nLab topological machine learning

Idea

In topological machine learning one tries to combine methods from both topological data analysis and machine learning for application to data analysis.

A popular approach (originating around RHBK15, KHNL15) is to use persistent homology as a pre-processing stage and train neural networks not on full data sets, but on their persistence diagram/barcode (which may still be a large amount of data), by making these amenable to kernel methods.

References

On feeding persistence diagrams into machine learning-algorithms by equipping them with kernels:

• Jan Reininghaus, Stefan Huber, Ulrich Bauer, Roland Kwitt, A Stable Multi-Scale Kernel for Topological Machine Learning, NIPS’15: Proceedings of the 28th International Conference on Neural Information Processing System, 2 (2015 3070–3078 $[$arXiv:1412.6821$]$

• Roland Kwitt, Stefan Huber, Marc Niethammer, Weili Lin, Ulrich Bauer, Statistical Topological Data Analysis – A Kernel Perspective, in: Advances in Neural Information Processing Systems (NIPS 2015) $[$ISBN:9781510825024, doi:10.5555/2969442.2969582$]$

• Bastian Rieck, Filip Sadlo, Heike Leitte, Topological Machine Learning with Persistence Indicator Functions, In: Topological Methods in Data Analysis and Visualization V TopoInVis (2017) 87-101 Mathematics and Visualization. Springer, $[$arXiv:1907.13496, doi:10.1007/978-3-030-43036-8_6$]$

• Raphael Reinauer, Matteo Caorsi, Nicolas Berkouk, Persformer: A Transformer Architecture for Topological Machine Learning $[$arXiv:2112.15210$]$

Review:

• Felix Hensel, Michael Moor, Bastian Rieck, A Survey of Topological Machine Learning Methods, Front. Artif. Intell., 26 (2021) $[$doi:10.3389/frai.2021.681108, pdf$]$

See also:

• Stefan Huber, Topological machine learning (webpage)