Computational Information Geometry

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Computational Information Geometry

Frank Nielsen,Frank Critchley,Christopher T. J. Dodson
Computational Information Geometry Book PDF

Author : Frank Nielsen,Frank Critchley,Christopher T. J. Dodson
Publisher : Springer
Page : 299 pages
File Size : 44,7 Mb
Release : 2016-11-24
Category : Technology & Engineering
ISBN : 9783319470580

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Computational Information Geometry by Frank Nielsen,Frank Critchley,Christopher T. J. Dodson Pdf

This book focuses on the application and development of information geometric methods in the analysis, classification and retrieval of images and signals. It provides introductory chapters to help those new to information geometry and applies the theory to several applications. This area has developed rapidly over recent years, propelled by the major theoretical developments in information geometry, efficient data and image acquisition and the desire to process and interpret large databases of digital information. The book addresses both the transfer of methodology to practitioners involved in database analysis and in its efficient computational implementation.

Information Geometry

Geert Verdoolaege
Information Geometry Book PDF

Author : Geert Verdoolaege
Publisher : MDPI
Page : 355 pages
File Size : 49,6 Mb
Release : 2019-04-04
Category : Juvenile Nonfiction
ISBN : 9783038976325

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Information Geometry by Geert Verdoolaege Pdf

This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.

Progress in Information Geometry

Frank Nielsen
Progress in Information Geometry Book PDF

Author : Frank Nielsen
Publisher : Springer Nature
Page : 274 pages
File Size : 49,5 Mb
Release : 2021-03-14
Category : Science
ISBN : 9783030654597

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Progress in Information Geometry by Frank Nielsen Pdf

This book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. The book project was initiated following discussions at the international conference GSI’2019 – Geometric Science of Information that was held at ENAC, Toulouse (France).

Matrix Information Geometry

Frank Nielsen,Rajendra Bhatia
Matrix Information Geometry Book PDF

Author : Frank Nielsen,Rajendra Bhatia
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 51,9 Mb
Release : 2012-08-07
Category : Technology & Engineering
ISBN : 9783642302329

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Matrix Information Geometry by Frank Nielsen,Rajendra Bhatia Pdf

This book presents advances in matrix and tensor data processing in the domain of signal, image and information processing. The theoretical mathematical approaches are discusses in the context of potential applications in sensor and cognitive systems engineering. The topics and application include Information Geometry, Differential Geometry of structured Matrix, Positive Definite Matrix, Covariance Matrix, Sensors (Electromagnetic Fields, Acoustic sensors) and Applications in Cognitive systems, in particular Data Mining.

Computational Geometry

Mark de Berg,Marc van Krefeld,Mark Overmars,Otfried Cheong
Computational Geometry Book PDF

Author : Mark de Berg,Marc van Krefeld,Mark Overmars,Otfried Cheong
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 52,9 Mb
Release : 2013-04-17
Category : Computers
ISBN : 9783662042458

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Computational Geometry by Mark de Berg,Marc van Krefeld,Mark Overmars,Otfried Cheong Pdf

This introduction to computational geometry focuses on algorithms. Motivation is provided from the application areas as all techniques are related to particular applications in robotics, graphics, CAD/CAM, and geographic information systems. Modern insights in computational geometry are used to provide solutions that are both efficient and easy to understand and implement.

Geometric Theory of Information

Frank Nielsen
Geometric Theory of Information Book PDF

Author : Frank Nielsen
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 53,7 Mb
Release : 2014-05-08
Category : Technology & Engineering
ISBN : 9783319053172

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Geometric Theory of Information by Frank Nielsen Pdf

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.

Handbook of Computational Geometry

J.R. Sack,J. Urrutia
Handbook of Computational Geometry Book PDF

Author : J.R. Sack,J. Urrutia
Publisher : Elsevier
Page : 1075 pages
File Size : 46,8 Mb
Release : 1999-12-13
Category : Mathematics
ISBN : 0080529682

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Handbook of Computational Geometry by J.R. Sack,J. Urrutia Pdf

Computational Geometry is an area that provides solutions to geometric problems which arise in applications including Geographic Information Systems, Robotics and Computer Graphics. This Handbook provides an overview of key concepts and results in Computational Geometry. It may serve as a reference and study guide to the field. Not only the most advanced methods or solutions are described, but also many alternate ways of looking at problems and how to solve them.

