| 書目名稱 | Mathematical Principles of Topological and Geometric Data Analysis | | 編輯 | Parvaneh Joharinad,Jürgen Jost | | 視頻video | http://file.papertrans.cn/627/626522/626522.mp4 | | 概述 | The first book to develop the geometric foundations of manifold learning.Provides the mathematical prerequisites for the dimension reduction techniques of machine learning.General notion of curvature | | 叢書名稱 | Mathematics of Data | | 圖書封面 |  | | 描述 | .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..Pri | | 出版日期 | Textbook 2023 | | 關(guān)鍵詞 | Riemannian geometry; Laplace operators; homology; category theory; Dimension reduction; Kernel technique; | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-031-33440-5 | | isbn_softcover | 978-3-031-33442-9 | | isbn_ebook | 978-3-031-33440-5Series ISSN 2731-4103 Series E-ISSN 2731-4111 | | issn_series | 2731-4103 | | copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
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