2017,
arXiv.
DOI:
10.48550/arXiv.1710.04019
arXiv ID:
1710.04019
An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists
Frédéric Chazal, Bertrand Michel
Abstract:
Topological Data Analysis is a recent and fast growing field providing a set
of new topological and geometric tools to infer relevant features for possibly
complex data. This paper is a brief introduction, through a few selected
topics, to basic fundamental and practical aspects of \tda\ for non experts.
of new topological and geometric tools to infer relevant features for possibly
complex data. This paper is a brief introduction, through a few selected
topics, to basic fundamental and practical aspects of \tda\ for non experts.
Related Links:
2024-02-28 22:09:00
尹志:
#paper An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists doi: https://doi.org/10.48550/arXiv.1710.04019 生成式AI风光无两,Sora甚嚣尘上,虽然我还做不到这样的效果(对,我就是酸),但我却认为这不是终极方案,特别是对于物理世界、生物系统。The Bitter Lesson中对scaling law的强调甚至信奉,在语言、视频这样的领域有其价值,但生命科学、物理系统有数十亿年的的历史(物理系统应该是创始之初把),生命的演化、物理系统的本源,人类对其千百年来积累的原理性探索,应该是更优的先验。哦,回到这篇paper的主题。拓扑数据分析,是一种将系统的拓扑与几何性质引入分析建模过程,从而对系统获取更深刻的理解的工具。本篇综述对这个工具做了细致的讲解并对它的应用领域做了分析和tutorial。对拓扑数据分析这门技术的数学前置也做了简单但细致的介绍,主要是代数拓扑和计算几何。之所以有前面一段的碎碎念,就是因为我结合最近的一些实践,切实感受到拓扑和几何这些抽象的数学工具与生成式AI的结合,对生物系统和物理世界的描述,也许是优于目前暴力怼计算的一种更高效的建模方式,能够更深入系统的物理本质。如果你也相信物理系统和生命世界的简单高效的,是美丽简洁的,建议尝试一下这些新的技术。对了,这篇综述的revison信息是[Submitted on 11 Oct 2017 (v1), last revised 25 Feb 2021 (this version, v2)], 是不是说明了点什么呢?