# Topological Information Data Analysis

@article{Baudot2019TopologicalID, title={Topological Information Data Analysis}, author={Pierre Baudot and M{\'o}nica Tapia and Daniel Bennequin and Jean-Marc Goaillard}, journal={Entropy}, year={2019}, volume={21} }

This paper presents methods that quantify the structure of statistical interactions within a given data set, and were applied in a previous article. It establishes new results on the k-multivariate mutual-information (Ik) inspired by the topological formulation of Information introduced in a serie of studies. In particular, we show that the vanishing of all Ik for 2≤k≤n of n random variables is equivalent to their statistical independence. Pursuing the work of Hu Kuo Ting and Te Sun Han, we…

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