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Author: Frank Nielsen Publisher: Springer ISBN: 3030025209 Category : Technology & Engineering Languages : en Pages : 392
Book Description
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.
Author: Frank Nielsen Publisher: Springer ISBN: 3030025209 Category : Technology & Engineering Languages : en Pages : 392
Book Description
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.
Author: Frédéric Barbaresco Publisher: Springer Nature ISBN: 3030779572 Category : Mathematics Languages : en Pages : 466
Book Description
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.
Author: Сергей Петрович Новиков Publisher: American Mathematical Soc. ISBN: 0821839292 Category : Diffentiable manifolds Languages : en Pages : 658
Book Description
Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.
Author: Jianzhong Wang Publisher: Springer Science & Business Media ISBN: 3642274978 Category : Computers Languages : en Pages : 356
Book Description
"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.
Author: Frank Nielsen Publisher: Springer Science & Business Media ISBN: 3319053175 Category : Technology & Engineering Languages : en Pages : 392
Book Description
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.
Author: Walter A. Poor Publisher: Courier Corporation ISBN: 0486151913 Category : Mathematics Languages : en Pages : 352
Book Description
This introductory text defines geometric structure by specifying parallel transport in an appropriate fiber bundle and focusing on simplest cases of linear parallel transport in a vector bundle. 1981 edition.
Author: Elmar Langetepe Publisher: A K Peters/CRC Press ISBN: Category : Computers Languages : en Pages : 344
Book Description
This book focuses on algorithms and geometric data structures that have proven to be versatile, efficient and fundamental. It endows practitioners in the computer graphics field with a working knowledge of a wide range of geometric data structures from computational geometry.
Author: Aurel Bejancu Publisher: Springer Science & Business Media ISBN: 1402037201 Category : Mathematics Languages : en Pages : 309
Book Description
Offers basic material on distributions and foliations. This book introduces and builds the tools needed for studying the geometry of foliated manifolds. Its main theme is to investigate the interrelations between foliations of a manifold on the one hand, and the many geometric structures that the manifold may admit on the other hand.
Author: Frank Nielsen Publisher: Springer Nature ISBN: 3030802094 Category : Computers Languages : en Pages : 929
Book Description
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.
Author: Tiansi Dong Publisher: Springer Nature ISBN: 3030562751 Category : Technology & Engineering Languages : en Pages : 155
Book Description
The unification of symbolist and connectionist models is a major trend in AI. The key is to keep the symbolic semantics unchanged. Unfortunately, present embedding approaches cannot. The approach in this book makes the unification possible. It is indeed a new and promising approach in AI. -Bo Zhang, Director of AI Institute, Tsinghua It is indeed wonderful to see the reviving of the important theme Nural Symbolic Model. Given the popularity and prevalence of deep learning, symbolic processing is often neglected or downplayed. This book confronts this old issue head on, with a historical look, incorporating recent advances and new perspectives, thus leading to promising new methods and approaches. -Ron Sun (RPI), on Governing Board of Cognitive Science Society Both for language and humor, approaches like those described in this book are the way to snickerdoodle wombats. -Christian F. Hempelmann (Texas A&M-Commerce) on Executive Board of International Society for Humor Studies
Author: Frank Nielsen
Author: Frank Nielsen
Author: Frédéric Barbaresco
Author: Сергей Петрович Новиков
Author: Jianzhong Wang
Author: Frank Nielsen
Author: Walter A. Poor
Author: Elmar Langetepe
Author: Aurel Bejancu
Author: Frank Nielsen
Author: Tiansi Dong