nLab topological machine learning

Contents

Context

Topology

topology (point-set topology, point-free topology)

see also differential topology, algebraic topology, functional analysis and topological homotopy theory

Introduction

Basic concepts

Universal constructions

Extra stuff, structure, properties

Examples

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Constructivism, Realizability, Computability

Contents

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:

See also:

Created on June 13, 2022 at 07:32:07. See the history of this page for a list of all contributions to it.