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Statistical and Knowledge Supported Visualization of Multivariate Data

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Analysis for Science, Engineering and Beyond

Part of the book series: Springer Proceedings in Mathematics ((PROM,volume 6))

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Abstract

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.

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Acknowledgements

I first of all would like to thank Gunnar Sparr for being a role model for me, and many other young mathematicians, of a pure mathematician that evolved into contributing serious applied work. Gunnar’s help, support and general encouragement have been very important during my own development within the field of mathematical modeling. I sincerely thank Johan Råde for helping me to learn almost everything I know about data exploration. Without him the here presented work would truly not have been possible. Applied work is best done in collaboration and I am blessed with Thoas Fioretos as my long term collaborator within the field of molecular biology. I am grateful for what he has tried to teach me and I hope he is willing to continue to try. Finally I thank Charlotte Soneson for reading this work and, as always, giving very valuable feed-back.

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Authors and Affiliations

  1. Centre for Mathematical Sciences, Lund University, 118, SE-22100, Lund, Sweden

    Magnus Fontes

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  1. Magnus Fontes
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Correspondence to Magnus Fontes .

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Editors and Affiliations

  1. Centre for Mathematical Sciences, Lund University, Sölvegatan 18, Lund, 221 00, Sweden

    Kalle Åström

  2. Dept. Mathematics, Luleå University of Technology, Luleå, 971 87, Sweden

    Lars-Erik Persson

  3. Centre for Mathematical Sciences, Lund University, Lund, Sweden

    Sergei D. Silvestrov

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Fontes, M. (2012). Statistical and Knowledge Supported Visualization of Multivariate Data. In: Åström, K., Persson, LE., Silvestrov, S. (eds) Analysis for Science, Engineering and Beyond. Springer Proceedings in Mathematics, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20236-0_6

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