Statistical and knowledge supported visualization of multivariate data

TL;DR

This paper introduces accessible statistical and mathematical tools for visualizing and exploring high-dimensional multivariate data, exemplified through genome-wide microarray datasets, aiming to stimulate further research in data exploration methods.

Contribution

It presents a comprehensive, accessible framework combining statistical tools and visualization techniques for multivariate data exploration, with applications to genomic datasets.

Findings

Applied methodology to genome-wide DNA microarray data

Proposed a general exploratory approach for high-dimensional datasets

Highlighted potential for future theoretical developments in data visualization

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.