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- Startseite
Bücher Englische Bücher Data Visualization with Category Theory and Geometry
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Data Visualization with Category Theory and Geometry
Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck (Gebundene Ausgabe, Englisch)
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Beschreibung
This open access book provides a robust exposition of the mathematical foundations of data representation, focusing on two essential pillars of dimensionality reduction methods, namely geometry in general and Riemannian geometry in particular, and category theory. Presenting a list of examples consisting of both geometric objects and empirical datasets, this book provides insights into the… different effects of dimensionality reduction techniques on data representation and visualization, with the aim of guiding the reader in understanding the expected results specific to each method in such scenarios. As a showcase, the dimensionality reduction method of “Uniform Manifold Approximation and Projection” (UMAP) has been used in this book, as it is built on theoretical foundations from all the areas we want to highlight here. Thus, this book also aims to systematically present the details of constructing a metric representation of a locally distorted metric space, which is essentially the problem that UMAP is trying to address, from a more general perspective. Explaining how UMAP fits into this broader framework, while critically evaluating the underlying ideas, this book finally introduces an alternative algorithm to UMAP. This algorithm, called IsUMap, retains many of the positive features of UMAP, while improving on some of its drawbacks. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
08.08.2025
Sprache
Englisch
EAN
9783031979729
Herausgeber
Springer International Publishing
Serien- oder Bandtitel
Mathematics of Data
Sonderedition
Nein
Autor
Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck
Seitenanzahl
272
Einbandart
Gebundene Ausgabe
Buch Untertitel
With a Critical Analysis and Refinement of UMAP
Schlagwörter
Open Access, Dimension reduction, Merging local metrics, Data visualization, Riemannian geometry, Applied category theory, UMAP, Simplicial complexes, Metric realization
Thema-Inhalt
UYA - Theoretische Informatik
PBF - Algebra
Höhe
235 mm
Breite
15.5 cm
Hersteller: Birkhäuser, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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