INFOTOPO - a Python Package for Information Topological Data Analysis
The INFOTOPO library is a generic open source suite of Python Programs (compatible with Python 3.4.x, on Linux, windows, or mac) for Information Topological Data Analysis. It is distrubuted freely under opensource GNU GPL V3 Licence and available on Github depository. The library offers state-of-the-art statistical high dimensional data structures analysis and algorithms to detect covarying patterns and clusters, multiscale data analysis.
INFOTOPO version 1.2
It computes all multivariate information functions: entropy, joint entropy between k random variables (Hk), mutual informations between k random variables (Ik), conditional entropies and mutual informations and provides their cohomological (and homotopy) visualisation in the form of information landscapes and information paths together with an approximation of the minimum information energy complex . It is applicable on any set of empirical data that is data with several trials-repetitions-essays (parameter m), and also allows to compute the undersampling regime, the degree k above which the sample size m is to small to provide good estimations of the information functions . The computational exploration is restricted to the simplicial sublattice of random variable (all the subsets of k=n random variables) and has hence a complexity in O(2^n). In this simplicial setting we can exhaustively estimate information functions on the simplicial information structure, that is joint-entropy Hk and mutual-informations Ik at all degrees k=<n and for every k-tuple, with a standard commercial personal computer (a laptop with processor Intel Core i7-4910MQ CPU @ 2.90GHz * up to k=n=21 in reasonable time (about 3 hours). The mathematical formalism can be found in [1,2,3,6], and its application as a neuroscience and data analysis method can be found in [1,4,5,6].
Baudot, Tapia, Goaillard, Topological Information Data Analysis: Poincare-Shannon Machine and Statistical Physic of Finite Heterogeneous Systems. PDF
 M. Tapia, P. Baudot, M. Dufour, C. Formisano-Tréziny, S. Temporal, M. Lasserre, J. Gabert, K. Kobayashi, JM. Goaillard . Information topology of gene expression profile in dopaminergic neurons PDF
 Baudot P., Bennequin D., The homological nature of entropy. Entropy, 2015, 17, 1-66; doi:10.3390. PDF
 Categories and Physics 2011. Classic and quantum Information topos.
 Information Topology: Statistical Physic of Complex Systems and Data Analysis -Topological and geometrical structures of information, CIRM LuminyFrance. 27-1 sept VIDEO-SLIDE
The INFOTOPO library is developed as part of the Channelomics project supported by the European Research Council, developped at UNIS Inserm 1072, and thanks previously to supports and hostings since 2007 of Max Planck Institute for Mathematic in the Sciences (MPI-MIS) and Complex System Instititute Paris-Ile-de-France (ISC-PIF) and Institut de Mathématiques de Jussieu - Paris Rive Gauche (IMJ-PRG)