Computational Geometry

Franco P. Preparata,Michael I. Shamos
Computational Geometry Book PDF

Author : Franco P. Preparata,Michael I. Shamos
Publisher : Springer Science & Business Media
Page : 413 pages
File Size : 44,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461210986

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Computational Geometry by Franco P. Preparata,Michael I. Shamos Pdf

From the reviews: "This book offers a coherent treatment, at the graduate textbook level, of the field that has come to be known in the last decade or so as computational geometry. ... ... The book is well organized and lucidly written; a timely contribution by two founders of the field. It clearly demonstrates that computational geometry in the plane is now a fairly well-understood branch of computer science and mathematics. It also points the way to the solution of the more challenging problems in dimensions higher than two." #Mathematical Reviews#1 "... This remarkable book is a comprehensive and systematic study on research results obtained especially in the last ten years. The very clear presentation concentrates on basic ideas, fundamental combinatorial structures, and crucial algorithmic techniques. The plenty of results is clever organized following these guidelines and within the framework of some detailed case studies. A large number of figures and examples also aid the understanding of the material. Therefore, it can be highly recommended as an early graduate text but it should prove also to be essential to researchers and professionals in applied fields of computer-aided design, computer graphics, and robotics." #Biometrical Journal#2

Geometric Structures of Information

Frank Nielsen
Geometric Structures of Information Book PDF

Author : Frank Nielsen
Publisher : Springer
Page : 392 pages
File Size : 46,5 Mb
Release : 2018-11-19
Category : Technology & Engineering
ISBN : 9783030025205

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Geometric Structures of Information by Frank Nielsen Pdf

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.

Information Geometry and Its Applications

Shun-ichi Amari
Information Geometry and Its Applications Book PDF

Author : Shun-ichi Amari
Publisher : Springer
Page : 378 pages
File Size : 46,9 Mb
Release : 2016-02-02
Category : Mathematics
ISBN : 9784431559788

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Information Geometry and Its Applications by Shun-ichi Amari Pdf

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.

Computational Geometry on Surfaces

Clara Grima,Alberto Marquez
Computational Geometry on Surfaces Book PDF

Author : Clara Grima,Alberto Marquez
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 43,6 Mb
Release : 2001-11-30
Category : Computers
ISBN : 1402002025

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Computational Geometry on Surfaces by Clara Grima,Alberto Marquez Pdf

In the last thirty years Computational Geometry has emerged as a new discipline from the field of design and analysis of algorithms. That dis cipline studies geometric problems from a computational point of view, and it has attracted enormous research interest. But that interest is mostly concerned with Euclidean Geometry (mainly the plane or Eu clidean 3-dimensional space). Of course, there are some important rea sons for this occurrence since the first applieations and the bases of all developments are in the plane or in 3-dimensional space. But, we can find also some exceptions, and so Voronoi diagrams on the sphere, cylin der, the cone, and the torus have been considered previously, and there are manY works on triangulations on the sphere and other surfaces. The exceptions mentioned in the last paragraph have appeared to try to answer some quest ions which arise in the growing list of areas in which the results of Computational Geometry are applicable, since, in practiee, many situations in those areas lead to problems of Com putational Geometry on surfaces (probably the sphere and the cylinder are the most common examples). We can mention here some specific areas in which these situations happen as engineering, computer aided design, manufacturing, geographie information systems, operations re search, roboties, computer graphics, solid modeling, etc.

