Hensel Felix, Moor Michael, Rieck Bastian
Machine Learning and Computational Biology Laboratory, ETH Zurich, Zurich, Switzerland.
Swiss Institute of Bioinformatics, Lausanne, Switzerland.
Front Artif Intell. 2021 May 26;4:681108. doi: 10.3389/frai.2021.681108. eCollection 2021.
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.
在过去十年中，计算拓扑领域得到了极大的推动：代数拓扑和微分拓扑中的方法和概念，以前仅限于纯数学领域，如今已在众多领域展现出其效用，比如计算生物学、个性化医学以及时间相关数据分析等等。这个由基于拓扑的技术所构成的新兴领域通常被称为拓扑数据分析（TDA）。除了在上述领域的应用，TDA方法在支持、增强和扩充经典机器学习和深度学习模型方面也已被证明是有效的。在本文中，我们回顾了一个新兴领域——我们称之为“拓扑机器学习”的技术现状，即基于拓扑的方法与机器学习算法（如深度神经网络）的成功融合。我们找出了其中的共同思路、当前应用以及未来挑战。
