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 stateoftheart statistical high dimensional data structures analysis and algorithms to detect covarying patterns and clusters, multiscale data analysis.New release:
INFOTOPO version 1.2It 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 [1]. It is applicable on any set of empirical data that is data with several trialsrepetitionsessays (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 [1]. 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 jointentropy Hk and mutualinformations Ik at all degrees k=<n and for every ktuple, with a standard commercial personal computer (a laptop with processor Intel Core i74910MQ 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].
References
[1]Baudot, Tapia, Goaillard, Topological Information Data Analysis: PoincareShannon Machine and Statistical Physic of Finite Heterogeneous Systems. PDF
[2] M. Tapia, P. Baudot, M. Dufour, C. FormisanoTréziny, S. Temporal, M. Lasserre, J. Gabert, K. Kobayashi, JM. Goaillard . Information topology of gene expression profile in dopaminergic neurons PDF
[3] Baudot P., Bennequin D., The homological nature of entropy. Entropy, 2015, 17, 166; doi:10.3390. PDF
[3] Categories and Physics 2011. Classic and quantum Information topos.
[4] Information Topology: Statistical Physic of Complex Systems and Data Analysis Topological and geometrical structures of information, CIRM LuminyFrance. 271 sept VIDEOSLIDEThe 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 (MPIMIS) and Complex System Instititute ParisIledeFrance (ISCPIF) and Institut de Mathématiques de Jussieu  Paris Rive Gauche (IMJPRG)