Computational Geometry, Topology and Physics of Digital Images with Applications

James F. Peters
Computational Geometry Topology and Physics of Digital Images with Applications Book PDF

Author : James F. Peters
Publisher : Springer Nature
Page : 440 pages
File Size : 41,5 Mb
Release : 2019-10-03
Category : Technology & Engineering
ISBN : 9783030221928

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Computational Geometry, Topology and Physics of Digital Images with Applications by James F. Peters Pdf

This book discusses the computational geometry, topology and physics of digital images and video frame sequences. This trio of computational approaches encompasses the study of shape complexes, optical vortex nerves and proximities embedded in triangulated video frames and single images, while computational geometry focuses on the geometric structures that infuse triangulated visual scenes. The book first addresses the topology of cellular complexes to provide a basis for an introductory study of the computational topology of visual scenes, exploring the fabric, shapes and structures typically found in visual scenes. The book then examines the inherent geometry and topology of visual scenes, and the fine structure of light and light caustics of visual scenes, which bring into play catastrophe theory and the appearance of light caustic folds and cusps. Following on from this, the book introduces optical vortex nerves in triangulated digital images. In this context, computational physics is synonymous with the study of the fine structure of light choreographed in video frames. This choreography appears as a sequence of snapshots of light reflected and refracted from surface shapes, providing a solid foundation for detecting, analyzing and classifying visual scene shapes.

New Trends in Discrete and Computational Geometry

Janos Pach
New Trends in Discrete and Computational Geometry Book PDF

Author : Janos Pach
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642580437

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New Trends in Discrete and Computational Geometry by Janos Pach Pdf

Discrete and computational geometry are two fields which in recent years have benefitted from the interaction between mathematics and computer science. The results are applicable in areas such as motion planning, robotics, scene analysis, and computer aided design. The book consists of twelve chapters summarizing the most recent results and methods in discrete and computational geometry. All authors are well-known experts in these fields. They give concise and self-contained surveys of the most efficient combinatorical, probabilistic and topological methods that can be used to design effective geometric algorithms for the applications mentioned above. Most of the methods and results discussed in the book have not appeared in any previously published monograph. In particular, this book contains the first systematic treatment of epsilon-nets, geometric tranversal theory, partitions of Euclidean spaces and a general method for the analysis of randomized geometric algorithms. Apart from mathematicians working in discrete and computational geometry this book will also be of great use to computer scientists and engineers, who would like to learn about the most recent results.

Information Geometry

Nihat Ay,Jürgen Jost,Hông Vân Lê,Lorenz Schwachhöfer
Information Geometry Book PDF

Author : Nihat Ay,Jürgen Jost,Hông Vân Lê,Lorenz Schwachhöfer
Publisher : Springer
Page : 407 pages
File Size : 49,6 Mb
Release : 2017-08-25
Category : Mathematics
ISBN : 9783319564784

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Information Geometry by Nihat Ay,Jürgen Jost,Hông Vân Lê,Lorenz Schwachhöfer Pdf

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.

Discrete and Computational Geometry

Satyan L. Devadoss,Joseph O'Rourke
Discrete and Computational Geometry Book PDF

Author : Satyan L. Devadoss,Joseph O'Rourke
Publisher : Princeton University Press
Page : 270 pages
File Size : 41,7 Mb
Release : 2011-04-11
Category : Mathematics
ISBN : 9781400838981

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Discrete and Computational Geometry by Satyan L. Devadoss,Joseph O'Rourke Pdf

An essential introduction to discrete and computational geometry Discrete geometry is a relatively new development in pure mathematics, while computational geometry is an emerging area in applications-driven computer science. Their intermingling has yielded exciting advances in recent years, yet what has been lacking until now is an undergraduate textbook that bridges the gap between the two. Discrete and Computational Geometry offers a comprehensive yet accessible introduction to this cutting-edge frontier of mathematics and computer science. This book covers traditional topics such as convex hulls, triangulations, and Voronoi diagrams, as well as more recent subjects like pseudotriangulations, curve reconstruction, and locked chains. It also touches on more advanced material, including Dehn invariants, associahedra, quasigeodesics, Morse theory, and the recent resolution of the Poincaré conjecture. Connections to real-world applications are made throughout, and algorithms are presented independently of any programming language. This richly illustrated textbook also features numerous exercises and unsolved problems. The essential introduction to discrete and computational geometry Covers traditional topics as well as new and advanced material Features numerous full-color illustrations, exercises, and unsolved problems Suitable for sophomores in mathematics, computer science, engineering, or physics Rigorous but accessible An online solutions manual is available (for teachers only).