Data Visualization Category Theory by Barth Lukas (20 results)
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Language: English
Published by Springer International Publishing AG, Cham, 2025
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Hardcover. Condition: 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 example…s 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.
Data Visualization With Category Theory and Geometry : With a Critical Analysis and Refinement of Umap
Barth, Lukas Silvester; Fahimi, Hannaneh; Joharinad, Parvaneh; Jost, Jürgen; Keck, Janis
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Data Visualization With Category Theory and Geometry : With a Critical Analysis and Refinement of Umap
Barth, Lukas Silvester; Fahimi, Hannaneh; Joharinad, Parvaneh; Jost, Jürgen; Keck, Janis
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Data Visualization with Category Theory and Geometry: With a Critical Analysis and Refinement of UMAP (Mathematics of Data, 3)
Barth, Lukas Silvester; Fahimi, Hannaneh; Joharinad, Parvaneh; Jost, Jürgen; Keck, Janis
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Data Visualization With Category Theory and Geometry : With a Critical Analysis and Refinement of Umap
Barth, Lukas Silvester; Fahimi, Hannaneh; Joharinad, Parvaneh; Jost, Jürgen; Keck, Janis
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Data Visualization With Category Theory and Geometry : With a Critical Analysis and Refinement of Umap
Barth, Lukas Silvester; Fahimi, Hannaneh; Joharinad, Parvaneh; Jost, Jürgen; Keck, Janis
- Hardcover
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Data visualization with category theory and geometry: With a critical analysis and refinement of UMAP (Mathematics of Data, 3)
Barth, Lukas Silvester; Fahimi, Hannaneh; Joharinad, Parvaneh; Jost, Jürgen; Keck, Janis
- Hardcover
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Language: English
Published by Springer International Publishing AG, Cham, 2025
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Hardcover. Condition: 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 example…s 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 our UK warehouse or from our Australian or US warehouses, depending on stock availability.
Data Visualization With Category Theory and Geometry: With a Critical Analysis and Refinement of Umap
Barth, Lukas Silvester/ Fahimi, Hannaneh/ Joharinad, Parvaneh/ Jost, Jürgen/ Keck, Janis
- Hardcover
Seller: Revaluation Books, Exeter, United KingdomRevaluation Books
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Hardcover. Condition: Brand New. 210 pages. 9.26x6.11x9.21 inches. In Stock.
Language: English
Published by Springer International Publishing AG, Cham, 2025
- Hardcover
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Hardcover. Condition: 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 example…s 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 our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability.
Data Visualization with Category Theory and Geometry
Lukas Silvester Barth, Hannaneh Fahimi, Parvaneh Joharinad, Jürgen Jost, Janis Keck
Language: English
Published by Springer International Publishing AG, CH, 2025
- Hardcover
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Hardback. Condition: 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.
Data Visualization With Category Theory and Geometry: With a Critical Analysis and Refinement of Umap
Barth, Lukas Silvester/ Fahimi, Hannaneh/ Joharinad, Parvaneh/ Jost, Jürgen/ Keck, Janis
- Hardcover
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Hardcover. Condition: Brand New. 210 pages. 9.26x6.11x9.21 inches. In Stock. This item is printed on demand.
Language: English
Published by Springer, Berlin, Springer Nature Switzerland, Max Planck Digital Library, Max-Planck-Institut Für Mathematik In Den Naturwissenschaften, Springer, 2025
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Buch. Condition: 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 particu…lar, 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.
Data visualization with category theory and geometry: With a critical analysis and refinement of UMAP (Mathematics of Data, 3)
Barth, Lukas Silvester; Fahimi, Hannaneh; Joharinad, Parvaneh; Jost, Jürgen; Keck, Janis
- Hardcover
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Data visualization with category theory and geometry: With a critical analysis and refinement of UMAP (Mathematics of Data, 3)
Barth, Lukas Silvester; Fahimi, Hannaneh; Joharinad, Parvaneh; Jost, Jürgen; Keck, Janis
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Data visualization with category theory and geometry
Barth, Lukas Silvester; Fahimi, Hannaneh; Joharinad, Parvaneh; Jost, Jürgen; Keck, Janis
- Hardcover
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Buch. Condition: Neu. This item is printed on demand - Print on Demand Titel. 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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 288 pp. Englisch.
Published by Springer, Berlin, Max Planck Digital Library, Max-Planck-Institut Für Mathematik In Den Naturwissenschaften, Springer
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Taschenbuch. Condition: 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.
