A Survey of Topological Machine Learning Methods.
A Survey of Topological Machine Learning Methods.
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DOI：
10.3389/frai.2021.681108
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发表时间：
2021
影响因子：
4
通讯作者：
Rieck B
中科院分区：
文献类型：
--
作者：
Hensel F;Moor M;Rieck B
在过去的十年里，计算拓扑学领域得到了巨大的发展：代数和微分拓扑学的方法和概念，以前仅限于纯数学领域，已经在许多领域证明了它们的实用性，如计算生物学、个性化医疗和时间依赖数据分析等。拓扑数据分析（TDA）是一个新兴的领域，包括基于拓扑的技术。除了在上述领域的应用外，TDA方法还被证明在支持、增强和扩充经典机器学习和深度学习模型方面是有效的。在本文中，我们回顾了我们称为“拓扑机器学习”的新兴领域的最新技术水平，即，基于拓扑的方法和机器学习算法（如深度神经网络）的成功共生。我们确定共同的线程，当前的应用程序和未来的挑战。
The last decade saw an enormous boost in the field of computational topology: methods and concepts from algebraic and differential topology, formerly confined to the realm of pure mathematics, have demonstrated their utility in numerous areas such as computational biology personalised medicine, and time-dependent data analysis, to name a few. The newly-emerging domain comprising topology-based techniques is often referred to as topological data analysis (TDA). Next to their applications in the aforementioned areas, TDA methods have also proven to be effective in supporting, enhancing, and augmenting both classical machine learning and deep learning models. In this paper, we review the state of the art of a nascent field we refer to as “topological machine learning,” i.e., the successful symbiosis of topology-based methods and machine learning algorithms, such as deep neural networks. We identify common threads, current applications, and future challenges.