Computational Information Geometry

Author : Frank Nielsen
Publisher : Springer
ISBN 13 : 3319470582
Total Pages : 299 pages
Book Rating : 4.80/5 ( download)

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Download or read book Computational Information Geometry written by Frank Nielsen and published by Springer. This book was released on 2016-11-24 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Frank Nielsen
Publisher : Springer Nature
ISBN 13 : 3030654591
Total Pages : 274 pages
Book Rating : 4.97/5 ( download)

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Download or read book Progress in Information Geometry written by Frank Nielsen and published by Springer Nature. This book was released on 2021-03-14 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Author : Geert Verdoolaege
Publisher : MDPI
ISBN 13 : 3038976326
Total Pages : 355 pages
Book Rating : 4.25/5 ( download)

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Download or read book Information Geometry written by Geert Verdoolaege and published by MDPI. This book was released on 2019-04-04 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Satyan L. Devadoss
Publisher : Princeton University Press
ISBN 13 : 1400838983
Total Pages : 270 pages
Book Rating : 4.81/5 ( download)

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Download or read book Discrete and Computational Geometry written by Satyan L. Devadoss and published by Princeton University Press. This book was released on 2011-04-11 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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).

Author : Mark de Berg
Publisher : Springer Science & Business Media
ISBN 13 : 3662042452
Total Pages : 370 pages
Book Rating : 4.58/5 ( download)

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Download or read book Computational Geometry written by Mark de Berg and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : J.R. Sack
Publisher : Elsevier
ISBN 13 : 0080529682
Total Pages : 1087 pages
Book Rating : 4.84/5 ( download)

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Download or read book Handbook of Computational Geometry written by J.R. Sack and published by Elsevier. This book was released on 1999-12-13 with total page 1087 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Franco P. Preparata
Publisher : Springer Science & Business Media
ISBN 13 : 1461210984
Total Pages : 413 pages
Book Rating : 4.86/5 ( download)

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Download or read book Computational Geometry written by Franco P. Preparata and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Shun-ichi Amari
Publisher : Springer
ISBN 13 : 4431559787
Total Pages : 378 pages
Book Rating : 4.88/5 ( download)

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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.

Author : J. Andreas Bærentzen
Publisher : Springer Science & Business Media
ISBN 13 : 1447140753
Total Pages : 330 pages
Book Rating : 4.57/5 ( download)

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Download or read book Guide to Computational Geometry Processing written by J. Andreas Bærentzen and published by Springer Science & Business Media. This book was released on 2012-05-31 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book reviews the algorithms for processing geometric data, with a practical focus on important techniques not covered by traditional courses on computer vision and computer graphics. Features: presents an overview of the underlying mathematical theory, covering vector spaces, metric space, affine spaces, differential geometry, and finite difference methods for derivatives and differential equations; reviews geometry representations, including polygonal meshes, splines, and subdivision surfaces; examines techniques for computing curvature from polygonal meshes; describes algorithms for mesh smoothing, mesh parametrization, and mesh optimization and simplification; discusses point location databases and convex hulls of point sets; investigates the reconstruction of triangle meshes from point clouds, including methods for registration of point clouds and surface reconstruction; provides additional material at a supplementary website; includes self-study exercises throughout the text.

Author : Frank Nielsen
Publisher : Springer Science & Business Media
ISBN 13 : 3642302327
Total Pages : 454 pages
Book Rating : 4.29/5 ( download)

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Download or read book Matrix Information Geometry written by Frank Nielsen and published by Springer Science & Business Media. This book was released on 2012-08-07 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.