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" Geometric and topological inference / "
Jean-Daniel Boissonnat, INRIA Sophia Antipolis ; Frédéric Chazal, Inria Saclay-Ile-de-France ; Mariette Yvinec, INRIA Sophia Antipolis.
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BL
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| Record Number
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839357
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| Main Entry
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Boissonnat, J.-D., (Jean-Daniel),1953-
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| Title & Author
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Geometric and topological inference /\ Jean-Daniel Boissonnat, INRIA Sophia Antipolis ; Frédéric Chazal, Inria Saclay-Ile-de-France ; Mariette Yvinec, INRIA Sophia Antipolis.
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| Publication Statement
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Cambridge :: Cambridge University Press,, 2018.
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, ©2018
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| Series Statement
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Cambridge texts in applied mathematics ;; 57
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| Page. NO
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1 online resource (xii, 233 pages) :: illustrations
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| ISBN
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1108297803
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: 9781108297806
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1108410898
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1108419399
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9781108410892
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9781108419390
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| Bibliographies/Indexes
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Includes bibliographical references (pages 224-230) and index.
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| Contents
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Topological spaces -- Simplicial complexes -- Convex polytopes -- Delaunay complexes -- Good triangulations -- Delaunay filtrations -- Triangulation of submanifolds -- Reconstruction of submanifolds -- Stability of distance functions -- Distance to probability measures -- Homology inference.
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| Abstract
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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.
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| Subject
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Geometric analysis.
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Pattern perception.
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Shapes-- Mathematical models.
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Topology.
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Geometric analysis.
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Pattern perception.
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Topology.
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| Dewey Classification
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514/.2
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| LC Classification
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QA491.B5995 2018
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| Added Entry
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Chazal, Frédéric,1971-
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Yvinec, Mariette,1953-
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