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Data Visualization with Category Theory and Geometry: With a Critical Analysis and Refinement of UMAP: 3 (Mathematics of Data, 3) - Tapa dura
Sinopsis
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.
"Sinopsis" puede pertenecer a otra edición de este libro.
De la contraportada
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.
"Sobre este título" puede pertenecer a otra edición de este libro.
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Data Visualization with Category Theory and Geometry (eng)
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Data Visualization with Category Theory and Geometry (Hardcover)
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ISBN 10: 3031979729
ISBN 13: 9783031979729
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Hardcover. Condición: new. Hardcover. 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. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Nº de ref. del artículo: 9783031979729
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Data Visualization With Category Theory and Geometry : With a Critical Analysis and Refinement of Umap
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Data Visualization With Category Theory and Geometry: With a Critical Analysis and Refinement of Umap
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Hardcover. Condición: Brand New. 210 pages. 9.26x6.11x9.21 inches. In Stock. This item is printed on demand. Nº de ref. del artículo: __3031979729
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Data Visualization with Category Theory and Geometry (eng)
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Data Visualization With Category Theory and Geometry : With a Critical Analysis and Refinement of Umap
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Data Visualization with Category Theory and Geometry: With a Critical Analysis and Refinement of UMAP (Mathematics of Data, 3)
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Data Visualization with Category Theory and Geometry
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Springer International Publishing AG, CH, 2025
ISBN 10: 3031979729
ISBN 13: 9783031979729
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Librería: Rarewaves.com USA, London, LONDO, Reino Unido
Calificación del vendedor: 5 de 5 estrellas
Hardback. Condición: New. 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. Nº de ref. del artículo: LU-9783031979729
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Data Visualization With Category Theory and Geometry : With a Critical Analysis and Refinement of Umap
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Data Visualization with Category Theory and Geometry
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Springer, Berlin, Springer Nature Switzerland, Max Planck Digital Library, Max-Planck-Institut Für Mathematik In Den Naturwissenschaften, Springer, 2025
ISBN 10: 3031979729
ISBN 13: 9783031979729
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Librería: BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Alemania
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Buch. Condición: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 272 pp. Englisch. Nº de ref. del artículo: 9783031979729
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