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- Startseite
Bücher Englische Bücher Mathematical Principles of Topological and Geometric Data Analysis
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Mathematical Principles of Topological and Geometric Data Analysis
Parvaneh Joharinad, Jürgen Jost (Broschiert, Englisch)
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Beschreibung
This book explores and demonstrates how geometric tools can be used in data analysis. Beginning with a systematic exposition of the mathematical prerequisites, covering topics ranging from category theory to algebraic topology, Riemannian geometry, operator theory and network analysis, it goes on to describe and analyze some of the most important machine learning techniques for dimension… reduction, including the different types of manifold learning and kernel methods. It also develops a new notion of curvature of generalized metric spaces, based on the notion of hyperconvexity, which can be used for the topological representation of geometric information. In recent years there has been a fascinating development: concepts and methods originally created in the context of research in pure mathematics, and in particular in geometry, have become powerful tools in machine learning for the analysis of data. The underlying reason for this is that data are typically equipped with somekind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately. Primarily aimed at mathematicians seeking an overview of the geometric concepts and methods that are useful for data analysis, the book will also be of interest to researchers in machine learning and data analysis who want to see a systematic mathematical foundation of the methods that they use. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
31.07.2024
Sprache
Englisch
EAN
9783031334429
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Mathematics of Data
Sonderedition
Nein
Autor
Parvaneh Joharinad, Jürgen Jost
Seitenanzahl
281
Einbandart
Broschiert
Schlagwörter
Riemannian geometry, Laplace operators, homology, category theory, Dimension reduction, Kernel technique, manifold learning, graph theory, curvature of metric spaces
Thema-Inhalt
PBW - Angewandte Mathematik
UYQM - Maschinelles Lernen
UYA - Theoretische Informatik
PBP - Topologie
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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