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Abstract: In the present work we have selected a collection of statistical andmathematical tools useful for the exploration of multivariate data and wepresent them in a form that is meant to be particularly accessible to aclassically trained mathematician. We give self contained and streamlinedintroductions to principal component analysis, multidimensional scaling andstatistical hypothesis testing. Within the presented mathematical framework wethen propose a general exploratory methodology for the investigation of realworld high dimensional datasets that builds on statistical and knowledgesupported visualizations. We exemplify the proposed methodology by applying itto several different genomewide DNA-microarray datasets. The exploratorymethodology should be seen as an embryo that can be expanded and developed inmany directions. As an example we point out some recent promising advances inthe theory for random matrices that, if further developed, potentially couldprovide practically useful and theoretically well founded estimations ofinformation content in dimension reducing visualizations. We hope that thepresent work can serve as an introduction to, and help to stimulate moreresearch within, the interesting and rapidly expanding field of dataexploration.



Author: Magnus Fontes

Source: https://arxiv.org/







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