Data Visualization with Category Theory and Geometry
Language: English
Published by Springer, Berlin, Springer Nature Switzerland, Max Planck Digital Library, Max-Planck-Institut Für Mathematik In Den Naturwissenschaften, Springer, 2025
- Hardcover
- New
Seller: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, GermanyBuchWeltWeit Ludwig Meier e.K.
AbeBooks seller since January 11, 2012
Condition: New
£ 47.34
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Add to basketItem description from seller
Seller Inventory # 9783031979729
- Title
- Data Visualization with Category Theory and Geometry
- Author
- Lukas Silvester Barth
- Publisher
- Springer, Berlin, Springer Nature Switzerland, Max Planck Digital Library, Max-Planck-Institut Für Mathematik In Den Naturwissenschaften, Springer
- Publication year
- 2025
- Condition
- Neu
- Binding
- Buch
- Language
- English
- ISBN 10
- 3031979729
- ISBN 13
- 9783031979729
- Item weight
- 543 grams
- Dimensions
- 235x155x19 mm
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.
"Synopsis" may belong to another edition of this title.
From the Back Cover
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.
"About the title" may belong to another edition of this title.
BuchWeltWeit Ludwig Meier e.K.
Bergisch Gladbach, Germany
AbeBooks seller since January 11, 2012
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