an example we point out some recent promising advances in the theory for random matrices that, if further developed, potentially could provide practically useful and theoretically well founded estimations of information content in dimension reducing visualizations. We hope that the present work can serve as an introduction to, and help to stimulate more research within, the interesting and rapidly expanding field of data exploration.
We give self contained and streamlined introductions to principal component analysis, multidimensional scaling and statistical hypothesis testing. Within the presented mathematical framework we then propose a general exploratory methodology for the investigation of real world high dimensional datasets that builds on statistical and knowledge supported visualizations.
We exemplify the proposed methodology by applying it to several different genomewide DNA-microarray datasets. The exploratory methodology should be seen as an embryo that can be expanded and developed in many directions. As an example we point out some recent promising advances in the theory for random matrices that, if further developed, potentially could provide practically useful and theoretically well founded estimations of information content in dimension reducing visualizations. We hope that the present work can serve as an introduction to, and help to stimulate more research within, the interesting and rapidly expanding field of data exploration.
Department/s
Publishing year
2012
Language
English
Pages
143-173
Publication/Series
Analysis for Science, Engineering and Beyond
Volume
Springer Proceedings in Mathematics Volume 6
Document type
Book chapter
Publisher
Springer
Topic
- Mathematics
Keywords
- Multidimensional scaling
- Principal component analysis
- Multivariate data
- Visualization
- Multiple hypothesis testing
Status
Published
ISBN/ISSN/Other
- ISSN: 2190-5622
- ISSN: 2190-5614
- ISBN: 978-3-642-20235-3 (print)
- ISBN: 978-3-642-20236-0 (online)