CT GSI Geometric Sciences of Information
Prochaines manifestations

Accueil
The objective of this group is to bring together pure/applied mathematicians, physicist and engineers, with common interest for Geometric tools and their applications. It notably aim to organize conferences and to promote collaborative european and international research projects, and diffuse research results on the related domains. It aims to organise conferences, seminar, to promote collaborative local, european and international research project, and to diffuse research results in the the different related interested domains.
It emphasizes an active participation of engineers and researchers to develop emerging areas of collaborative research on “Information Geometry and Their Advanced Applications”. Current and ongoing uses of Information Geometry in applied mathematics are the following:
 Thermodynamic, statistical physic.
 Advanced Signal/Image/Video Processing, medical imaging
 Complex Data Modeling and Analysis, Topological data analysis, dimension reduction, clustering, pattern detection
 Information Ranking and Retrieval, Coding, Compression
 Cognitive Systems, Artificial intelligence, Neural networks, Optimal Control, biological modelisation and computational morphology, Speechsound recognition, natural language treatment.
 Quantum information, correlations, coding
 Statistics on Manifolds, Machine Learning, Manifold Learning
 etc...
which are also substantially relevant for industry and current social challenges.
Informations
JeanLouis Koszul passed away January 12^{th} 2018. This tribute is a scientific exegesis and admiration of JeanLouis Koszul’s works on homogeneous bounded domains that have appeared over time as elementary structures of Information Geometry. Koszul has introduced fundamental tools to characterize the geometry of sharp convex cones, as KoszulVinberg characteristic Function, Koszul Forms, and affine representation of Lie Algebra and Lie Group. The 2nd Koszul form is an extension of classical Fisher metric. Koszul theory of hessian structures and Koszul forms could be considered as main foundation and pillars of Information Geometry.
The community of “Geometric Science of Information” (GSI) has lost a mathematician of great value, who informed his views by the depth of his knowledge of the elementary structures of hessian geometry and bounded homogeneous domains. His modesty was inversely proportional to his talent. Professor Koszul built in over 60 years of mathematical career, in the silence of his passions, an immense work, which makes him one of the great mathematicians of the XX’s century, whose importance will only affirm with the time. In this troubled time and rapid transformation of society and science, the example of Professor Koszul must be regarded as a model for future generations, to avoid them the trap of fleeting glories and recognitions too fast acquired. The work of Professor Koszul is also a proof of fidelity to his masters and in the first place to Prof. Elie Cartan, who inspired him throughout his life. Henri Cartan writes on this subject “I do not forget the homage he paid to Elie Cartan’s work in Differential Geometry during the celebration, in Bucharest, in 1969, of the centenary of his birth. It is not a coincidence that this centenary was also celebrated in Grenoble the same year. As always, Koszul spoke with the discretion and tact that we know him, and that we love so much at home”.
We will conclude by quoting Jorge Luis Borges “both forgetfulness and memory are apt to be inventive” (Doctor Brodie’s report). Our generation and previous one have forgotten or misunderstood the depth of the work of JeanLouis Koszul and Elie Cartan on the study of bounded homogeneous domains. It is our responsibility to correct this omission, and to make it the new inspiration for the Geometric Science of Information. We will invite readers to listen to the last interview of JeanLouis Koszul for 50th birthday of Joseph Fourier Institute https://www.youtube.com/watch?v=AzK5K7Q05sw
Frédéric Barbaresco & Michel Boyom
References:
the fundamental theorem of information geometry, and illustrate some uses of these information
manifolds in information sciences. The exposition is selfcontained by concisely introducing the
necessary concepts of diﬀerential geometry with proofs omitted for brevity.
[32] TODHUNTER, I., A History of Mathematical Theory of Probability from the Time of Pascal to that of Laplace, Cambridge et Londres, Macmillan, 1865.
Organization
Président
Fr Barbaresco 
Bureau
Pierre Baudot  Frank Nielsen 
Links
Sub groups/sites
Events
2019

2018
2017


2015

2014

2013

Documents
Opening and closing sessions (chaired by Frédéric Barbaresco, Frank Nielsen, Silvère Bonnabel)
the fundamental theorem of information geometry, and illustrate some uses of these information
manifolds in information sciences. The exposition is selfcontained by concisely introducing the
necessary concepts of diﬀerential geometry with proofs omitted for brevity.
Bibliography
This Special Issue "Differential Geometrical Theor y of Statistics" collates selected invited and contributed talks presented during the conference GSI'15 on "Geometric Science of Information" which was held at the Ecole Polytechnique, ParisSaclay Campus, France, in October 2015 (Conference web site: http://www.see.asso.fr/gsi2015).
www.mdpi.com/journal/entropy/special_issues/entropystatistics
ISBN 9783038424246 (print) • ISBN 9783038424253 (electronic) 

Author: Frédéric Barbaresco, Ali MohammadDjafari
Publisher: MDPI (2015), Binding: Paperback, 542 pages


EditorinChief: Shinto Eguchi
CoEditors: N. Ay; F. Nielsen; J. Zhang


This book focuses on information geometry manifolds of structured data/information and their advanced applications featuring new and fruitful interactions between several branches of science: information science, mathematics and physics. It addresses interrelations between different mathematical domains like shape spaces, probability/optimization & algorithms on manifolds, relational and discrete metric spaces, computational and Hessian information geometry, algebraic/infinite dimensional/Banach information manifolds, divergence geometry, tensorvalued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audioprocessing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information. 

News
Topics of interests will include, but not be limited to, the Fisher–Rao metric, dual connections, divergence functions, entropy/crossentropy, Hessian geometry, exponential/mixture geodesics and projections, Qstatistics, quantum statistical inference and computation, computational information geometry, algebraic statistics, optimal transportation problems, deep neural networks, and related topics.
The authors and audience of the journal will be interdisciplinary, coming from mathematics, statistics, machine learning, statistical and quantum physics, information theory, control theory, neural computation, complex networks, cognitive science, and allied disciplines.