Combinatorial typicality test in geometric data analysis

Abstract

In the present article, we present a method of statistical inference for Geometric Data Analysis (GDA) that is not based on random modeling but on a combinatorial framework, that highlights the role of permutation tests. The method is applicable to any Individuals×Variables table, with structuring factors on indi-viduals, and numerical variables possibly produced by a GDA method. We develop procedures dealing with the typicality of a subcloud with respect to an overall cloud of individuals, which is the generalization of the test–values to the multidimen-sional case in a combinatorial framework. We outline the geometric interpretation of the observed p–value and study a compatibility zone (confidence zone). We pro-pose exact and approximate solutions. The method is applied to data from medical research on Parkinson’s disease.