Geometric Science Of Information

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Geometric Science of Information

Author : Frank Nielsen
Publisher : Springer Nature
ISBN 13 : 3030802094
Total Pages : 929 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer Nature. This book was released on 2021-07-14 with total page 929 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.

Geometric Science of Information

Author : Frank Nielsen
Publisher : Springer
ISBN 13 : 331925040X
Total Pages : 790 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2015-10-24 with total page 790 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Second International Conference on Geometric Science of Information, GSI 2015, held in Palaiseau, France, in October 2015. The 80 full papers presented were carefully reviewed and selected from 110 submissions and are organized into the following thematic sessions: Dimension reduction on Riemannian manifolds; optimal transport; optimal transport and applications in imagery/statistics; shape space and diffeomorphic mappings; random geometry/homology; Hessian information geometry; topological forms and Information; information geometry optimization; information geometry in image analysis; divergence geometry; optimization on manifold; Lie groups and geometric mechanics/thermodynamics; computational information geometry; Lie groups: novel statistical and computational frontiers; geometry of time series and linear dynamical systems; and Bayesian and information geometry for inverse problems.

Geometric Science of Information

Author : Frank Nielsen
Publisher : Springer Nature
ISBN 13 : 3031382714
Total Pages : 641 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer Nature. This book was released on 2023-07-31 with total page 641 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.

Geometric Science of Information

Author : Frank Nielsen
Publisher : Springer
ISBN 13 : 3030269809
Total Pages : 764 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2019-08-19 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications.

Geometric Science of Information

Author : Frank Nielsen
Publisher : Springer Nature
ISBN 13 : 3031382994
Total Pages : 670 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer Nature. This book was released on 2023-07-31 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.

Geometric Science of Information

Author : Frank Nielsen
Publisher : Springer
ISBN 13 : 3319684450
Total Pages : 877 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2017-10-30 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the Third International Conference on Geometric Science of Information, GSI 2017, held in Paris, France, in November 2017. The 101 full papers presented were carefully reviewed and selected from 113 submissions and are organized into the following subjects: statistics on non-linear data; shape space; optimal transport and applications: image processing; optimal transport and applications: signal processing; statistical manifold and hessian information geometry; monotone embedding in information geometry; information structure in neuroscience; geometric robotics and tracking; geometric mechanics and robotics; stochastic geometric mechanics and Lie group thermodynamics; probability on Riemannian manifolds; divergence geometry; non-parametric information geometry; optimization on manifold; computational information geometry; probability density estimation; session geometry of tensor-valued data; geodesic methods with constraints; applications of distance geometry.

Geometric Science of Information

Author : Frank Nielsen
Publisher : Springer
ISBN 13 : 3642400205
Total Pages : 879 pages
Book Rating : 4.6/5 (424 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2013-08-19 with total page 879 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the First International Conference on Geometric Science of Information, GSI 2013, held in Paris, France, in August 2013. The nearly 100 papers presented were carefully reviewed and selected from numerous submissions and are organized into the following thematic sessions: Geometric Statistics on Manifolds and Lie Groups, Deformations in Shape Spaces, Differential Geometry in Signal Processing, Relational Metric, Discrete Metric Spaces, Computational Information Geometry, Hessian Information Geometry I and II, Computational Aspects of Information Geometry in Statistics, Optimization on Matrix Manifolds, Optimal Transport Theory, Probability on Manifolds, Divergence Geometry and Ancillarity, Entropic Geometry, Tensor-Valued Mathematical Morphology, Machine/Manifold/Topology Learning, Geometry of Audio Processing, Geometry of Inverse Problems, Algebraic/Infinite dimensional/Banach Information Manifolds, Information Geometry Manifolds, and Algorithms on Manifolds.

Information Geometry and Its Applications

Author : Shun-ichi Amari
Publisher : Springer
ISBN 13 : 4431559787
Total Pages : 378 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Information Geometry and Its Applications by : Shun-ichi Amari

Download or read book Information Geometry and Its Applications written by Shun-ichi Amari and published by Springer. This book was released on 2016-02-02 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first comprehensive book on information geometry, written by the founder of the field. It begins with an elementary introduction to dualistic geometry and proceeds to a wide range of applications, covering information science, engineering, and neuroscience. It consists of four parts, which on the whole can be read independently. A manifold with a divergence function is first introduced, leading directly to dualistic structure, the heart of information geometry. This part (Part I) can be apprehended without any knowledge of differential geometry. An intuitive explanation of modern differential geometry then follows in Part II, although the book is for the most part understandable without modern differential geometry. Information geometry of statistical inference, including time series analysis and semiparametric estimation (the Neyman–Scott problem), is demonstrated concisely in Part III. Applications addressed in Part IV include hot current topics in machine learning, signal processing, optimization, and neural networks. The book is interdisciplinary, connecting mathematics, information sciences, physics, and neurosciences, inviting readers to a new world of information and geometry. This book is highly recommended to graduate students and researchers who seek new mathematical methods and tools useful in their own fields.

