Abstract
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.
Highlights
Topological machine learning recently started to emerge as a field at the interface of topological data analysis (TDA) and machine learning
It is driven by improvements of computational methods, which make the calculation of topological features increasingly flexible and scalable to more complex and larger data sets
We provide some background on basic concepts from algebraic topology and persistent homology
Summary
Reviewed by: Raphael Reinauer, École Polytechnique Fédérale de Lausanne, Switzerland. A Survey of Topological Machine Learning Methods. 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). To their applications in the aforementioned areas, TDA methods have proven to be effective in supporting, enhancing, and augmenting both classical machine learning and deep learning models. 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.
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