Computational Topology for Data Analysis
Computational Topology for Data Analysis
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DOI：
10.1017/9781009099950
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发表时间：
2022-02
期刊：
影响因子：
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通讯作者：
T. Dey;Yusu Wang
中科院分区：
文献类型：
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作者：
T. Dey;Yusu Wang
拓扑数据分析（TDA）是近年来出现的一种分析复杂数据的可行工具，该领域在方法和适用性方面都有了很大的发展。为TDA技术提供计算和算法基础，这本全面，独立的文本向数学和计算机科学领域的学生和研究人员介绍了该领域的现状。这本书的特点是描述数学对象和结构背后的最新进展，所涉及的算法，计算考虑，以及拓扑结构或思想，可以在应用程序中使用的例子。它提供了一个彻底的治疗持久同源性与各种扩展-如锯齿持久性和多参数持久性-和他们的应用程序不同类型的数据，如点云，三角测量，或图形数据。涵盖的其他重要主题包括离散莫尔斯理论，映射器结构，最佳生成周期，以及在机器学习框架中嵌入TDA的最新进展。
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.