Geometric Structures of Information

Author : Frank Nielsen
Publisher : Springer
ISBN 13 : 3030025209
Total Pages : 392 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Geometric Structures of Information by : Frank Nielsen

Download or read book Geometric Structures of Information written by Frank Nielsen and published by Springer. This book was released on 2018-11-19 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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, tensor-valued morphology, optimal transport theory, manifold & topology learning, and applications like geometries of audio-processing, inverse problems and signal processing. The book collects the most important contributions to the conference GSI’2017 – Geometric Science of Information.

Geometric Theory of Information

Author : Frank Nielsen
Publisher : Springer Science & Business Media
ISBN 13 : 3319053175
Total Pages : 392 pages
Book Rating : 4.3/5 (19 download)

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Book Synopsis Geometric Theory of Information by : Frank Nielsen

Download or read book Geometric Theory of Information written by Frank Nielsen and published by Springer Science & Business Media. This book was released on 2014-05-08 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together geometric tools and their applications for Information analysis. It collects current and many uses of in the interdisciplinary fields of Information Geometry Manifolds in Advanced Signal, Image & Video Processing, Complex Data Modeling and Analysis, Information Ranking and Retrieval, Coding, Cognitive Systems, Optimal Control, Statistics on Manifolds, Machine Learning, Speech/sound recognition and natural language treatment which are also substantially relevant for the industry.

Geometric Structures of Statistical Physics, Information Geometry, and Learning

Author : Frédéric Barbaresco
Publisher : Springer Nature
ISBN 13 : 3030779572
Total Pages : 466 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Geometric Structures of Statistical Physics, Information Geometry, and Learning by : Frédéric Barbaresco

Download or read book Geometric Structures of Statistical Physics, Information Geometry, and Learning written by Frédéric Barbaresco and published by Springer Nature. This book was released on 2021-06-27 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Machine learning and artificial intelligence increasingly use methodological tools rooted in statistical physics. Conversely, limitations and pitfalls encountered in AI question the very foundations of statistical physics. This interplay between AI and statistical physics has been attested since the birth of AI, and principles underpinning statistical physics can shed new light on the conceptual basis of AI. During the last fifty years, statistical physics has been investigated through new geometric structures allowing covariant formalization of the thermodynamics. Inference methods in machine learning have begun to adapt these new geometric structures to process data in more abstract representation spaces. This volume collects selected contributions on the interplay of statistical physics and artificial intelligence. The aim is to provide a constructive dialogue around a common foundation to allow the establishment of new principles and laws governing these two disciplines in a unified manner. The contributions were presented at the workshop on the Joint Structures and Common Foundation of Statistical Physics, Information Geometry and Inference for Learning which was held in Les Houches in July 2020. The various theoretical approaches are discussed in the context of potential applications in cognitive systems, machine learning, signal processing.

Geometric Science of Information

Author : Frank Nielsen
Publisher : Springer
ISBN 13 : 9783031382987
Total Pages : 0 pages
Book Rating : 4.3/5 (829 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by Springer. This book was released on 2023-08-30 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 6th International Conference on Geometric Science of Information, GSI 2023, held in St. Malo, France, during August 30-September 1, 2023. The 125 full papers presented in this volume were carefully reviewed and selected from 161 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: geometry and machine learning; divergences and computational information geometry; statistics, topology and shape spaces; geometry and mechanics; geometry, learning dynamics and thermodynamics; quantum information geometry; geometry and biological structures; geometry and applications.

