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Cambridge Texts in Applied Mathematics
— —
Jean-Daniel Boissonnat Frederic Chazal
Cambridge Texts in Applied Mathematics by Jean-Daniel Boissonnat at Abbey's Bookshop,

Cambridge Texts in Applied Mathematics

Jean-Daniel Boissonnat Frederic Chazal Mariette Yvinec


9781108410892

Cambridge University Press


Data analysis: general;
Mathematics & Sciences;
Geometry;
Topology;
Mathematical theory of computation


Paperback

300 pages

$52.95
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Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of topological data analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this self-contained book covers key aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.

By:   Jean-Daniel Boissonnat, Frederic Chazal, Mariette Yvinec
Imprint:   Cambridge University Press
Country of Publication:   United Kingdom
Volume:   57
Dimensions:   Height: 229mm,  Width: 153mm,  Spine: 14mm
Weight:   350g
ISBN:   9781108410892
ISBN 10:   1108410898
Pages:   300
Publication Date:   February 2019
Audience:   Professional and scholarly ,  College/higher education ,  Undergraduate ,  Further / Higher Education
Format:   Paperback
Publisher's Status:   Active

Part I. Topological Preliminaries: 1. Topological spaces; 2. Simplicial complexes; Part II. Delaunay Complexes: 3. Convex polytopes; 4. Delaunay complexes; 5. Good triangulations; 6. Delaunay filtrations; Part III. Reconstruction of Smooth Submanifolds: 7. Triangulation of submanifolds; 8. Reconstruction of submanifolds; Part IV. Distance-Based Inference: 9. Stability of distance functions; 10. Distance to probability measures; 11. Homology inference.

Jean-Daniel Boissonnat is a Research Director at the Institut national de recherche en informatique et en automatique, France. His research interests are in computational geometry and topology. He has published several books and more than 180 research papers, and is on the editorial board of the Journal of the ACM and of Discrete and Computational Geometry. He received the IBM award in Computer Science in 1987, the EADS award in Information Sciences in 2006 and was awarded an advanced grant from the European Research Council in 2014. He has taught at several universities in Paris and at the College de France. Frederic Chazal is a Research Director at the Institut national de recherche en informatique et en automatique, France, where he is heading the DataShape team, a pioneering and world leading group in computational geometry and topological data analysis. His current primary research is on topological data analysis and its connections with statistics and machine learning, and he has authored several reference papers in this domain. He is an associate editor of four international journals and he teaches topological data analysis in various universities and engineering schools in the Paris area. Mariette Yvinec was a Researcher at the Institut national de recherche en informatique et en automatique, France. She is a specialist in the field of shape reconstruction and meshing, and taught master's courses on the subject in various universities in Paris. She co-authored a reference book on computational geometry with Jean-Daniel Boissonnat, and played an active role in the design and development of the software library CGAL.


'How do you make sense of a cloud of points in high dimension? This book will tell you. Be ready for a merry ride through the awesome canyons of geometry and topology with, ever lurking in the shadows, the dreaded curse of dimensionality. Destined to become an instant classic, this book treats its reader to a gentle introduction to the subject while providing a laser-sharp focus on the hottest topics of the day. For students and researchers alike, this delightful volume will be the go-to reference in the field of geometric inference.' Bernard Chazelle, Princeton University, New Jersey 'Problems related to understanding the relationship between a space and points sampled from within it - perhaps with noise and perhaps not too densely - are important in areas ranging from data analysis, approximation theory, and graphics to differential geometry and topology. This book emphasizes the algorithmic side of the subject explaining both classical and recent ideas carefully and clearly. While not encyclopedic, it is the finest kind of exposition: masters of the field have picked and explained a number of the most important ideas, many of which are scattered in the research literature, building a vantage point from which the reader can explore the broad terrain of applications, refinements, and variations.' Shmuel Weinberger, University of Chicago 'Rooted in geometry and topology, the problem of inferring a shape from its point-samples is at the heart of many applications in science and engineering. In the past two decades, researchers, primarily in the field of computational geometry, have studied this problem from the viewpoint of designing algorithms with certified guarantees. Written by three experts in the field, this book epitomizes these research efforts. By focusing on high dimensions, the authors offer views complementary to recent learning techniques.' Tamal K. Dey, Ohio State University 'How do you make sense of a cloud of points in high dimension? This book will tell you. Be ready for a merry ride through the awesome canyons of geometry and topology with, ever lurking in the shadows, the dreaded curse of dimensionality. Destined to become an instant classic, this book treats its reader to a gentle introduction to the subject while providing a laser-sharp focus on the hottest topics of the day. For students and researchers alike, this delightful volume will be the go-to reference in the field of geometric inference.' Bernard Chazelle, Princeton University, New Jersey 'Problems related to understanding the relationship between a space and points sampled from within it - perhaps with noise and perhaps not too densely - are important in areas ranging from data analysis, approximation theory, and graphics to differential geometry and topology. This book emphasizes the algorithmic side of the subject explaining both classical and recent ideas carefully and clearly. While not encyclopedic, it is the finest kind of exposition: masters of the field have picked and explained a number of the most important ideas, many of which are scattered in the research literature, building a vantage point from which the reader can explore the broad terrain of applications, refinements, and variations.' Shmuel Weinberger, University of Chicago 'Rooted in geometry and topology, the problem of inferring a shape from its point-samples is at the heart of many applications in science and engineering. In the past two decades, researchers, primarily in the field of computational geometry, have studied this problem from the viewpoint of designing algorithms with certified guarantees. Written by three experts in the field, this book epitomizes these research efforts. By focusing on high dimensions, the authors offer views complementary to recent learning techniques.' Tamal K. Dey, Ohio State University

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