Geometric Structures of Information - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Structures of Information write by Frank Nielsen. This book was released on 2018-11-19. Geometric Structures of Information available in PDF, EPUB and Kindle. 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
Geometric Theory of Information - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Theory of Information write by Frank Nielsen. This book was released on 2014-05-08. Geometric Theory of Information available in PDF, EPUB and Kindle. 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 Structure of High-Dimensional Data and Dimensionality Reduction
Geometric Structure of High-Dimensional Data and Dimensionality Reduction - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Structure of High-Dimensional Data and Dimensionality Reduction write by Jianzhong Wang. This book was released on 2012-04-28. Geometric Structure of High-Dimensional Data and Dimensionality Reduction available in PDF, EPUB and Kindle. "Geometric Structure of High-Dimensional Data and Dimensionality Reduction" adopts data geometry as a framework to address various methods of dimensionality reduction. In addition to the introduction to well-known linear methods, the book moreover stresses the recently developed nonlinear methods and introduces the applications of dimensionality reduction in many areas, such as face recognition, image segmentation, data classification, data visualization, and hyperspectral imagery data analysis. Numerous tables and graphs are included to illustrate the ideas, effects, and shortcomings of the methods. MATLAB code of all dimensionality reduction algorithms is provided to aid the readers with the implementations on computers. The book will be useful for mathematicians, statisticians, computer scientists, and data analysts. It is also a valuable handbook for other practitioners who have a basic background in mathematics, statistics and/or computer algorithms, like internet search engine designers, physicists, geologists, electronic engineers, and economists. Jianzhong Wang is a Professor of Mathematics at Sam Houston State University, U.S.A.
Information Geometry and Its Applications
Information Geometry and Its Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Information Geometry and Its Applications write by Shun-ichi Amari. This book was released on 2016-02-02. Information Geometry and Its Applications available in PDF, EPUB and Kindle. 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 Science of Information
Geometric Science of Information - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Geometric Science of Information write by Frank Nielsen. This book was released on 2021-07-14. Geometric Science of Information available in PDF, EPUB and Kindle. 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.