Geometric Science of Information

Author : Frank Nielsen
Publisher :
ISBN 13 : 9783030802103
Total Pages : 0 pages
Book Rating : 4.8/5 (21 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by . This book was released on 2021 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 5th International Conference on Geometric Science of Information, GSI 2021, held in Paris, France, in July 2021. The 98 papers presented in this volume were carefully reviewed and selected from 125 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications. The papers are organized in the following topics: Probability and statistics on Riemannian Manifolds; sub-Riemannian geometry and neuromathematics; shapes spaces; geometry of quantum states; geometric and structure preserving discretizations; information geometry in physics; Lie group machine learning; geometric and symplectic methods for hydrodynamical models; harmonic analysis on Lie groups; statistical manifold and Hessian information geometry; geometric mechanics; deformed entropy, cross-entropy, and relative entropy; transformation information geometry; statistics, information and topology; geometric deep learning; topological and geometrical structures in neurosciences; computational information geometry; manifold and optimization; divergence statistics; optimal transport and learning; and geometric structures in thermodynamics and statistical physics.

Information Geometry

Author : Nihat Ay
Publisher : Springer
ISBN 13 : 3319564781
Total Pages : 407 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Information Geometry by : Nihat Ay

Download or read book Information Geometry written by Nihat Ay and published by Springer. This book was released on 2017-08-25 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book provides a comprehensive introduction and a novel mathematical foundation of the field of information geometry with complete proofs and detailed background material on measure theory, Riemannian geometry and Banach space theory. Parametrised measure models are defined as fundamental geometric objects, which can be both finite or infinite dimensional. Based on these models, canonical tensor fields are introduced and further studied, including the Fisher metric and the Amari-Chentsov tensor, and embeddings of statistical manifolds are investigated. This novel foundation then leads to application highlights, such as generalizations and extensions of the classical uniqueness result of Chentsov or the Cramér-Rao inequality. Additionally, several new application fields of information geometry are highlighted, for instance hierarchical and graphical models, complexity theory, population genetics, or Markov Chain Monte Carlo. The book will be of interest to mathematicians who are interested in geometry, information theory, or the foundations of statistics, to statisticians as well as to scientists interested in the mathematical foundations of complex systems.

Methods of Information Geometry

Author : Shun-ichi Amari
Publisher : American Mathematical Soc.
ISBN 13 : 9780821843024
Total Pages : 220 pages
Book Rating : 4.8/5 (43 download)

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Book Synopsis Methods of Information Geometry by : Shun-ichi Amari

Download or read book Methods of Information Geometry written by Shun-ichi Amari and published by American Mathematical Soc.. This book was released on 2000 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: Information geometry provides the mathematical sciences with a fresh framework of analysis. This book presents a comprehensive introduction to the mathematical foundation of information geometry. It provides an overview of many areas of applications, such as statistics, linear systems, information theory, quantum mechanics, and convex analysis.

Geometric Data Analysis

Author : Brigitte Le Roux
Publisher : Springer Science & Business Media
ISBN 13 : 1402022360
Total Pages : 475 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Geometric Data Analysis by : Brigitte Le Roux

Download or read book Geometric Data Analysis written by Brigitte Le Roux and published by Springer Science & Business Media. This book was released on 2006-01-16 with total page 475 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric Data Analysis (GDA) is the name suggested by P. Suppes (Stanford University) to designate the approach to Multivariate Statistics initiated by Benzécri as Correspondence Analysis, an approach that has become more and more used and appreciated over the years. This book presents the full formalization of GDA in terms of linear algebra - the most original and far-reaching consequential feature of the approach - and shows also how to integrate the standard statistical tools such as Analysis of Variance, including Bayesian methods. Chapter 9, Research Case Studies, is nearly a book in itself; it presents the methodology in action on three extensive applications, one for medicine, one from political science, and one from education (data borrowed from the Stanford computer-based Educational Program for Gifted Youth ). Thus the readership of the book concerns both mathematicians interested in the applications of mathematics, and researchers willing to master an exceptionally powerful approach of statistical data analysis.

Geometric Science of Information

Author : Frank Nielsen
Publisher :
ISBN 13 : 9783030269814
Total Pages : 770 pages
Book Rating : 4.2/5 (698 download)

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Book Synopsis Geometric Science of Information by : Frank Nielsen

Download or read book Geometric Science of Information written by Frank Nielsen and published by . This book was released on 2019 with total page 770 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 4th International Conference on Geometric Science of Information, GSI 2019, held in Toulouse, France, in August 2019. The 79 full papers presented in this volume were carefully reviewed and selected from 105 submissions. They cover all the main topics and highlights in the domain of geometric science of information, including information geometry manifolds of structured data/information and their advanced applications.